Author Archives: drericsilverman

Connection Games II: Y, Poly-Y, Star and *Star

Welcome to part II of my series of posts about games, part of my mission to keep my brain busy while I’m on strike!

Moving on from the last post about Hex, this time we’re going to explore a whole series of connection games, each by the same designer and each a clear progression from the last.  By the time we get to the final game in the series, we’ll see one of the more complicated and sophisticated connection games out there.

The Game of Y

First though, let’s start with something simple.  In fact, this game is even simpler than Hex, which scarcely seems possible!  Recall that in Hex, each player has a slightly different goal — both seek to connect across the board, but each player is connecting different sides.

In the Game of Y, created by Craige Schensted (who later renamed himself Ea Ea) and Charles Titus in 1953, players have the same goal — to connect all three sides of a triangular board made of hexagons.  To sum it up:

  1. Players take turns placing one stone of their colour in any empty hexagon on the triangular board.  Once placed, stones do not move and are never removed.
  2. The first player to connect all three sides of the board wins.  Corner hexes count as part of both sides to which they are adjacent.

And that’s it!  Winning connections spanning the three sides look kind of like the letter Y, hence the name.  Just like Hex, Y cannot have draws, one player will always win eventually.  The first player has a winning advantage here, as well, so using the swap/pie rule is recommended to alleviate this.

Y is sometimes thought to be even more elemental than Hex, given the greater purity of the win condition.  In fact, Hex can be shown to be a special case of Y, but in practice the games are pretty distinct in terms of the tactics required.

Here’s a sample game I played against a simple AI on a triangular board 21 hexes on a side; I used Stephen Taverner’s excellent Ai Ai software that comes with a plethora of great connection games:

 

y-win-1

Y benefits from playing on a larger board, given the shorter distances between sides when compared to a Hex board.

One issue with Y is that, even more so than Hex, the centre hexes are very powerful.  Whichever player controls the centre is very likely to win.  Schensted and Titus developed a number of ideas for new boards that would reduce emphasis on the centre, and eventually the ‘official’ Y board became this interesting geodesic hemisphere:

y-17-curvedThis board reduces the connectivity of the central points, giving the sides and edges greater influence on play.  Some theorise however that on this board basically every first move should be swapped by the second player, although I don’t believe there’s any hard evidence that this is true.  Kadon Enterprises sells a lovely wooden version of this board, albeit smaller than the one above, with 91 points available for stone placement. 

In any case, Y is another simple-yet-deep experience and highly recommended.  You can play against the AI using the Ai Ai software linked above, or against humans in real time via igGameCenter, or by correspondence on Richard’s PBEM Server.  The geodesic version is only playable on Gorrion — definitely give it a try.

Finally, I want to note that Y has a ‘Misère’ version, much like Hex, where you try to force the opponent to connect all three sides before you do.  This variant of Y is called ‘Y-Not’.  I just love that.

 

Mudcrack Y and Poly-Y

The next step in Y’s evolution came when Schensted and Titus published a gorgeous little book called Mudcrack Y and Poly-Y (you can still buy it from Kadon), which contained hundreds of strange hand-drawn boards for Y players.  They intended for players to use these boards by marking spaces with their chosen colour using coloured pencils.  These weird little boards seem totally different from the normal Y triangle or geodesic hemisphere, and yet turn out to be topologically equivalent.  Here’s a sample page:

mudcrack y1

A sample page of Mudcrack Y boards.  Print them out, grab a couple of coloured pencils and give them a go!

As part of their continued quest to improve on the Game of Y, this book also reveals Poly-Y, a follow-up game intended to be a further generalisation of Y:

  1. Players take turns placing a stone of their colour on any empty space on the board.  Once placed stones cannot move and are never removed.
  2. If a player’s stones connect two adjacent sides and a third non-adjacent side, that player controls the corner between the two adjacent sides.
  3. If a player controls a majority of the corners on the board, that player wins.

As you might have guessed, once again this game permits no draws (as long as you play on a board with an odd number of corners), so one player will always win.   The pie rule is used to mitigate the first-player advantage.

Wikipedia and BoardGameGeek claim there is no ‘official’ Poly-Y board, but this isn’t correct.  On the archived version of Craige/Ea Ea’s website you can find his summary of the history of Y/Poly-Y/Star/*Star, where he says this:

“Craige tried boards with more and more corners, 5, 7, 9, 15 … . At first it seemed that the more corners the better — there were more points to contest and a beautiful global strategic picture emerged. But as the number of corners increased, of necessity the length of the edges decreased. When the edges became too short it was found that it was too easy to make a Y touching 3 consecutive edges, thus “capturing” the middle edge and the two corners bounding it. This “edge capture” tended to make the game more tactical and local, focused on quick gains along the edge, thus losing the elegant global strategic flavor . So the strategic depth increased at first as the number of corners increased, but then decreased. Finally a board with 9 corners and 7 cells along each edge was chosen as the ideal balance….  Craige chose the 208 cell board with the 7-sided regions halfway to the center as the standard Poly-Y board.”

The same document has a picture of the standard board compared to two other candidates:

poly-y-board-official

The ‘standard’ Poly-Y board is in the centre.  The highlighted spaces on each board are the heptagons, required to allow the board to have 9 corners and still consist mostly of hexagons.

Here’s an example Poly-Y game won by Black on a board with 106 spaces and five corners — note here that the other player is Grey, and the yellow spaces are unoccupied:

poly-y-sample-game2

Black controls the corners on the left side, and has blocked Grey from catching up.

While Craige/Ea Ea endorses the 208-cell nonagon as the best Poly-Y board, in Mudcrack Y and Poly-Y they also state the game plays well on any board with the following characteristics:

  • Equal numbers of spaces along each side
  • Mostly six-sided board spaces
  • An odd number of sides (they prefer 5- and 9-sided boards)

Here’s sample 5-, 7- and 9-sided boards to print and play on:

poly-y-5-sided

5-sided Poly-Y board

poly-y-7-sided

7-sided Poly-Y board

poly-y-board9

9-sided Poly-Y board

 

Poly-Y is a clever game, and very deep; the win condition pushes players to extend their groups of stones all over the board, linking corners together through the centre to block the other player from securing their corners.  The oddly-shaped boards are also fun to play on, and give the game a certain quirky aesthetic appeal.  However, perhaps due to the rapid-fire iterations on Y produced by Schensted, Poly-Y never got the same level of recognition as Y itself.

 

Star

Schensted wasn’t quite done yet — far from it.  His next invention was Star, which ramped up the complexity of the scoring system from Poly-Y and created a game that pushes players to connect all over the board.  Star is another very deep game, and even on a small board presents a considerable challenge.

Star is played on a board of tessellated hexagons with uneven sides — in the sample small board below, you can see that three sides are five hexes long, and the other three are six hexes long; this ensures that there’s an uneven number of edge cells so that draws are impossible:

Star

A small board for Star with 75 hexes and 33 border cells.

Here’s how to play Star:

  1. Players take turns placing one stone of their colour on any empty hex.  Once placed, stones do not move and are never removed.
  2. A connected group of stones touching at least three of the dark partial hexes around the edge of the board is called a ‘star’.  Each star is worth two points less than the number of dark border hexes it touches.
  3. When both players pass or when the board is full, the player with the most points wins.
  4. As per usual, the pie rule is used to mitigate the first player advantage.

This may sound a bit opaque, but the basic gist is: form as many stars as you can, but connect them together to maximise your points.  The end result of a game of Star is an intricate web of connections snaking across the board for each player, attempting to connect and block simultaneously wherever possible.  Since the entire edge of the board is available for scoring, the whole board interior tends to come into play as well, and unlike most connection games the board tends to be nearly full when the game finishes.

Unfortunately, despite pretty much universal praise for this game it’s very difficult to find sample games of Star, so here’s the only one I could find from Cameron Browne’s book Connection Games — I can’t emphasise enough that this is a great book that you should definitely buy!

star-sample1

In this example, the edge scoring cells are marked by X’s rather than a border of partial hexagons.  Note that the completed game takes up nearly the entire board, and the pattern of connections formed is quite intricate even on this small playing area.

As with other connection games, playing on larger boards amps up the strategy.  I found these boards lurking around the Wayback Machine, do give them a try:

Star2

This board has 192 interior cells and 51 border cells.

Star3

This board has 243 interior cells and 57 border cells.

Unfortunately, despite the coolness of this game it’s been thoroughly overshadowed by its successor; Star does appear to be playable at Richard’s PBEM Server, albeit only with an ASCII interface.

 

*Star

Finally we come to the last in the line of games spawned from our old friend the Game of Y.  *Star takes yet another leap up in complexity, and to be completely honest, I don’t fully understand how this game works.  This is partly because the instructions are written in what feels like an alien language — scoring refers to things called ‘peries’ and ‘quarks’ and it’s all a bit strange.  However the abstract strategy game community praises this game nearly universally, so I remain keen to try and figure it out.

My understanding, questionable though it may be, is that the game essentially takes the core concept of Star — connect groups of edge-adjacent pieces together to maximise your points — to the next level by adding a scoring bonus for controlling corner spaces, and a significant scoring penalty (equal to twice the difference in the number of groups between the two players) for the player with the larger number of groups.  This heavily incentivises the players to connect their groups, and the end result of this is some beautiful patterns of stones snaking across the board, as in these two sample games from the manual (one tiny one and one normal-sized one):

Here’s a closeup of that awesome board:

starstar-board1

The *Star board.  The centre star can be used by either player as a connection between groups — neither player may place their stones on it.

Note that the board has thicker lines to define smaller board sub-regions, which allows players to ease themselves into the full game.  The game is popular enough to be produced in physical form by Kadon Enterprises, who make a wooden board set for *Star that I absolutely must buy at some point:

star-wood-board2starwood

How cool is that!  Someday I shall own this game, and I shall figure out exactly how to play it.

Luckily there’s a simpler game also playable on this board — Star-Ywhere the players compete to be the first to complete a connection between two adjacent sides and one side not adjacent to either of those two.  For *Star veterans there’s also Double-Star, where players place two stones per turn and the other rules remain the same; this seems like a small change but it significantly alters the play.  New tactics and strategies are necessary to cope with the new threats that are possible with two stone placements.

So there we have it — a hectic journey from the elemental Game of Y through to the complex but highly-regarded *Star, courtesy of the brilliant minds of Craige Schensted/Ea Ea and Charles Titus.  Craige/Ea Ea has stated that *Star is ‘what the other games were trying to be’, so from his perspective each game was improving on the last, and *Star is the best of the lot.

While researching and playing/trying to play these games, I’ve found that Star and *Star are frequently compared to Go, despite having connective goals rather than territorial ones.  Given the much more flexible nature of the connective goals in these two games, I can see why — instead of connecting specific sides, players define for themselves the key parts of the board as they play.  This is much more ‘Go-like’ in that the board is more of a blank slate, and does not inherently define the direction of play as much as in other connection games.  So, if you’re a Go fan and skeptical of connection games, maybe try these two.

If you’re new to connection games in general, I’d start with Hex, then Y, then Poly-Y.  You might enjoy Star and *Star more after trying some other games with more freeform connective goals, but with easier-to-grasp rules.  I’d recommend maybe trying Havannah and Starweb for that purpose — and lucky you, they’ll be in my next post 🙂

 

Tagged , , , , ,

Connection Games I: Hex

As you all have probably figured out by now, I really enjoy complicated board games — dense modern board games with tons of special components, 500-year-old Shogi variants with hundreds of pieces, all that stuff.  But I also have a great fondness for games on the other end of the scale: elegant abstract games with minimal rules and maximal depth.

Now an oft-cited example of this category might be Go — it’s certainly an elegant game, with rules that are easy to summarise yet a level of depth nearly unrivalled in board games.  But Go is also hard to understand, in that the goal is clear — secure more territory than your opponent — but working out how to get there is hard.  Most beginning players, myself included, are completely flummoxed by the empty board at the start of the game, and have no idea where to start.  And at the end of the game, it’s very difficult for newbies to figure out when the game is actually over!  There’s a reason a common proverb for beginning Go players is ‘lose a hundred games as fast as possible’ — building familiarity with the basics takes time and repetition.  It’s worth it, though.

But what I’m going to talk about here are games that are so simple as to be almost elemental, as in, it’s hard to imagine games with rules simpler than these.  For my money the best examples of these types of games are in the category of connection games.  In a connection game, players vie to be the first to connect key points on the board with their pieces — a simple goal, easy to see and easy to understand.  But underneath that these games offer surprising depths of strategy and tactics.

Now, the current bible for connection games is the book by Cameron Browne called — wait for it — Connection Games, which summarises the genre beautifully and includes rules and examples of play for numerous games.  It’s a great book that I certainly can’t compete with, so in this brief series of posts I’m just going to give you some details of my picks for the best games of this type, along with some useful resources and links to where you can play.

Hex

Any discussion of connection games has to start with Hex, the originator of the whole genre.  Strangely, despite the simplicity of these games, they weren’t around until quite recently.  Hex has a tangled history — now unravelled in the recent, and excellent, book Hex, Inside and Out: The Full Storyso I won’t attempt to summarise it all here.  The game was invented by Danish mathematician Piet Hein in 1942, and was initially called Polygon.  Hein sought to create a game that reflected his interests in topological properties of the plane and the four-colour theorem, and was stuck on this idea for some time, as any attempts to build his imagined game on a square grid didn’t work, as the players could easily become deadlocked.  Eventually he realised that a hexagonal grid would prevent this issue, and thus Polygon was born:

polygon-board-1

The Polygon board, an 11×11 rhombus composed of hexagons.

The rules of Polygon are incredibly simple:

  • Players turns placing a single symbol of their chosen type — star or circle — in any empty hexagon on the board.  Once placed, symbols don’t move and can never be removed.
  • The first player to connect the sides of the board marked with their symbol with an unbroken line of their symbols is the winner.

Easy, right?  But once he started playing, Hein realised the game was far more complicated than the rules suggested.  Soon after he launched the game in the Danish magazine Politiken with the board, rules and a call for challenging Polygon puzzles from readers.  It wasn’t long before pen-and-paper Polygon pads were selling like hotcakes all over Denmark, and the game became a bonafide hit.

polygon-puzzle-1

The famous first-ever Polygon puzzle.  The circle player has the move.  How can they win?

Eventually Hein sold a 12×12 version of Polygon with a very nice wooden board called Con-Tac-Tix, which enjoyed some small success as well — and in fact you can still buy a version of this today from Hein’s grandson.  But the game didn’t really take off around the world until later, when famous mathematician John Nash (of A Beautiful Mind fame) rediscovered the game in 1948.

When Nash started sharing his discovery with colleagues at Princeton, the game rapidly gained adherents.  They often called it Nash, for obvious reasons, but legend has it some called it John instead — not because of Nash’s name, but as a nod to the fact they played it on the hexagonal tiles of the bathroom in the department!  Nash became Hex when Parker Brothers tried to market the 11×11 game with that name.  Around the same time Nash was attempting to market the game and was quite upset to discover he’d been scooped.  He wasn’t aware at that time that Piet Hein had in fact scooped him several years earlier anyway.

In any case, the game became an object of enthusiastic study by Nash and his colleagues, and they made numerous interesting discoveries about its properties.  Hex was largely just an object of interest for academics for the most part, as Parker Brothers’ attempt to sell the game didn’t amount to much.  A few years later the mathematician Martin Gardner played a pivotal role in the eventual worldwide popularisation of the game — his 1957 Scientific American column on Hex brought the game to a whole new audience.

Hex remains highly popular with mathematicians and computer scientists today, as well as with gamers, as it has some fascinating properties.  For example, draws are completely impossible in Hex — no matter how inept or random the players’ moves, eventually one of the players will always make a winning connection across the board.  This result is actually a consequence of something called the Brouwer fixed-point theorem, which I won’t get into here.  We also know that a winning strategy for the first player exists, but we have no idea what it is (well, we’ve found it by brute-force computer calculation for 9×9 boards and smaller, but not on the boards we actually play on).  A quick browse of the literature on Hex will reveal some fascinating contributions from big names in maths and computer science.

The current state of play

In the years since Piet Hein’s invention of Polygon, Hex has evolved somewhat.  The classic 11×11 board is still popular, since it has a nice balance of speed of play and intricacy.  Games on the 11×11 board are over relatively quickly, yet these 121 hexagons allow for a staggering 1056 possible board positions, 10 billion times more than the number of possible Chess positions (1046)!

However many Hex players nowadays are using larger boards, with 13×13 and 19×19 being particularly popular. 14×14 is fairly common as well, particularly as that was John Nash’s preferred board size. In any case, larger boards push the game further into the realm of strategy rather than tactics, allowing for deeper moves with greater subtlety. Here’s how a 13×13 Hex board looks today:

hex13-sample

A 13×13 Hex board.

Note too that we’ve abandoned the circles and stars of Polygon’s heyday and opted for the two players using black and white stones to mark their hexes, with the board edges marked accordingly.  Often you’ll see blue and red stones used instead.

More importantly, now that we know that Hex gives the first player a winning advantage, we play Hex using the swap rule, an ingenious way to even things out.  When the first player places their stone, the second player may choose to play one of their colour in response, after which the game proceeds normally, or they may choose to swap colours and take that move for their own first move!

This clever rule change means that the first player must intentionally play a weaker opening move to avoid a swap, thereby mitigating their first-player advantage instantly.  In practice the strongest opening moves are in the centre of the board, as these allow for connecting stones to extend in every direction, so generally the first player will play around the edges at the start to avoid a swap.  As you might expect, the first-player advantage is somewhat diminished on larger boards, given that the impact of individual moves is smaller in general.

Side note — the swap rule is often called the pie rule as well, as it mirrors the fairest way to divide up a slice of pie between two people: one person cuts, the other chooses which slice they will eat.

 

Playing Hex

So, once we’ve grabbed a funky rhomboid board of our preferred size, a couple piles of stones and sat round a table to play, how does the game actually work?  Here’s a quick sample game, showing me defeating a basic computer opponent on the 11×11 board:

hex11-win1

I played this game using a fantastic bit of free Java-based software called Ai Ai, which has numerous awesome abstract strategy games available to play with a variety of AI opponents — find it here: http://mrraow.com/index.php/aiai-home/aiai/

 

The play in this game was reasonably simple, but if you jump onto the most popular site for playing Hex, Little Golem, and check out the larger boards you’ll soon see that the end result of a Hex game can look pretty complicated:

hex13-sample2

A game played earlier today on Little Golem (https://www.littlegolem.net/jsp/game/game.jsp?gid=2145661)

 

Black resigned after 70 moves, admitting defeat.  The reason why Black resigned may not be immediately obvious; after all, Black seems to have made good progress along the left side!  However, we can start to understand how games of Hex evolve once we understand some basic positions, particularly the bridge:

hex-bridge

An example of a bridge: White’s stones 2 and 4 can be connected no matter what Black does.

The bridge means that connection between the two relevant stones is unstoppable.  As you can see above, if Black plays at A to attempt to break apart White’s stones, White simply plays at B, and vice versa.  The bridge is a simple example of a template, a formation of stones and empty hexes that facilitates an unstoppable connection.

If you look again at the sample games above, you’ll see several examples of bridges being used to establish connections between stones.  Using this formation is far more efficient than placing stones methodically next to one another, but the connection they provide is just as solid!  Using bridges and similar templates allows you to build connections in fewer moves.  As you learn more of these templates in Hex, you’ll be able to spot a win or a loss coming long before the final stone is placed.

By the way, now that you know what a bridge is, you should be able to solve Piet Hein’s puzzle above!

Another key concept of Hex is that defence and offence are the same thing.  Remember that in Hex one player will always win — from this we can work out that if we prevent any possible win by the opponent, that means we have to win instead!  So when playing Hex, don’t be focussed just on your own bridge-building and forget your opponent — spending your moves on blocking them still gets you closer to a win.  Sometimes the best offence is a good defence.

To get started with Hex, I suggest you just jump right in and start playing some games.  You can play Hex  on Little Golem, Richard’s PBEM Server, Amecy Games, Gorrion, Hexy.games and igGameCenter among others.  You’ll soon find that Hex is an intricate and precise game with enormous amounts of depth.  If you work on building bridges, blocking your opponent, and getting a general feel for the flow of the game, you’ll soon start to get the hang of the basics.

After losing a few times and hopefully stumbling across a win or two, go and visit Matthew Seymour’s incredibly detailed guide on Hex strategy.  His site is details key concepts like ladders and edge templates, walks you through some sample games, and provides lots of useful resources, plus everything is demonstrated through interactive diagrams!  It’s an incredible guide.  The bridge example above is a screenshot from this site, which I hope will encourage you to visit.  On the real site you can experiment and play moves on all the diagrams, which really helps cement the concepts explained in the guide.

 

Hex Variants

As you might expect with a game this elemental, numerous Hex variants have been devised over the years to spice things up.  There’s a tonne of these so I’ll just briefly highlight a few interesting ones:

Misère HexThink of this as Opposite Hex — the first player to connect their sides of the board loses!  It’s an odd style of play to get your head around, where you need to force the opponent to connect while avoiding making progress yourself.  Interestingly, it’s been proven that the losing player has a strategy that guarantees every hex on the board will be filled before the game finishes.

Pex:  The rules here are the same as Hex, but the game is played on an unusual board — instead of hexagons, the board is tiled with irregular pentagons.  This changes the tactics significantly, given that the board spaces now have different connectivity, and makes for an interesting change of pace.   You can play Pex online at igGameCenter.

pex-iggc

An 8×8 Pex board.

Nex:  This intriguing variant uses the standard Hex board, but alongside your White and Black stones you add neutral Grey stones.  Grey stones can’t be part of either player’s winning connection, so they are obstacles to both players.  But what makes this game brilliant is the new options available — a player’s turn now gives them two possible moves:

  1. The player to move may add one stone of their colour AND one neutral stone to any empty hexes on the board, OR
  2. They may swap out two neutral stones for stones of their colour, and then replace one stone of their colour with a neutral one.

This means that moves are not permanent in Nex — your stones can be recycled when the board situation changes, and seemingly innocuous neutral stones can suddenly become new threats for either side when they transform.

Just like in Hex, there are no ties and one player must win.  You can play Nex on igGameCenter.

nex-sample-game1

A sample Nex game from the book Mathematical Games, Abstract Games — Black resigned.

Chameleon: Another intriguing variant that significantly changes up the play, Chameleon decouples players from colours.  In Chameleon, one player is Vertical and must make a connection of either colour from top to bottom, and the other is Horizontal and must make a connection of either colour from side to side.  On each turn a player may place a Black stone OR a White stone on the board on any empty hex.

The consequence of this is that players have to be aware of threats in the opponent’s direction from stones of either colour, making each move feel incredibly consequential!  It’s a bit of a mind-bender.  Chameleon benefits from playing on larger boards, as connections can happen too quickly on smaller ones given that players use both colours.  You can play it online using Richard’s PBEM Server.

 

What next?

Now that you’ve had an intro to the original connection game, you’ll be well-equipped to try your hand at Hex’s many fascinating cousins.  The basic concepts of Hex are helpful in a lot of other connection games too, although each of them adds their own unique wrinkles.

Over the next few posts, I’ll highlight some more connection games with interesting properties that are fun to play, including the Game of Y, TwixT, Havannah, ConHex, Unlur, and more.

Tagged , , ,

An Introduction to Shogi

ANNOUNCEMENT:  There will be a special event at my workplace, the MRC/CSO Social and Public Health Sciences Unit, running at 5PM on 7 February 2020.  Dr Shuzo Sakata of the University of Strathclyde, Shogi player and teacher, will be showing us all how to play Shogi!  Sets will be provided — please RSVP to me directly if you plan to come, to ensure we have enough sets.  

What is Shogi?

Shogi is the Japanese form of Chess, the ‘royal game’, in which two players vie to be the first to checkmate their opponent’s King — meaning their King is unable to escape capture on the next move.  Many centuries ago, when the ancient ancestor of Chess called Chaturanga was developed in India, the game spread across Asia and Europe, spawning new variations in every region that embraced the game.  Shogi is first recorded in the Heisei Era in ancient Japan — around the 11th century — where it rapidly developed into its own, unique take on the royal game.

shogi-set-cropped

My traditional Shogi set — a Shin-Kaya board, with hand-carved pieces made from Japanese maple, with the kanji (Japanese characters) carved in the Minase calligraphy style in lacquer

How is Shogi different from Chess?

Shogi does share the same goals as Chess — checkmating the enemy King — and shares some of the same pieces.  However, many of the fundamentals are quite different:

  • The Board: a Shogi board is a 9×9 playing area of 81 squares, compared to the 64 squares of the chessboard.  The board is not chequered either.
  • The Pieces: Chess has six types of pieces: Pawns, Knights, Bishops, Rooks, Queens, and Kings.  Shogi has ten: Pawns, Knights, Silver Generals, Gold Generals, Lances, Rooks, Bishops, Dragons (Promoted Rooks), Horses (Promoted Bishops), and Kings.  Some of the shared pieces move differently, too: Knights make the same L-shaped jump but only forward; and Pawns move and capture only directly forward.
  • Promoting Pieces: In Chess, pawns that reach the enemy’s back rank can promote to become a Knight, Bishop, Rook, or Queen.  In Shogi, any piece that reaches the enemy camp (the three rows where their pieces begin the game) can promote.  A promoted piece flips over, and the other side of the piece indicates their promoted form.  Promoted Bishops (Horses) and promoted Rooks (Dragons) are the most powerful pieces in the game.

Shogi’s Ingenious Addition: Drops

There’s one major rule change that was added to Shogi in the 16th century and has come to define the game ever since: drops.

In Shogi, when a piece is captured, it is truly captured — it becomes the property of the capturing player.  The capturer places the piece on a small side-board called a komadai (piece stand) and holds it in reserve.  At any point from then on, they may forgo a normal move and instead drop a captured piece to any empty square on the board!  

However, an important point to remember: promoted pieces, when captured, are demoted.  Any dropped piece must be moved into the promotion zone again to be promoted.  Two other key exceptions: Pawns cannot be dropped so that you have more than one of your pawns on a single vertical line; and pieces cannot be dropped in a space where they have no legal moves.

Drops make Shogi play and feel very different from Western Chess.  Since captured pieces come back to life throughout the game, the number of pieces on the board stays roughly the same throughout — there are no endgame situations with near-empty boards, as in Chess.  The constant back-and-forth of captures and drops makes a Shogi game dynamic, aggressive and fierce — attacks are frequent, and giving up the initiative to play defensively is risky.

Thanks to drops, Shogi is also much more decisive than Chess — less than 2% of professional Shogi games end in a draw, a staggering difference from the ~60% draw rate of professional chess!

Is Shogi hard to learn?

Not really!  The biggest obstacle for most new players is learning the pieces — as you can see in the photo of my Shogi set above, all Shogi pieces are the same shape and colour, and the two players’ armies are distinguished by the pieces’ orientation (aim pointy bits at the enemy!).  The different pieces have their names written on them in Japanese kanji characters, which are not so easy to learn for people who don’t speak Japanese.

However, the best way to learn is to simply dive in — after a game or two, the kanji fade away and are easy enough to recognise.  I find it helps beginners to forget they are letters — this tends to prime us to try to divine their meaning, which makes them more intimidating.

Instead, just think of them the same way as you think of the shapes of Western Chess pieces — both are abstract shapes, and neither really relates to what the piece does or how it moves.  The kanji are effectively just symbols, just like the odd shapes of Chess pieces.  Also, you only really need to recognise the top characters on each piece — that’s enough to distinguish all the pieces from each other.

Other than that, it’s just a bigger version of Chess!  The steepest part of the learning curve after that is getting comfortable with the powerful impact of drops — this is especially strange for seasoned Chess players, who will be accustomed to captured pieces playing no further role in the game.  But again, given a few games, you’ll soon start to see the exciting, combative play allowed by the drop rule, and you’ll be chucking Gold Generals at your opponent like a pro.

How the Shogi Pieces Move:

Here’s a quick reference to the moves of the Shogi pieces:

evans-shogi-move

As you can see, the King, Rook and Bishop move the same as in Chess.  The Knight moves the same as in Chess too, but can only jump forward.  The Pawn moves forward and captures forward — no diagonal capturing like in Chess.  The Gold General moves one space in any direction except diagonally backward, while the Silver General can move one space diagonally in any direction or one space directly forward.

The promoted pieces are easy to remember — all promoted pieces move the same as the Gold General, with the exception of the Horse and Dragon.  The Horse moves like a Bishop, but can also choose to move one square orthogonally; the Dragon moves like a Rook but can also move one square diagonally in any direction.

You might notice that the Shogi pieces have a general forward bias in their movement patterns, and most are short-range movers.  This works very well with the drop rule — the combination of forward movement and drops favours attacking play, and the short-range movements prevent the game from becoming too chaotic, as it might be with powerful pieces appearing wherever they like on the board.

The flip side to this is that you can very occasionally have a condition called entering Kings, where both players’ Kings have moved into each others’ promotion zones.  This makes it very difficult for anyone to win, as most of the pieces attack forward rather than backward.  This is one of the few ways you can have a draw in Shogi.  In practice this rarely happens, especially between beginners, who normally dive heedlessly into battle and neglect King safety entirely!

Note that the Horse provides a good reason for the Shogi board to not be chequered.  In Chess your Bishops are confined forever to half of the board — either the black diagonals or the white ones.  The Horse however can spend a move to shift from one set of diagonals to the other, so it’s less useful to have the chequers to indicate where the Bishops go — once promoted they can go anywhere.

Shogi: A whole family of amazing games

One of the things I love about Shogi is that, in a sense, it’s part of a whole game system rather than a single game.

To unpack that a little bit — you may be aware that there are many hundreds of Chess variants out there, variations on the game with different boards, pieces and rules.  Shogi has these too, but unlike in Chess, many of the Shogi variants are hundreds of years old, and were refined over the centuries into fantastic games in their own right!  Shogi variants are well-designed, well-balanced, and offer just as much intrigue and fascination as the traditional form of the game.

In fact, before the introduction of the drop rule made the modern game dominant, there used to be three variants of Shogi that were commonly played: Sho Shogi, or ‘Small Shogi’, which added drops later and become modern Shogi; Chu Shogi, or ‘Middle Shogi’, a much bigger game played on a 12×12 board of 144 squares; and Dai Shogi, or ‘Large Shogi’, played on an even bigger 15×15 board of 225 squares.  Shogi used to come in Small/Medium/Large sizes!  Alongside these main variations, there were numerous other variants of Shogi developed over the centuries, some of which I’ll describe below.

Today, besides Sho Shogi only Chu Shogi maintains a small presence — the Chu Shogi Renmei in Japan is the official governing body, and holds regular tournaments.  This is unfortunate, really, as the Shogi variants are quite unique — particularly the larger variants, which are far larger than any commonly-played Chess variants, and offer hugely creative pieces and styles of play.

Thankfully, the efforts of one George Hodges in the late 20th century led to the revival of these ancient forms of Chess, and remarkably he even manufactured affordable sets for most of the large variants.  Sadly George left us a few years ago, but his wife carries on that business, and she remains the only source on the planet for physical sets of most of the Shogi variants.  I of course have bought several of them myself 🙂

Without further ado, here’s a brief intro to a few of the more spectacular Shogi variants — several of which I will bring with me to the Shogi event in a few weeks time!

Tori Shogi

Tori Shogi, or ‘Bird Shogi’, is an action-packed small variant of Shogi that packs a lot of action into its 7×7 board of 49 squares.  At the start of the game, each player has 16 pieces in their camp — the board is more dense with pieces than in any other Shogi variant.  To play you need to remember nine distinct piece movements, one less than normal Shogi.

Unlike most Shogi variants, which build on a common foundation of pieces that generally behave the same across many games, Tori Shogi uses an entirely new set of pieces named after birds (hence ‘Bird Shogi’).  Instead of Pawns we have Swallows, we have Quails that move differently depending on which side of the board they start on, the King is now a Phoenix, and so on.

Like modern Shogi the game uses the drop rule, but with one major modification — in Tori Shogi you can drop a second pawn (Swallow) on a file where you already have one.  In fact this is already happening in the start position, as you can see below!  This rule heavily impacts Tori tactics, and also helps the board to not feel too constrained despite having so many pieces everywhere.

Tori-shogi-board1

A Tori Shogi set from Angela/George Hodges — the top pieces have been flipped to show off their promoted forms.  In this game only Swallows and Falcons promote.  Note that the Swallows are in conflict right from the start of the game!

Tori Shogi is somewhat unusual among Shogi variants in that it was invented more recently — in 1799 to be precise.  This means we have a fair bit more information on high-level play in this game than some of the others, where unfortunately top players’ games are lost in the mists of time.  For Tori Shogi we have a few games from a tournament played between top-level Shogi professionals, some clever tsumeshogi (checkmate puzzles), and even a recently-updated English book on the game, The Way of Tori Shogi!

Tori plays in a very unique way, not just because of the small board and two-pawn drop rule, but also because the pieces are somewhat strange.  The movements themselves are odd, but also the promoted Swallow turns into a Goose that moves in a bizarrely useless way (jumping one square diagonally forward left or right, or one square backward).  Promotion is manda-Tori (sorry) in this game, so you have to have some clever plans afoot to use these weird pieces to achieve checkmate.

In any case, Tori Shogi is an exciting and unique game, and unlike some of the other variants there’s some good information out there on how to play well.  I recommend picking up a set and a copy of The Way of Tori Shogi and giving it a go!  Or just play with me, I already have a set 🙂

Tori-shogi-moves

The moves of the Tori Shogi pieces.  Clockwise from top left: Swallow, Falcon, Left Quail, Right Quail, Crane, Goose, Eagle, Pheasant, Phoenix.

Wa Shogi

Wa Shogi, or ‘Harmony Shogi’, marks our first step into the world of the larger Shogi variants played on boards bigger than the standard 9×9 grid.  This game is played on an 11×11 grid of 121 squares, with each player having 27 pieces at the start of the game (compared to 20 in Shogi).  To play, you have to remember 20 distinct movement patterns for your pieces (compared to 10 in Shogi).

Wa Shogi is an interesting beast — similar to Tori Shogi, Wa Shogi uses all non-standard pieces, and none of the pieces share their names with the standard Shogi pieces.  Some do have equivalent moves to the standard pieces, but most are different.  The pieces in Wa Shogi are named after animals — moving beyond just birds, as in Tori Shogi, we have fun stuff here like the Violent Wolf and the Climbing Monkey.

Not only that, but out of the initial starting setup for each player, there are only multiples of the Sparrows (pawns) — all the other pieces are different.  That means there’s quite a few interesting tactical options in this game.

Wa Shogi is also unusual in that, unlike the other large Shogi variants, Wa Shogi was quite possibly played with drops.  The game was invented after the drop rule became popular in 9×9 Shogi, and the Edo Era sources we have on Wa Shogi mention additional tactical options over the other variants, without specifying precisely what they mean; this could indicate the use of the drop rule.  Additionally, some promoted pieces have identical moves, but are named differently and come from different unpromoted pieces; some suggest this indicates the use of drops, as dropped pieces are unpromoted so these cases would benefit from differentiating the promoted forms for ease of play.

Most modern players play Wa with drops, and the general consensus is that the game plays very well this way, so I definitely recommend using them.  Wa Shogi is a fun change of pace from the traditional game, with the odd new pieces with weird moves and cool names, and the increased freedom of the larger board with drops adds a fun dynamic.

wa-shogi-tsa-1

The starting setup for Wa Shogi, with the second player’s pieces flipped to show their promoted sides.  Only three pieces don’t promote in Wa.

wa-shogi-closeup

A closeup of the Crane King — in the centre of the bottom row — protected on either side by a Violent Stag (left) and Violent Wolf (right).  Lot of violence going down in this game.

wa-shogi-moves-1

wa-shogi-moves-2

A move reference for Wa Shogi, included here mainly to show off the cool names for the pieces!

Chu Shogi

Chu Shogi is a spectacular game.   Those lucky few who have played it frequently class it as one of the finest Chess games ever invented — and I thoroughly agree.  The game is thought to have been invented in the 13th century and is one of the oldest forms of Shogi.

The game is not super accessible at first — the board is much larger than in Shogi (144 squares vs 81), and there are far more pieces on the board (46 pieces per player, compared to 20 each in Shogi).  All told, you’ll have to remember 28 different piece movements instead of 10 like in Shogi!  But the rewards are very much worth it.

Chu Shogi, like the other larger Shogi variants, does not use the drop rule — otherwise the games would go on far too long!  Instead captured pieces are lost permanently, as in Chess.

Despite the large board and huge armies, Chu Shogi maintains a pretty swift pace.  Each player starts with powerful pieces on the board from the beginning — including multiple Dragons and Horses, and the Free King which moves as a Queen in Chess.  Interesting to note here that the Queen in Chess was invented three centuries later — Chu was an extremely innovative game for the time.

The most powerful piece, and the piece that defines Chu Shogi, is the Lion.  The Lion effectively moves twice in one turn — it can make two consecutive King moves in any direction, with all that implies: it can capture twice; capture once and return to its starting square, appearing to capture without moving; or it can move once then return to its starting point, effectively passing its turn.  All of these abilities are staggeringly powerful for different reasons.  The Lion is so important and so engaging that the Chu community wisely added some rules to prevent players trading them off early in the game — it’s a bit complicated, but essentially you can’t sacrifice your Lion for your opponent to recapture unless you captured a sufficiently powerful enemy piece in the process.

Notably, Chu Shogi includes a piece called a Drunk Elephant, which moves like a King except it can’t move directly backward.  This piece promotes to Crown Prince, which is a second King — and both Kings and Princes must be captured to win the game!  Because of this, Chu and the other large variants with Drunk Elephants (most of them) don’t actually have a checkmate rule — any royal pieces must be actually captured to win the game.  This allows you to sacrifice a Prince or King for tactical reasons — although honestly that’s rarely advisable!

At any rate, it’s a fabulous game, definitely worth your time if you’ve ever enjoyed a game of Shogi or Chess.  It’s also the root of many of the larger Shogi games, meaning if you can play Chu it’s easier to jump up to the larger games afterward.

chu-shogi-set

My Chu Shogi set, in the initial position.  Board purchased from Aoyama Gobanten in Tokyo, pieces from Angela/George Hodges in the UK.  The powerhouse Lion is two squares above the King, if you’re wondering.

chu-shogi-end

The end of a Chu Shogi game — White wins after 288 moves (!), fittingly enough with a Lion checkmate.  Check out the huge piles of dead pieces on the side of the board!

chu-shogi-mega-tsume1

A rather spectacular Chu Shogi checkmate puzzle I found online — Black (bottom) to win in 3,257 moves!  The puzzle is well-formed, meaning there’s only one possible solution.  Good luck finding that one!

Dai Shogi

Dai Shogi, big brother to Chu, is much bigger than its sibling but not that much more complicated to learn.  Essentially, take Chu, add eight more piece types with fairly easy-to-remember short-range moves, all of which promote to Gold General, and you have Dai!

Some criticise Dai as being too slow or not exciting enough, given that it’s essentially a scaled-up version of Chu with more pieces and a bigger board.  But I strongly disagree — the larger board significantly expands the options available to players, the larger armies make the game more forgiving given the lower importance of material losses, and the powerhouse Lion is less dominating on the larger playing area.  The game is indeed slower, but it’s also strategic, intriguing, and a great introduction to the larger Shogi variants given it’s easy to pick up once you know Chu.

dai dai vs shogi comparison

A comparison of Dai Shogi (left) vs modern Shogi (right) — turns out that Large Shogi is, in fact, large

dai shogi closeup

A close-up view of the King’s vast entourage in Dai Shogi.  To either side he’s flanked by his faithful Gold  and Silver Generals; to the front a Drunk Elephant and two Blind Tigers; then in front of those, dangerous beasts like the Lion, Kirin, Phoenix, Evil Wolves, Dragon Kings and more.

dai-shogi-aftermath-568moves copy

A Dai Shogi game I won online — after a mere 568 moves.  Note my opponent threw a ‘spite check’ at me when he knew he was done for — even if I didn’t have checkmate on my next move, my Cat Sword (cool piece name) would’ve instantly recaptured his attacker anyway.

Tenjiku Shogi

Tenjiku Shogi — sometimes translated as ‘Exotic Shogi’ — is one of the most unique and dynamic games of Chess ever devised.  The game is played on a massive 16×16 board (256 squares), and each player starts with 78 pieces in their army — and yet, the pieces are so powerful that the game can be over in less moves than a game of regular Shogi!

Like Chu Shogi is defined by the Lion, Tenjiku is defined by the Fire Demon.  Each player starts with two of these.  The Fire Demon can move as far as it wants in six directions — already extremely powerful by Shogi standards.  Not only that, it can make a three-step area move — three consecutive King moves in any directions (but only one capture, for reasons that will soon become obvious).  But on top of that, it burns everything it touches!

In other words, the Fire Demon instantly kills any piece adjacent to it when it finishes moving, meaning it can capture up to eight pieces in one move.  Not only that, but if the opponent isn’t thinking and moves a piece next to it on his turn, that piece is also instantly captured — and that doesn’t count as your turn!

In addition to the two Fire Demons, your army also contains a Lion, five other pieces that can capture multiple times in a turn, two pieces called Water Buffaloes that promote to Fire Demons, and a number of range-capturing Generals — these are pieces that can jump over any number of enemy pieces in order to make a capture (each player has six of these).  The upshot of all this is that, right from the opening, Tenjiku is a dynamic and dangerous game — attacks start immediately, and your huge 78-piece army starts dwindling very quickly.  No other Chess variant plays like this, and it’s an absolute blast.

tsa tenjiku1

A Tenjiku Shogi set from Angela/George Hodges — the top player’s pieces have been flipped to show off their promoted sides.  Of course I also own one of these sets.

tenjiku vs shogi comparison

Traditional Shogi lined up beside Tenjiku — just think how much damage one Fire Demon could do in that Shogi game!

tenjiku firedemon

A closeup of the deadly Fire Demon, ready to wreak havoc

Dai Dai Shogi

Dai Dai Shogi — or, literally translated, ‘Big Big Shogi’ — definitely fits its name.  The game is played on a 17×17 board of 289 squares, with each player leading an army of 96 pieces!  The starting setup, unlike most Shogi variants, is highly asymmetric — amongst the 96 pieces in your army, there are 64 different types of pieces, so many of your army are unique single pieces.  All told, you need to remember 68 different piece moves — again unlike most variants, only 20 pieces promote in this game, and none of those promotions are to Gold General.

Dai Dai is quite a fascinating game, with a style of play all its own.  This is the first large Shogi game to introduce promotion by capture — pieces promote as soon as they capture any enemy piece, and don’t have to wait until they reach the promotion zone.  Promotion is also mandatory, whereas it’s optional in standard Shogi.  This creates some intriguing tactical decisions, as some pieces effectively demote, becoming weaker when they make a capture — so you’d better make that capture count!

Dai Dai also introduces two powerful hook-moving pieces: the Tengu, or long-nosed goblin, that can make two consecutive Bishop moves at right angles to each other; and the aptly-named Hook Mover, which makes two consecutive Rook moves at right angles to each other.  If that doesn’t sound so amazing, consider that a Hook-Mover on an empty board can reach any square in one move — hard to keep your King safe from that!

Dai Dai Shogi is well worth a try if you’re interested in a unique twist on Shogi — the asymmetric setup, huge piece variety and powerful hook-movers make for a surprisingly aggressive game, considering the size of the board.

dai dai vs shogi comparison

Big Big Shogi indeed!  Board and pieces from Angela/George Hodges once again.

tsa dai dai shogi1

Dai Dai Shogi set with the second players’ pieces flipped to show the promoted sides.  Note how few of the pieces promote — not even the pawns!

dai-dai-king-closeup

The King’s entourage grows ever larger, and more diverse.  Out of the 64 starting pieces, a full 47 of them are solo pieces, making for a complex and asymmetric starting position.

Maka Dai Dai Shogi

Maka Dai Dai Shogi is yet another step up in size from Tenjiku, played on a 19×19 board of 361 squares, with each player starting with an army of 96 pieces.  The name is a bit interesting — ‘Dai’ means big or large, as we know, and ‘Maka’ is a word derived from Sanskrit that means something like ‘Superior’.  So ‘Maka Dai Dai Shogi’ means basically ‘Superior Large Large Shogi’, or less awkwardly, ‘Superior Ultra-Large Shogi’.  I would argue this is pretty accurate — it’s definitely ultra-large, and has a number of superior qualities.

One of the standout qualities of Shogi as compared to Chess is that most of the pieces can promote, and the large variants for the most part carry on this tradition.  Maka Dai Dai, however, takes it to the next level, and allows the King himself to promote!  A promoted King becomes an Emperor, the most powerful piece to exist in any variant of Chess: the Emperor can instantly teleport to any unprotected square on the board, including squares occupied by enemy pieces.  In other words, the Emperor can instantly go anywhere and capture anything, so long as that square isn’t directly threatened with recapture by an enemy piece.

Alongside this, in Maka Dai Dai promotions occur by capture, as in Dai Dai Shogi — however here the promotion is optional, unless the captured piece is a promoted piece, in which case promotion is mandatory!  This helps to speed up the pace of the game, as on such a large board reaching the promotion zone would take forever.  Hook-moving pieces appear again in this game, but here they demote to Gold General on capture, so they’re effectively one-shot nuclear weapons if used to take out a promoted piece — use them wisely.

Promotion-by-capture also makes attacking the enemy King a risky proposition — if you mess it up, the King might capture an attacking piece, thereby immediately becoming an Emperor, which is both extremely powerful and desperately hard to checkmate!

“If you come at the King, you best not miss.”

–Omar Little

Maka Dai Dai, like most of the large Shogi variants, was invented by Buddhist monks — after all they have lots of time on their hands.  This is more apparent in Maka Dai Dai than the other variants, as it includes pieces drawn from Buddhist mythology that behave in unusual ways.  The Deva and Dark Spirit, for example, promote to Buddhist Spirit and Teaching King respectively — and any piece that captures them becomes a Buddhist Spirit or Teaching King, so these immortal creatures effectively never leave the board.

Substantial research has been done on this game by Professor Tomoyuki Takami, who states that Heian-Era sources suggest that Maka Dai Dai was actually one of the earliest forms of Shogi to exist, dating from as early as the 10th century.  He says that the pieces of the game are inspired by Chinese astrology and traditional masked dances and festivals of the early Heian era, and that in the early days the game was played as a form of ritual rather than entertainment.  Over the centuries, the game was reduced down to smaller forms, like Dai Dai Shogi, Dai Shogi and Chu Shogi, once they discovered that this ritual game was actually quite fun to play, but pretty long….

How long, you ask?  Well, George Hodges once compared the lengths of various versions of Shogi — this is the number of total moves in an average game for each variant:

  • Chess: 80
  • Shogi: 110
  • Dai Shogi: 400
  • Dai Dai Shogi: 800
  • Maka Dai Dai Shogi: 1100
  • Tai Shogi: 2000

Wow, that’s long.  If you start up a game of Maka Dai Dai Shogi, make sure you have the weekend free 🙂  I should say that I, of course, own a physical set for this game and would happily play it with anyone who asks.  The board is too big for my table, however, so we’d have to find a place big enough!

tsa maka set1

A Maka Dai Dai set by Angela/George Hodges — promoted pieces on top.

maka dai dai closeup1

Maka Dai Dai is such a large game that it can be quite intimidating — staring across the board at your opponent’s massive army lurking across the horizon feels quite different from more normal-sized Chess games.

maka dai dai emperor

The Mighty Emperor

 

Tai Shogi

OK, now this is getting ridiculous — Tai Shogi, or ‘Supreme Shogi’, is a spectacularly huge game played on a 25×25 board of 625 squares, invented in the 15th century by Buddhist monks (of course).  Each player marches into battle with an army of 177 pieces each, and in order to play you need to remember 99 distinct piece movements.

I’ve never personally played this, but remarkably, you can actually buy a set of this from Angela Hodges here in the UK.  The board is more than a metre square!  Even experienced players take upwards of two hours to set up the pieces in their initial position.  As you can see below, each players’ starting ranks are absolutely chock full of pieces — in fact the opening phase is a bit like a sliding-block puzzle as you try to free up lines for your pieces to get into the action.

Notably, there are actually no Kings on the board — each player starts with an Emperor in play (!), and a Crown Prince that moves like a King.  Both must be captured to win the game.  Many of the other pieces have strong promotions, which occur by capture as in Dai Dai and Maka Dai Dai rather than by entering the promotion zone — so carelessly leaving pieces out to be gobbled up can rapidly turn the game against you!

Those who’ve played Tai say it’s an extremely challenging game, because it’s very hard to formulate any kind of sensible whole-board strategy in a game this large.  As a result the game plays more like a wargame, with intensely tactical local skirmishes of great complexity breaking out across the board.  Meanwhile, the everpresent Emperors make each move feel consequential — leave anything hanging and you may give the Emperor a chance to start some carnage.  Given how old this game is, the creativity of all this is astounding — it’s kind of like an ancient version of Warhammer or something.

I don’t yet own this game but certainly plan to at some point — consider this a standing challenge to all!  Once I get a set for this, I’m happy to give it a go with anyone who’s interested.

tai shogi vs shogi comparison

Regular Shogi just looks tiny compared to Tai Shogi!  Without a doubt you could play an entire Shogi tournament in the time it takes to play one game of Tai Shogi.

tai shogi central files

A closeup of the Emperor’s immediate surroundings — quite a dense wall of protectors he has!  The Emperor is at the centre of the bottom row, the Crown Prince (taishi)  is directly above him, and the Drunk Elephant three pieces above the Prince.

Taikyoku Shogi

Unbelievably, Tai Shogi is not the biggest Chess game to ever exist.  It used to be, until some documents were uncovered in 1997 with rules for a 16th-century Shogi variant called Taikyoku Shogi, or ‘Ultimate Shogi’.

This preposterous game is played on a 36×36 board of 1,296 squares.  Each player has an army of 402 pieces, and to play you must remember 253 distinct movement patterns.  Each side starts with a King and Crown Prince on the board, and a Drunk Elephant who can promote to Crown Prince — meaning you may have to capture three royal pieces to eventually win.

Unlike the other huge variants, in Tai Shogi promotion is once again by entering the enemy camp rather than by capture.  Each army contains a huge variety of pieces with whimsical names like the Running Bear, Vermillion Sparrow, Violent Ox, Enchanted Badger, and — my favourite — the Vertical Puppy.  If I ever play this game somehow, I’m going to devote my entire strategy toward devising a way to checkmate my opponent using the Vertical Puppy.

Amazingly, a real-life wooden set for Taikyoku Shogi was carved and used for a special segment on the Japanese variety show Fountain of Trivia back in 2004.  Two Shogi pros faced off in a game of Taikyoku Shogi, using a little reference book to help them remember how the pieces moved.  The game lasted 32 hours and 41 minutes, and ended in checkmate for the first player after 3,805 moves!

There’s a clip of the match on YouTube, unfortunately the quality isn’t great but the whole segment is there: https://www.youtube.com/watch?v=_c0Y26iTPSM

At the end of the match, the winning player says ‘I don’t want to do that again’; the loser says something hard to translate, but it’s kind of like ‘I have no regrets’, conveying the impression he doesn’t mind losing something so bizarre, and is mostly glad it’s over.

taikyoku-shogi-setup

A closer look at one player’s setup in Taikyoku Shogi — imagine trying to remember all 402 of these pieces!

taikyoku-real1

A fanmade version of Taikyoku Shogi — quite impressive!

 

Notes on the large Shogi variants

For much more detail on the Shogi variants, I recommend checking out this GeekList on Boardgamegeek.com from Shogi enthusiast The Player of Games that describes a large number of them.  Numerous resources are linked there, and I borrowed a bunch of the images in this post from there as the photos the author took of his sets are far better than any others I could find.  Many thanks to TPoG for taking the time to produce such crisp and high-resolution images of these great games!

Most importantly, TPoG’s list includes a detailed discussion of some discrepancies in the moves for certain pieces — the three main Edo Era sources for the larger games differ slightly in how they describe some moves.  For the most part these differences are very minor, and in games this size aren’t really going to have any influence at all on the overall play.

However, the recommended changes in that list for the upgraded forms of the Lion make much more sense than the currently-available moves in the English versions of these games.  They actually build on the Lion’s powers rather than weakening them.  For reasons of consistency I highly recommend using the updated moves suggested in that list when playing Dai Dai Shogi, Maka Dai Dai Shogi or Tai Shogi.

Where do I go from here?

Well, as you can see, Shogi offers a whole world of interesting games.  I wrote far too much here, and yet still didn’t cover anywhere near all the variants — there’s a number of smaller ones too, but I just love the big monster games.  If you fancy trying a variant of Shogi, and want to pick just one, I’d recommend Chu Shogi — it’s monstrous without being ponderous, and the Lion is such a creative and beautifully-balanced addition to the game.  Leaving aside my nerdy fascination with all things Shogi, it’s a genuinely delightful game.  Tori Shogi is also a great choice, as it’s small and easy to learn but still has tons of depth.

If you want to dive headfirst into one of the monster games, I highly recommend Maka Dai Dai Shogi.  It’s a fascinating game not just in terms of its unique play style and unusual pieces, but also because of its intriguing history and cultural relevance.  When playing this game you can feel that it could have been a ritual experience, a rumination on Buddhist thought as well as a battle playing out on a (huge) chessboard.  Sure, it’ll take awhile, and will require patience and dedication to get through a game — but those are quite Buddhist qualities, are they not?

Your best bet of course is to play modern Shogi — in my opinion it’s the finest version of Chess by quite some distance, and can easily support a lifetime of play and study.  There are numerous places these days to play online, like 81dojo  which is free, available in English and supports several variants as well.  Obviously modern Shogi has by far the largest playing community of any version of Shogi, and rightfully so — it strikes a balance between complexity and simplicity that’s hard to beat.

For a taste of Shogi, come on down to our Shogi event next month and get acquainted with the modern game!  I’m sure you’ll enjoy it, even if just as a peek into a corner of Japanese culture most of us never see.  For those of you who really take a fancy to the game, you’re welcome to join Shuzo and myself in our soon-to-be-launched Shogi club, which will meet regularly in Glasgow to play Shogi and learn about the game.

And, if you’re a weirdo like me who can easily spend all day playing games, join me for a game of Tori, Chu, Dai, Tenjiku or Maka Dai Dai Shogi!  Just make sure you free up your schedule first 🙂

 

 

Tagged , , , , , , , , ,

Chess Engine Update: Endgame Tablebases

In the background, while tons of work stuff has been happening, I’ve been continuing my mission to write a fully-featured computer chess engine in the C programming language.  My engine is named SpaceDog, in honour of my dog Laika, who is from space.

Work on SpaceDog has been proceeding well, with lots of additions to its evaluation function, convenience features like outputting fully-diagrammed logs of each game you play against it, outputting games in PGN format, etc.  Now I’m diving into adding more substantive features, in this case support for Syzygy endgame tablebases.

Endgames have always been a prominent feature of chess study, and over the centuries millions of players have stared uncomprehendingly at difficult endgame studies, mate-in-3 puzzles, and similar things.  For the improving player, endgame study is interesting but also very challenging, in that there are innumerable situations where a seemingly simple or natural move can lead to disaster, or conversely the failure to find a very specific and unintuitive move can lead to a missed win.

Naturally this is just as much of an issue for computer chess engines as it is for humans.  Many engines over the years have been programmed with specific rules for winning typical endgames like KPvsK (King and pawn versus a lone king) and some of the particularly long-winded and tedious ones like KRvsK (King and Rook versus King) or the dreaded KBNvsK (King, Bishop and Knight vs King — you get it now, abbreviations only from now on!).  Some of these endgames require remembering rules particular to each endgame, or even memorising long strings of winning moves in order to not mess up and give your opponent a stalemate.

Before we go any further, a quick reminder of the basic rules of ending a chess game:

  • Checkmate: opponent’s King is in check (attacked) and unable to escape to safety
  • Stalemate: opponent’s King is not in check, but your opponent has no legal moves, (remember it’s illegal to move into check)
  • Draw: declared when players repeat an identical board position 3 times in a row, OR when 50 moves have elapsed without a pawn move or capture taking place

These rules and the complicated nature of some endgames make things difficult for humans to succeed in their endgame play, and chess engines struggle too, even when looking ahead many more moves.  Let’s see, for example, how SpaceDog copes with the tricky KBNvsK ending:

KBNvsK no TBs 2

Here’s a snippet of SpaceDog’s attempt (before my recent additions) to play KBNvsK (the full PDF record is available here).  I actually stopped the engine after 26 moves as it was clearly making no progress!  If you check the full game log out, you’ll see that SpaceDog manoeuvres bravely, but is unable to work out the correct plan to trap the enemy King, even though it was looking ahead 25 moves at this point.  SpaceDog needed to trap the enemy King against the side or corner of the board to make it easier to deliver checkmate, but couldn’t coordinate its pieces correctly, and so the ending barrelled irretrievably toward a draw by the 50-move rule.

It’s worth saying that SpaceDog, even armed with only its core evaluation function and search, is more than capable of winning many endgames.  But even in those cases, it can make the occasional mistake that can allow a clever opponent to salvage a draw or stalemate, or can be simply inefficient and take longer than it should to mate the opponent.  Let’s take this KPPvsKP ending as an example:

KPPvsKP no TBs 2 This endgame looks simple, but the black King is in the way of White’s protected passed pawn on c4, so getting that pawn to promote and become a Queen requires some finesse.  SpaceDog manages this quite well without any additional help, mating the opponent in 24 moves.  However, with clever play it should be possible to checkmate Black quicker and with a greater material advantage.

And that clever play is what endgame tablebases are all about.  Endgame tablebases in chess came about thanks to Richard Bellman, who in 1965 proposed analysing chess endgames using retrograde analysis — starting from checkmate positions, and working backward from there to find the optimal moves to reach that position.  The end result of this would be a massive database containing every possible configuration of pieces on both sides of an endgame with small numbers of pieces, with complete information on how to reach the best possible ending from that position.  In 1977 computer science legend Ken Thompson used the first endgame tablebase in an engine against a human opponent, and from there chess engine programmers were off to the races.

Today thanks to widely available supercomputer power we have access to tablebases that enumerate all the optimal moves for both players from every possible endgame position containing seven or fewer total pieces.  This is a truly staggering number of positions — 423,836,835,667,331 to be exact!  Yes that’s 423 trillion positions.  There are 512 billion KRBNvsKBN endgames alone!  For every single one of these positions, we know: the game-theoretic value of the position (Win, Lose or Draw, or WDL for short); the distance-to-zero (moves before a pawn move or capture that zeroes out the 50-move drawing rule, or DTZ); and the distance-to-mate (number of moves for the winning side to mate, or DTM).  You can explore any and all of these positions and view the winning moves and various stats about endgames at Syzygy-Tables.info; the front page also has handy links for downloading all the tablebases for yourself.

I should note that of course given the size of these databases, the actual files are very large.  The best available compression algorithm for full WDL and DTZ tables is Syzygy, which is what I’ve added to SpaceDog.  The 3, 4 and 5-piece endgames will take about 1GB of storage, but you’ll need 149GB for the 6-piece endgames, and a staggering 18.4TB for the 7-piece endgames!  To use them most efficiently, make sure the WDL tables are on very fast storage like a solid-state drive (SSD), as these are accessed by engines very frequently to guide the engines toward favourable endgame positions, whereas the DTZ tables are only accessed once the engine actually enters an endgame position and needs to know the best moves.

So, after a weekend of work, SpaceDog can now use the Syzygy endgame tablebases, and thus plays endgames perfectly.  This makes it far better for practicing endgame play, for learning difficult endgame and mating sequences, and for analysing games.  To see how dramatic the change is, let’s go back to that KBNvsK endgame from earlier, where SpaceDog stumbled about uselessly for 26 moves heading for a draw, despite having a massive advantage in material.  Once we add Syzygy tablebases, SpaceDog obliterates its opponent in only 7 moves:

KBNvsK TBs 2

Look at that lovely short move listing!  This time, SpaceDog uses all of its pieces in concert, confining the enemy King to the corner by occupying the short f1-h3 diagonal with its bishop.  Shortly afterward, we end up with an effectively and efficiently checkmated opponent:

KBNvsK TBs mate 2

Even when we revisit endgames that SpaceDog can win easily, the Syzygy tablebases provide significant improvements.  Going back to the KPPvsKP endgame from earlier, SpaceDog checkmates five moves faster:

KPPvsKP TBs 2

SpaceDog not only wins faster, but it ends up with two queens instead of just one!  The opponent doesn’t stand a chance:

KPPvsKP TBs mate 2

Of course these are far from the most complicated endgames available.  SpaceDog can now win endgames that take potentially hundreds of moves, without making a single mistake.  The Syzygy tablebases are built with the 50-move rule in mind, so in some longer endgames you’ll see clever trickery as SpaceDog just manages to make or allow a pawn move or capture before the deadline, to reset the clock and deliver checkmate later on.  Take for example this KBBvsKQ endgame, in which SpaceDog achieves mate in 52 moves:

KBBvsKQ TBs

Here SpaceDog methodically manoeuvres the Queen to neutralise both of White’s bishops, until it captures one of those bishops at the last possible moment (the last half-move of move 50):

KBBvsKQ move 50

That gives SpaceDog the time to finally deliver forced checkmate two moves later:

KBBvsKQ mate

As you might imagine, remembering forced sequences of so many moves and using them with such impeccable timing is impossible even for the top Grandmasters — there are simply too many endgame possibilities to make rote memorisation worth the trouble.  Even if it were worth it, remembering sequences like that over the board under time pressure against live opponents would be a very tall order!

During my testing I found a particularly cruel example of this kind of brutal efficiency in this KNNvsKP endgame, where White delivers a tricky checkmate with two knights after 52 moves:

KNNvsKP TBs

Note that the first move, Na2, immediately immobilises Black’s passed pawn, where it stays frozen until move 50, when White lets it run free.  ‘Yay!’ says Black, ‘I’m making a Queen!  I’m back in this!’

KNNvsKP move 50

Black does make a Queen, as it happens, but it’s ultimately pointless as they get checkmated immediately:

KNNvsKP mate

SpaceDog, that’s just harsh!

Anyway, these are just some fun examples from 5-piece endgames — there’s some amazing endgames in the 6- and 7-piece databases of course, with forced checkmate sequences lasting hundreds of moves, totally bizarre-looking moves that turn out to be the only path to win or draw, and intricate piece play that has done wonders for our understanding of endgames.  I highly recommend taking a look at some cool endgames using an engine, or just browsing them via the web interface linked above — you’re bound to find something fascinating.  Assuming you care about chess, obviously.

So what’s next for SpaceDog?  Well first, my Syzygy tablebase support is only half-finished — endgame play is now perfect, but I have yet to implement searching of the WDL tables during midgame play to guide SpaceDog toward the best possible endgame positions.  That’s a relatively straightforward addition and will take much less time than adding the DTZ support, thankfully!

After that, I’m aiming to beef up SpaceDog’s search, making it more efficient to allow searching to greater depths, and making it much faster by using multi-threading (multiple CPU cores).  At that point, SpaceDog will have all the main features of a modern alpha-beta chess engine, and will make a worthy opponent for its eventual successor: SpaceDogNeuro.

You can download the latest SpaceDog executables for Windows and MacOS (Linux forthcoming, when I remember) at the Github repository, by the way, but bear in mind it’s a messy hobby project, and a major work-in-progress with bugs lurking everywhere!  If I were you I’d wait for version 1.0.  In the meantime, for serious chess analysis, Stockfish is the superior choice (and it’s free and open-source too).

Tagged , ,

(Re-)Learning C Via Computer Chess

In recent months I haven’t had much time to do a lot of programming, what with the demands of my work. One thing I’d been meaning to do, whether it factors into my research directly or not, was to re-acquaint myself with the C programming language. I used it way back in the day, but then as time went on I fell in love with Python, which despite being ridiculously slow in comparison, is extremely fun to use. But the fact remains that it’s very useful to be able to write compact, speedy code from time to time, either for writing simulations for work or for passion projects.

So, I decided to find myself just such a passion project to rediscover the joy of programming in C, and given that I’ve been playing and studying a hell of a lot of chess and shogi in my spare time of late, I decided to learn how to program a fast and relatively powerful chess engine in C. A traditional chess engine uses brute force to search a very large number of possible moves on its turn, evaluating each one in turn until it chooses what it thinks is the best move for the situation. Given how much computing power is available these days, even a half-decent smartphone can now play chess at a level greater than any human, including Grandmaster-level professionals.

In order to do this I followed a great series of videos on YouTube called ‘Programming a Chess Engine in C’, which is 95 videos long (!), but covers a ton of stuff, helping you build a fully-functional chess engine in C which uses the standard techniques in chess programming — alpha-beta search with null-move pruning and some other optimisations. The engine is capable of playing a game of chess via text commands with the user, or by communicating with graphical chess software using the UCI or WinBoard/CECP protocols to let you play a game with mouse control and lovely graphics for the pieces.

After watching all that and feeling my way around C again, I’ve now produced a chess engine of my own, which I’ve named SpaceDog, in honour of my dog who is from space.  At the moment it’s basically the same as the VICE engine which comes from the videos above, but has a few small additions in the evaluation function to make it a little stronger (hopefully), as well as a few quality-of-life improvements here and there.  It works great, and plays a mean game of chess already — which perhaps isn’t surprising since it searches and evaluates about 3.5 million chess positions per second!  In comparison a master-level human player might evaluate perhaps 3 or 4 positions per second.

Here’s a screenshot of SpaceDog playing in text mode:

Screen Shot 2018-10-14 at 03.23.34As you can see, it prints out a nice little text-based board for you (white pieces are capital letters, black pieces are lowercase).  Moves are entered in long algebraic notation — so to move white’s queen at the bottom of the board to the square above white’s king, you’d enter d1e2.  SpaceDog also prints out its search results and position evaluations on each move, so here you can see at the bottom that it searched nine moves ahead (depth:9) and spent 2.9 seconds evaluating 11.9 million moves before choosing the move e7e4 (taking my pawn with its queen) based on what it thinks of the resulting position and its future prospects.

Every searched position is evaluated quite simply, with a score calculated on the basis of material balance, the position of the pieces, and things like whether there are isolated pawns and other key features.  Right now I’m adding some additional evaluation terms that better capture how the relative value of certain pieces, and their ideal placement on the board, changes as you proceed from the opening to the endgame.  Hopefully this will make SpaceDog a bit more shrewd at finding checkmate!

The engine can also use opening books — these are files generated by processing millions of opening moves from many hundreds of thousands of professional chess games, choosing a repertoire of openings based on what moves proved to be most successful.  This means SpaceDog essentially has a huge file of opening moves already catalogued in the book, with an enormous selection of replies and counter-replies for all the best possible responses from the opponent.  These moves then don’t need to be searched, meaning that SpaceDog saves tons of time for searching much deeper in difficult middlegame and endgame positions.

At this point SpaceDog probably plays well enough to beat anyone I know, but would likely still lose to players above Master level.  That would probably change at fast time controls — i.e., quick game setups like blitz (5 or 10 minute time limit for each player) or bullet (1 minute each!).  At these time controls, humans simply can’t make much use out of our superior long-term strategic planning abilities, so even SpaceDog’s rudimentary but tactically sound play should be tough to beat when us human meat-bags are sweating over the clock and feeling the pressure.

Anyway, it’s been a lot of fun so I plan to keep it going!  Next steps are to continue to enhance the evaluation function to better account for things like keeping the king safe and setting up outposts for bishops and knights.  I’ll also work on some more technical enhancements like multi-PV search (searching multiple lines of play on multiple CPU cores simultaneously) and adding support for endgame tablebases to allow SpaceDog to achieve perfect endgame play.

Most importantly though, I want to add a mode so SpaceDog can play Crazyhouse and Chessgi, variants of chess in which captured pieces become yours and can be dropped back onto the board as part of your army.  This is a feature taken directly from shogi which is a game I also love, so I’m looking forward to implementing these.  Eventually I may try to build on that foundation and add a shogi mode as well.

‘What’s the point of all this?’ you’re probably asking at this point — after all, SpaceDog will never be as good as current strongest engine Stockfish, and plenty of other engines play Crazyhouse and lots of other variants besides (such as this version of the mighty Stockfish).  There are even innovative neural-network-based engines coming out now like LCZero that are challenging for the throne of toughest computer opponent.  But nevertheless writing SpaceDog has been satisfying and fun, and it’s given me another way to learn more about chess and enjoy the game from a different angle.  I’d also forgotten how satisfying coding in C can be — the final SpaceDog program takes up only 74KB (!), yet it effortlessly plays chess better than I can.

Anyway, I thought I’d post this up just on the off chance anyone else might get something out of learning a bit about chess programming.  I highly recommend the tutorial videos I linked above from Bluefever Software — they’re really easy to follow and provide excellent explanations of the key concepts you’ll need to know to write a chess engine.

Someday I’ll post up the code for SpaceDog too, once I add a few more additional features in!

Tagged , , ,

The Game of Go

I’ve been off work for a couple of weeks now, and rather than going on holiday I’ve mainly been trying to rest up after several months of really intense work.  As part of my attempted recuperation I’ve been playing a lot of the board game Go, a game I have a tremendous fondness for but go through long periods of slacking off when my brain is busy with work stuff.  I’ve been enjoying the opportunity to play more and thought that some of my friends and colleagues might enjoy the game too, so I decided to put together an intro to the game, alongside copious links to resources and ways to play online.  I hope this might spur some of you out there to give it a try.

Go is a board game that’s been around for a very long time, and is generally believed to be the oldest board game still being played today; Go was invented about 3000 years ago in ancient China.  The game is still immensely popular in Japan, China (where it is known as weiqi), and Korea (baduk), where professional play is well-established, and it boasts a  growing following in America and Europe as well.

I’ll start by giving you a very brief summary of the rules of the game, then link you to some resources that will help you get started.

Playing Go

Go is known as a game of great complexity and subtlety, but the actual rules are simple.  There are two players, White and Black, and each has 180 stones of the appropriate colour.  Black always goes first, which confers a slight advantage, so in compensation White receives a bonus (komi) of 6.5 points at the end of the game (under Japanese rules, it’s 7.5 under Chinese rules).

The players start with an empty board of 19×19 squares, like so:

empty go board

Notice that the board has nine marked star points which help players to orient themselves in this large playing space.

The players take it in turns to place a stone on an unoccupied point on the board.  Once placed, a stone never moves, although it can be removed when captured.  Stones are captured if all of the empty points surrounding them (their liberties) are occupied by stones of the opposing colour.  This GIF shows an interesting example, where Black keeps capturing White stones only to eventually have his entire group captured himself by cutting off his own stones’ liberties:

go capturing gif

Over time as stones are placed and some groups are captured or fortified, the players will sketch out and secure territory where their opponent cannot play without being captured.  At the end of the game, both players total up the amount of territory surrounded by their stones, add in the number of stones they’ve captured from their opponent, and compare the totals (plus the 6.5 points komi for White) — the player with the highest total of territory and prisoners wins the game.

Below is an animated gif showing an example of play: a complete record of the famous ‘Game of the Century’ between Go Seigen (Black) and Honinbo Shusai (White).  In this match players could adjourn to think at any time, so this game dragged on for three months!  White won by two points in the end and the game is celebrated for some brilliant moves and fierce fighting over territory.

seigen shusai gotc

You can download a huge archive of 48,000 historic Go games in SGF format here, or if you want to view records of professional games in a handy web applet you can check out GoKifu.com.

The Style of Play

From the simple rules of Go, very complex patterns of play emerge.  Unlike other prominent competitive board games like chess, in Go the board starts empty, and the number of available points to play a piece is very large (361 points on a Go board vs 64 squares on a chess board).  The sheer number of possible moves is so huge that players must rely on intuition, a solid grasp of fundamental principles of play, and keen awareness of their opponent’s movements to play well.

This reliance on intuition makes Go a surprisingly emotional game — pick up any book by a serious professional and you’ll see them speak with great passion about how various moves and games made them feel.  This in turn leads to some seriously intense contests — watch professional matches and you’ll see the players’ faces often contort with pain as they confront a powerful move by their opponent.

As a result of the complexity of the game, you’ll see Go players start their play in the corners and edges of the board — this is because it’s easier to make territory on the sides and corners, since you can use the edges as boundaries for your territory.  As the sides and corners are decided, players begin reaching toward the centre of the board, attempting to connect their strongest groups of stones together and grasp larger chunks of territory.

The beginning of a Go game is often overwhelming for new players, who struggle to figure out where to start placing stones on this massive empty board.  Generally the Black player will start play on the upper-right star point, which is considered polite to your opponent — it’s close to their end of the board and gives them a clear idea of where to start play.  This helps somewhat, but the opening is still the toughest part of the game for newcomers.

As a result, most experienced players recommend that new players start on a smaller board, either 9×9 or 13×13.  These are less intimidating to start with and get you into territory fights right away, giving you an immediate introduction to the moment-to-moment tactics of Go.  Just bear in mind that you should try to advance to the full 19×19 board as soon as you can, as it’s a very different game at that scale.  On the full board strategy becomes as important as tactics, and stones in distant corners have powerful implications elsewhere as patterns of territory shift and evolve over large swathes of the board.

Learning the Game

Learning Go is a long process, as the game requires an understanding of a lot of complex interactions between stones.  There’s also a bit of a language barrier, as many Go terms derive from Japanese and are difficult to translate, so most players just use the Japanese words.  As a result you’ll need to understand things like what it means when stones are in atari (stones that will be captured on the next move unless you do something to save them), or in seki (opposing groups of stones that can’t capture one another without endangering themselves).

Luckily there are some great introductory books I can recommend that will give you copious examples of these terms and many helpful and illustrative Go problems (tsumego) to test your skills.

For complete newbies I highly recommend Go: A Complete Introduction to the Game by Cho Chikun.  Cho Chikun is one of the greatest players alive today, being the only player in history to hold all four main Japanese titles at the same time.  His book is surprisingly short but very dense with helpful illustrations of key go concepts, and it rewards deep study and playing out the examples on a real or computerised board to experience each pattern for yourself.

From here you can check out the Elementary Go Series from Kiseido Publishing.  This series covers key concepts of the game in detail in each volume.  Many players recommend these books for players seeking to advance to intermediate levels of play.

When you’ve fully digested all this, you can try Lessons in the Fundamentals of Go by Toshiro Kageyama.  This book is thicker than the others and quite dense with content — expect getting through this to take weeks, not days.  But the concepts he explores are critical to good high-level play, and if you master them you’ll be well on your way to a thorough understanding of the game.

For online resources, I recommend studying the games of great masters, which you can easily find via the archives linked above and at places like GoKifu.com.  The LifeIn19x19 forum is a great place to get tips from other Western players, with many members happy to give guidance on your development as a player.  Finding good software is also key to learning the game, as this will be how you view and study the games of great players, or analyse your own games to examine your own strengths and weaknesses.

 

Go Software

This section will be relatively short, because in my view there’s really just one piece of software you really need to study Go, and that’s Sabaki.  Sabaki is free, open-source, and works perfectly on Windows, Mac and Linux.  It also nicely captures the austere aesthetics of the game, showing you a lovely 19×19 wooden board sat on a tatami mat and simple black and wide stones.  You can customise the look with themes as well, if you like.

A subtle touch that I really appreciate is that each stone is placed with a slight random touch, rather than precisely on the relevant point on the board, giving the whole thing a slightly more organic look as the game evolves.

Looks aside, Sabaki is a great piece of Go software, allowing you to view SGF files (the move-by-move records of Go games, as in the archives linked above), edit your own, and play against any AI Go engine that supports the GTP protocol (basically all of them).  In particular I recommend using Tencent’s PhoenixGo engine, which is very strong and comes with instructions on how to link it with Sabaki on Windows and Mac.

Here’s a screenshot, stolen from Sabaki’s GitHub page:

Sabaki screenshot

If you’re a more advanced user and want sophisticated analysis of your games from a strong AI, you can use Lizzie, which uses the Leela Zero engine to analyse your moves and show you what the engine recommends in each situation.  Download the latest version from the Releases page at the link, then follow the instructions in the Readme file to get started.  The results can be helpful, but bear in mind Leela Zero can only show us what she thinks, not explain why she thinks it, so still it’s better in my opinion to get input from human players and learn Go fundamentals rather than just ape the moves the computer engines recommend.

Here’s an example of Lizzie’s output, showing the user its recommended moves (the cyan-coloured one is Leela’s top recommendation):

lizzie screenshot

 

Go Equipment

Go equipment, much like the game itself, is steeped in centuries of history and tradition.  Japanese aesthetics in particular have had a profound influence on Go equipment.  Today most high-level players or keen amateurs in search of fine equipment will go to Japan to get it.

go set1

The finest Go boards are made from the Japanese Kaya tree, and makers prefer that the tree is between 700-1000 years old when the wood is harvested.  This combined with the fact that Kaya trees are protected in Japan means that true Kaya boards can be ludicrously expensive; free-standing boards with legs can rise well into the tens of thousands of pounds.  Normal people go for so-called ‘Shin Kaya’ boards, usually made of Alaskan spruce, which looks close enough to the right colour and feel for most people and can be had for £100 or so for a tabletop board of 3cm thickness.

go stones 2

The finest Go stones, meanwhile, come from a place called Hyuga in Miyazaki Prefecture in Japan.  The black stones are made of nachiguro slate stone, while the white stones are meticulously carved from clamshells, resulting in a beautiful shining surface striped with subtle lines.  The finer the stone, the thicker it is and the denser and thinner the lines are.  As with the Kaya boards, genuine Hyuga stones are incredibly rare and have price tags far beyond most mortals.  However, these days you can get clamshell and slate stones made from imported Mexican clams that are nearly as perfect as the real thing, and a good set of decent thickness will set you back about £200-300 rather than tens of thousands.

go bowls1

Finally you have the Go bowls, which hold each player’s stones.  Traditionally you place the bowls next to the board with the lid upside-down in front of it, and place any captured pieces in the upturned lid.  This is polite to your opponent, who needs to know how many pieces you’ve captured as that affects the game’s final score.  Go bowls again can cost ridiculous amounts for traditional Japanese wooden articles, but beautiful and functional bowls hand-carved from cherry and other woods needn’t set you back more than £150 or so.

The overall effect of a fine Go set should be a beautiful, smooth board with a soft yellow tone that perfectly compliments the black and white stones.  When you place a stone on the board, it should make a satisfying ‘click’ against the wood — in particular on the free-standing boards, which have a chunk hollowed out of the interior to ensure it makes a pleasing sound.

In total, if you purchase a nice table Go set from a prized Japanese maker like Kuroki Goishi-ten, expect to pay about £300-400 for the lot (plus shipping/Customs fees of course).  This is assuming a 3cm or 6cm Shin Kaya board, ‘Blue Label’ Mexican clamshell stones, and mid-level bowls of sakura wood or similar.  Various distributors do sell some of their products in Europe — check Masters of Games in the UK, or Go-Spiele.de in Germany.  Both stores also offer budget sets with Korean glass stones that are more than fine for most people; a set with a nice Shin Kaya board, Korean glass stones and Go bowls made with European wood should cost no more than about £200.

One of my great regrets from my time in Japan is that despite my intense desire for one, I never purchased a fine Go set for myself.  They really are lovely.  As a consequence of not taking that leap, I have this masochistic ritual of checking Kuroki Goishi-ten’s sales every summer, finding myself unable to justify the ~£100 in shipping costs on top of the cost of the set, and end up torturing myself over it for weeks.  Someday I’ll take the plunge; in the meantime I do hope to get a Shin Kaya/glass stones set someday soon, and then eventually upgrade to proper clamshell stones.

Go vs Chess

For those of us in the West, the average person’s familiarity with abstract strategic board games often starts and ends with chess — even people who don’t play have probably heard of Garry Kasparov and Bobby Fischer.  Both chess and go are intellectually challenging and stimulating, but they differ in quite fundamental ways.  I’ll say up front that I enjoy both, and feel each one offers something the other doesn’t.

As described above, Go is simpler than chess as far as the rules go — stones are simply placed and never moved, and complex interactions between pieces arise from their configurations, not from the rules themselves.  Meanwhile, in chess each piece moves, different types of pieces move differently, and the goal of the game is to trap the opposing king, which again depends on intimate knowledge of the roles and movements of the different major and minor pieces.

For the chess player, Go can initially seem a bit incomprehensible.  Chess openings have been so thoroughly explored by humans and computers that many experienced players play the first 10-15 moves essentially from memory (depending on their choice of opening), while in Go this vast empty board makes the opening phase really perplexing.  Note that Go players also have opening patterns they study called joseki, but these aren’t overly necessary except at high levels of play, and in fact many pros discourage new players from studying them until they’re quite advanced in their play.

The smaller boards and armies of chess mean the game also turns much more on tactics than Go.  Chess does have lots of strategy to it of course, but on the whole it’s more likely that a single move can change the course of a chess game than a single move massively changes a Go game on that huge 19×19 board.  So, if you’re more interested in intricate tactics and moment-to-moment attacking play, chess may be more your game; whereas if you’re interested in sweeping strategic movements and more intuitionist play styles, Go may be for you.

Honestly though, I’d say just play both — each game is rewarding in its own way, and I suspect a strong tactical chess background will serve you well in Go, just as strong strategic instincts in Go should surely help your chess game.  I also recommend trying chess’ East Asian cousins Shogi, Xiangqi and Janggi.  Shogi (Japanese chess) allows captured pieces to re-enter the game on the capturing player’s side which creates an interesting dynamic feel.  Xiangqi (Chinese chess) has unique pieces and a larger board with territorial restrictions; Janggi (Korean chess) is very close to Xiangqi but with some rules differences that make it a very interesting variant.  In fact I may post about these games someday down the line, as all are very accessible now with free apps for online play, and both Shogi and Xiangqi have some excellent English-language resources available (less so Janggi).

Playing Go Online

Speaking of online play, Go is likewise more accessible than ever thanks to the efforts of an extremely dedicated global community of players.

There are a number of great free services that enable online play against opponents all over the world, 24/7/365.  A few of them specialise in real-time games, in which you and your opponent finish the game in one sitting, while others focus on correspondence games, where you take your time with each move and update the game on the server when you’ve chosen your move, and games take place at a leisurely pace over weeks or even months.

All of these services are free, by the way, though some offer subscriptions with extra benefits.

Real-Time Servers

IGS (The Internet Go Server) — By far the oldest of the bunch, the IGS has been around since 1992 (!).  It started in Japan and still has the largest Japanese player community; many professionals play here.  A nice software client, CGoban2, is available for all major operating systems, and there’s a good app as well for Android and iOS.

KGS — Popular with Westerners, KGS is well-known for being a chatty server where more experienced players will offer learning games for newbies and analyse your games to help you improve.  Has lost popularity somewhat in recent years and the Android app is apparently a bit unreliable, however.  I’ve heard some players recently recommending people shift to other servers, as they have difficulty finding good opponents here nowadays.

TygemBaduk — A Korean server but has an English-language website and client.  Quite popular and apparently a good place to face strong opposition, though the client only works on Windows and iPad so be aware of that.  The web client will work on any platform, though.

WBaduk — A very large Korean server, immensely popular.  Another great place to face strong opposition, but they’ve also got problems with accessibility — just a few days ago the English client disappeared off the Google Play Store (!).  Worth joining once you’re ready for strong opponents, but perhaps worth keeping on eye on things to see whether some changes to the service might be forthcoming.

Fox Weiqi — An absolutely massive Chinese server that’s becoming increasingly popular among Westerners due to having an English-language client and a polished Android app.  Do note however that you have to sideload the app onto your Android phone, presumably due to China not really being a fan of Google services.  Also the app is in Chinese only as far as I can tell.  I’m installing the app as I write this so we’ll see if I can manage to find what buttons to mash to play a game with someone!

Correspondence Servers

Online Go (OGS) — A fabulous place to play correspondence Go.  Uses a constantly-updated, modern web interface with responsive design — meaning it works perfectly and looks great regardless of whether you use it on desktop, laptop, phone or tablet.  At any given time there are tens of thousands of correspondence games going.  Real-time play is also supported, but most players do opt for correspondence games.

Dragon Go Server — A bit old-school design-wise, but has been around a long time.  I’ve never personally played here but my impression is the userbase is pretty loyal.  The web interface works fine for what it is, but definitely miles behind OGS.  For playing on Android you can use a free plugin for the Go app BW-Go.

 

Go Apps

AQGo — An Android app that lets you play against the super-strong neural-net go bot LeelaZero, which is a community attempt to replicate Google’s super-powerful AlphaZero go bot.  Needs to be sideloaded onto your phone.

Crazy Stone Deep Learning — A beautifully polished Go app that lets you play against a strong neural network opponent.  The Pro version is a bit pricey as apps go (£12.99), but it’s been worth it for me to have an ever-present strong opponent that will analyse my games in-depth.  Also available on Steam for a much higher price but also has a stronger rating (7-dan).

GridMaster Pro — A cheap, no-frills Go app that lets you play against a variety of Go engines, including Leela Zero.  A slight caveat here in that in my experience, sometimes Leela Zero will refuse to make a move until I forcibly shut and reopen the app, but your mileage may vary.  Leela and other engines can be downloaded directly through the app and installed instantly — check the app’s website for details.

TsumeGo Pro — An app for tsumego problems, Go puzzles that test your knowledge of key Go concepts.  Extremely useful for polishing your skills and furthering your understanding of the complexities of keeping groups of stones alive — or killing your opponents groups!  In-app purchases get you more problems to solve.

Pandanet IGS — The app for the Internet Go Server above.  Free and works really well in my experience.

 

Well, that’s quite enough for one day — I hope this info might prove useful to someone out there who’s curious about Go.  It’s a wonderful game and more accessible than ever, so if you’re interested in giving it a try, just pick your choice of app and get in there!

Tagged , , ,

Diversions: Fun with FRACTRAN

Recently I’ve been learning to use Mathematica, a piece of software I was curious about for a long time.  Luckily my university has a licence for all staff, so I snagged a key as soon as I learned this and have been mucking around with some serious stuff — namely it’s surprisingly good neural network features — and some less serious stuff to get my head around the Wolfram Language.

This weekend I’ve been messing around with FRACTRAN, a fascinating esoteric programming language and model of computation developed by John H Conway, who’s perhaps most famous amongst computer types for inventing the Game of Life cellular automaton.  FRACTRAN is a language in which programs consist entirely of lists of fractions, like so:

primeProg = {17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 
 1/17, 11/13, 13/11, 15/14, 15/2, 55/1};

Now that may seem nonsensical, but bear with me here.  FRACTRAN works with really simple rules; given a list of fractions and an initial input N:

  1. Find the first fraction F in the program listing which becomes an integer when multiplied by N, then replace N by N*F
  2. Repeat until N doesn’t produce any integers when multiplied by any fraction in the program, then halt.

Easy peasy!  So we can write a FRACTRAN interpreter in Mathematica quite easily.  This one outputs each stage of program execution in order to a list called outputFrac, to allow us to manipulate the results later if need be:

fracRunList[fracProg_, input_, steplimit_] := Module[{j, state},
 j = 0;
 state = input;
 outputFrac = {};
 While[j <= steplimit, newProg = state *fracProg;
 integerList = IntegerQ[#] & /@ newProg;
 intSpots = Position[integerList, True];
 AppendTo[outputFrac, state];
 If[Length[intSpots] == 0, Break[]];
 state = newProg[[intSpots[[1, 1]]]]; j++]];

So, when you call this function with fracRunList[{list of fractions}, N, timestep limit], it multiplies N through the list, checks that new list for integer values, appends that value to the list outputFrac, then starts again.  The function will halt either when it reaches the timestep limit you specified, or when no more integers result from multiplying N through the list.

When we run the program above — suspiciously called ‘primeProg’ — with an initial N=2 for 50 steps, we get this:

{2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 
132, 116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 
67375, 79625, 14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 
10780, 12740, 2380, 2184, 408, 152, 92, 380, 230, 950, 575, 2375, 
9625, 11375, 2125, 1950, 1650, 1450, 3850, 4550, 850, 780, 660, 580, 
1540, 1820, 340, 312, 264, 232, 616, 728, 136, 8, 60}

That may look like nonsense, but note that scattered through that list of numbers we have 2, 4, and 8 — which are respectively 2^1, 2^2, and 2^3.  So what PrimeProg does is actually output all the prime numbers, in the form of prime exponents of 2!

We can see this easily if we run a simple filter on the list outputFrac after running the program for 50,000 steps:

findPrimes2[list_] :=
 Log[2, Select[list, IntegerQ[Log[2, #]] &]];

fracRunList[primeProg, 2, 50000]
findPrimes2[outputFrac]

Output: {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}

After 50,000 steps, our clever little list of fractions has produced the first 13 prime numbers!  Theoretically we can run this forever, and produce every prime number.  Although each one takes longer to come out than the last, unsurprisingly, so I don’t recommend it.

Another variation of the prime-finder program I found from the Esolang wiki is more efficient, using only 9 fractions to output prime exponents of 10.  We’ll test it out below, this time filtering the resulting output list for prime exponents of 10:

prime10Short = {3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 
 36/5};

findPrimes10[list_] :=
 Log[10, Select[list, IntegerQ[Log[10, #]] &]];

fracRunList[prime10Short, 10, 50000]
findPrimes10[outputFrac]

Output: {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41}

This prime-finder has managed to dig up 15 primes in 50,000 steps, rather than 13 like the original.

The really remarkable thing about FRACTRAN, though, is that it’s actually Turing-complete — it can in principle calculate anything calculable by any other programming language.  A simple example of a multiplication programme shows off how this works:

multiFrac = {455/33, 11/13, 1/11, 3/7, 11/2, 1/3};

fracRunList[multiFrac, 72, 50]

Output: {72, 396, 5460, 4620, 63700, 53900, 4900, 2100, 900, 4950, 68250, 
57750, 796250, 673750, 61250, 26250, 11250, 61875, 853125, 721875, 
9953125, 8421875, 765625, 328125, 140625, 46875, 15625}

What’s happened here is that we gave our FRACTRAN program a single number that actually represents our two input numbers — in this case 3 and 2 — as a product of prime numbers raised to appropriate powers — 2^3 * 3^2 = 8 * 9 = 72.  FRACTRAN then outputs the result as the power of a different prime — 15,625 = 5^6 = 5^(2 * 3).  A fairly roundabout way to get multiplication done, but it works!

What this shows is that it’s possible to have FRACTRAN programs operate on multiple inputs, so long as those inputs are encoded as products of prime powers.  In fact, we can assign specific primes to be our data registers and use carefully-constructed fractions to operate on those registers, and even construct complicated programs with loops!  As this StackOverflow answer shows, it turns out FRACTRAN is exactly equivalent to a Minsky Register Machine, which have been proven to be Turing-equivalent — hence confirming that FRACTRAN is actually a Turing-complete language.

As a consequence some intrepid folk have built some impressive constructs in FRACTRAN.  One of my favourites is a FRACTRAN interpreter which is itself written in FRACTRAN!  Using just 48 fractions, this program takes as input an encoded FRACTRAN program and initial state, and correctly interprets the program and outputs the result.  Here’s everything you need to try it:

fracInFrac = {5/19, 1558654261983398483185/122130132904968017083, 
 185/1822837804551761449, 4996917562403854655/41, 272365/67, 43/5, 
 43/71, 125173/47, 145915005923554298917151/952809757913927, 
 950886101246622507133/41426511213649, 160585150715989139597/13, 
 8752951/23, 17/43, 17/29, 6409/47, 5/17, 31/53, 17042839/7, 
 1829/41, 59/73, 331639/23, 4307/41, 89/59, 3713/31, 79/83, 
 268837/23, 31/79, 8633/7, 101/97, 68579/11, 9797/13, 9797/47, 
 35/101, 9167/13, 103/107, 1774381/47, 109/103, 109/113, 578899/23, 
 11227/13, 127/109, 127/131, 16637/47, 16637/11, 1114679/61, 2/127, 
 5/2, 3/37};

(* Encode a FRACTRAN program as a base-11 number for input into 
fracInFrac interpreter *)
base2 = 11;
pad2[f_] :=
 Block[{n = IntegerDigits[Numerator[f], base2 - 1],
 d = IntegerDigits[Denominator[f], base2 - 1], len},
 len = Max[Length[n], Length[d]]; n = PadLeft[n, len]; 
 d = PadLeft[d, len]; Flatten[{0, Riffle[n, d], base2 - 1}]];
digits2[progList_] := Join[Flatten[pad2 /@ progList], {base2 - 1}];
encode2[progList_] := FromDigits[Reverse[digits2[progList]], base2];

(* FracInFrac input state encoder function *)

fracInput[fracProg_, init_] := 5*7^init*67^(encode2[fracProg]);

In order to encode our FRACTRAN program into a format the interpreter can understand, we first need to encode the program as a single number.  In this case the encode2 function reverses the list of fractions in the program, then encodes the digits as base-10 numbers within a base-11 number.  Then we need to combine that with our initial state into a single number that we can pass to the interpreter.  We do this using the fracInput function, which gives us a ridiculous huge number that consists of 5 * 7^(initial state) * 67^(encoded program).  In fact, the resulting numbers are far too huge to print here as examples even for the simple adding program (which is just {3/2}!), and Mathematica can’t even cope with encoding larger programs and simply spits out an error.  Changing the encoding to use a smaller prime for the program is possible, but I leave that as an exercise for the reader.

Another intrepid StackOverflow commenter produced a FRACTRAN interpreter for FRACTRAN in 84 fractions, which has a slightly less ginormous program encoding:

fracInFrac3 = {197*103/(2^11*101), 101/103, 103*127/(2*101), 101/103, 
 109/101, 2*23/(197*109), 109/23, 29/109, 197*41*47/(31*59), 
 11^10*53/(127*197), 197/53, 37/197, 7^10*43/(11^10*37), 37/43, 
 59/(37*47), 59/47, 41*61/59, 31*67/(41*61), 61/67, 7*67/(127*61), 
 61/67, 101/71, 73/(127^9*29), 79/(127^2*73), 83/(127*73), 
 89/(2*29), 163/29, 127^11*89/79, 337/83, 2*59/89, 71/61, 
 7*173/(127*163), 163/173, 337*167/163, 347/(31*337), 337/347, 
 151/337, 1/71, 19*179/(3*7*193), 193/179, 157/(7*193), 17*181/193, 
 7*211/(19*181), 181/211, 193/181, 157/193, 223/(7*157), 157/223, 
 281*283/239, 3*257*269/(7*241), 241/269, 263/241, 7*271/(257*263), 
 263/271, 281/263, 241/(17*281), 1/281, 307/(7*283), 283/307, 
 293/283, 71*131/107, 193/(131*151), 227/(19*157), 71*311/227, 
 233/(151*167*311), 151*311/229, 7*317/(19*229), 229/317, 
 239*331/217, 71*313/157, 239*251/(151*167*313), 239*251/(151*313), 
 149/(251*293), 107/(293*331), 137/199, 
 2^100*13^100*353/(5^100*137), 2*13*353/(5*137), 137/353, 349/137, 
 107/349, 5^100*359/(13^100*149), 5*359/(13*149), 149/359, 199/149};

To encode the program, we reverse the order of the fractions in the program, put ’10’ between each numerator and denominator, and encode the whole list as a base-11 number:

(* Encode a FRACTRAN program in reversed base-11 digits *)

baseConvert[frac_] := 
 {Numerator[frac], 10, Denominator[frac], 10};
baseDigits[fracList_] := 
 Most[Flatten[Reverse[Join[baseConvert /@ fracList]]]];
baseEncode[fracCode_] := FromDigits[baseDigits[fracCode], 11];

(* Sample encoding: Simple adding program {3/2} *)
encodedAdder = baseEncode[addProg]

Output: 475

That seems manageable, right?  But then we have to encode the initial state 72, as well, and this program uses the format (3^(state) * 5^(encoded program) * 199)…

(* Complete encoded initial state for FRACTRAN interpreter *)
(* 3^initial_state*5^encoded_program*199 *)

encodeFracProgState[fracList_, init_] := (3^init)*(5^baseEncode[fracList])*199;

(* Sample complete encoding: Adder, initial state 72 *)

encodeFracProgState[addProg, 72]

Output: 4595528627302514457847822534456305637274485006848124607416562426715142
2223431883566346800946031635723355137742896740401730524435178459281271
4997262424758884123382086634982376119146502282302917806400755768226744
1829230852502546067970809133366591936071662069537535458381098407899190
9230824160175285935800563682805991749525746897352823649995912091981153
9351940155029296875

…Yikes.  Well, because I love you guys so much, I tested this out.  I ran the encoded program through the 84-fraction interpreter, and piped the output to a text file which rapidly blew up to 4.8MB of numbers.  The correct answer pops out after 6,030 lines of gibberish and looks like this:

1331690264838856002293720794993649380710435784303038760424759391768076
4462808226237499620786133558911763356798565240461593352120399425752403
5496560518676882088942416619737846495343367625845408913052935028877605
1678370577471585522503962029887317190284834394621170248161337171206903
0172712146158755426661553931885800712601024170227364957005027071924897
2557777777294510307702117543602421742701115006472526481890849420208766
6735678794793784618377685546875

Which is actually the expanded form of:

3^243 * 5^475 * 149

And you’ll note that 3^243, which is also 3^(3^(3+2)), giving us the answer to our original request to add 3 and 2, buried up in the second layer of exponents.  Whew!

Anyway, as you can see it’s easy to get lost in FRACTRAN despite its apparent simplicity.  It’s really interesting to play with, though, and it’s an odd moment when you realise that these simple lists of fractions are actually capable of some remarkable things.  The weekend is nearly over now and I have to prepare for actual work, but perhaps next weekend I’ll return to this and construct a compiler for FRACTRAN, making it possible to write programs in a higher-level language and squish them into FRACTRAN form.

Or I might start fooling around with different nerd stuff instead, who knows?

 

 

 

 

 

 

 

 

 

 

 

Tagged , , , ,

Book now available via SpringerLink

Good news everyone!  Well, maybe not everyone, but at least people who love academic books about agent-based modelling might be happy about this news.

My book is now available, open access (free, in other words), via SpringerLink.  You can download the whole thing as a PDF or an ebook in EPUB format.  The website is mobile-friendly, too, so if you’re slightly mad and want to read this on your phone, you can certainly do so.

You can also download individual chapters, if you want, but I’d recommend *not* doing this; each chapter pretty much builds on the previous one, so you’ll get more out of it if you read the all the chapters in sequence.

Hardcover copies are not yet available, but I’m told they will be soon, and it seems like you can order print-on-demand softcovers via the Springer website now if you feel like it.

Tagged , , , ,

February update

Screen Shot 2018-02-02 at 09.47.08

I’ve just been sent a preview of the cover for my book, now due to be released in early March — so get your pre-orders in now!

Or don’t, it’s open-access and you can just download a PDF for free when it comes out.  I’ll post here again once it releases for real.

In other news:

  • Our team submitted a funding proposal for a cross-disciplinary network focused on the use of agent-based modelling for designing complex public health interventions
  • I contributed to another proposal, part of which will use ABM to study environmental and policy changes that might encourage more people to take up walking and cycling rather than driving
  • We’re working on a position paper for the public health crowd, to clear up some misconceptions and concerns about the use of ABM in health research
  • Another paper is in the works on a free simulation platform under development
  • Last but by no means least, John Bryden and I have a really exciting paper under review at the moment — watch this space!

I’m also excited about our ongoing work modelling social care provision in Scotland — we’ve just hit a major development milestone.  We’re planning to submit a paper on this first stage in March, and follow that up with further development of the model with help from social care experts here in Glasgow and in Stirling.  We’ll soon start producing  detailed documentation for the model — I’ll post some of those details here in the next month or two.

 

Tagged , , ,

Buddhism and Meditation

As some of you are aware, I’ve been suffering with chronic pain for more than three years now.  It’s been an exhausting, distressing and confidence-shattering experience in many ways, and medical science still struggles to find solutions to this problem, so most days the best I can hope for is that things simply stay stable.  I have to accept that it’s quite possible I will never have a day in my life again where I feel totally healthy and pain-free.

In my own case, pain management experts within the NHS have been extolling the virtues of complementary therapies, most particularly mindfulness practices and meditation (with a side-order of yoga).  In the medical context, mindfulness and meditation have proven very successful in their own right, divorced from their original Buddhist context and presented in a Westernised, clinical framework.  Mindfulness has been shown to increase psychological well-being, reduce symptoms of stress, and crucially, reduce pain.

I have a long relationship with Buddhist thought and practice, having discovered both during a period of mental health difficulty as a teenager.  For a number of years after that I maintained an interest in Buddhist meditation and philosophy, practicing meditation regularly and reading thousands of pages of sutras, commentaries and guides to Buddhist thought.  Then, bizarrely, I moved to a country with a rich Buddhist tradition (Japan) and largely fell out of Buddhist practice.

Now that I’ve been reminded of the benefits of these practices I left behind, I’ve jumped back into mindfulness and meditation recently.  For me, while mindfulness has benefits even outside the Buddhist context, its benefits are much more far-reaching when that context is maintained.  Then mindfulness goes far beyond a calming influence, and becomes a means to re-orient your understanding of self, consciousness, and the nature of mental and physical suffering.  It’s also really interesting to read and nerd out on this stuff.

So, this is all a very long way of saying I’ve been reading a lot of Buddhist stuff again and doing daily meditation.  Along the way I’ve been speaking to some people about it, and realised there are some major misconceptions out there about the nature of Buddhism and meditation.  So partly for those who are interested, and partly to put down in words my own understanding and remind myself of areas that require further study, I’ve decided to put together a little guide to the basics of Buddhist thought and hopefully provide you all some interesting stuff to read along the way.

Before I start all that, if you’re interested in practicing mindfulness and meditation, I can highly recommend the book Mindfulness in Plain English by Bhante Gunaratana.  In my opinion it’s the most readable, detailed, and well-organised guide to Buddhist mindfulness practice available.  If you read this book and follow the advice within it, you’ll have all the tools you need to start an effective and comprehensive mindfulness practice in your daily life.

Also, a disclaimer: all of this represents my own understanding of core Buddhist principles and practices.  Don’t take my word as being 100% accurate.  Some of it is heavily simplified, some of it will have my own misconceptions layered in there.  Take it as one guy’s summary and fill out the gaps with more authoritative sources!

———————————————————-

Common Questions about Buddhism and Meditation

Doesn’t Buddhism involve worshipping the Buddha?  I thought you were an atheist.

I am an atheist, and lucky for me, Buddhists do not believe in a creator god.  The Buddha is not a god, he was a human who spent years struggling to understand his place in the world, and eventually achieved enlightenment, and offered the knowledge he gained to the world.  He’s an object of respect and admiration, but not worship as some of us might offer to figures like Jesus Christ — and worship would be somewhat antithetical to the Buddha’s teachings, which encourage us to strive for enlightenment on our own terms, and only follow those teachings which match our own experiences and critical analysis.

Doesn’t Buddhism require belief in a soul, so that reincarnation can work?  Again that seems antithetical to your scientific mindset.

Not at all.  There are three core concepts, the three marks of existence, that define the Buddhist concept of the world: anicca (impermanence); dukkha (suffering); and anatta (not-self).  In short, everything in the universe is subject to decay and eventual destruction (impermanence), our existence is plagued with feelings of unsatisfactoriness and discontent (suffering), and our concept of a defined, eternal ‘self’ is an illusion (not-self).

To unpack the ‘not-self’ concept a bit, Buddhists believe that we are not defined, separate individuals with a unique essence, or soul.  I, for example, was once a baby — I was tiny, looked really different, had no beard, and my brain couldn’t even properly encode memories.  Yet I still say that baby is ‘me’, despite having a different physical and mental existence in every aspect.  I have an innate tendency to believe that this highly changeable and temporary existence is somehow united by some unique, ineffable essence that makes me, me.  For some of us that essence is an eternal, non-physical soul.

Buddhists deny this, and say that this concept of self is an illusion.  Our existence is actually an amalgam of the five skandhas, or five aggregates: form (matter), or rupa; sensations (feelings), or vidana; perceptions, or samjna; mental activity, or sankhara; and consciousness, or vijnana.  These five aggregates constitute our experience of physical and mental existence, and create the illusion of self to which we cling.  Part of the Buddhist path to liberation is to realise that our existence is a consequence of the constant interaction of these five changeable aggregates, and further, that these aggregates are without fundamental independent existence.

So, the idea of an eternal, unchangeable ‘soul’ is actually incompatible with Buddhist thought.  The sense of self we have is the direct result of constantly changing interactions with our surrounding reality.  There is no eternal soul, and further there is no separate ‘spirit realm’ in which it could exist.

It’s worth noting that the Buddhist concept of these aggregates is broken down even further into extensive detail, but I won’t go into this here.  It’s extremely interesting though so I may do that — again for self-study reasons as well — in a later post.

Wait, hang on a minute — how does that work, don’t Buddhists believe in reincarnation?  How can we reincarnate if we don’t have souls?

No, they don’t.  Buddhists believe in a cycle of life, death and rebirth, called samsara.  Rebirth is not the same thing as reincarnation.  Reincarnation is something we see in other religions, wherein our eternal soul transfers into a new body after death and experiences a continued existence in another physical form.

Buddhism, as explained above, doesn’t accept the idea of a soul.  Buddhists believe that when we die, we die — our experience ceases completely, nothing is transferred beyond death.  When I die, the being known as Eric ceases to exist, my consciousness and self-identity as Eric dissipates, and my body becomes worm food.

However, that’s not the end of the story.  This is where karma, or kamma to stick to the Pali versions of terms I’ve been using, comes into the frame.  Our actions in each existence cause positive or negative kamma, not as some sort of supernatural judge of good or ill will in our beliefs and actions, but as a physical cause-and-effect relationship — if I do a good/bad thing, good/bad results will inevitably develop later.

It is this kamma that continues beyond death.  The Buddhist belief, at its core, is that once we die, the consequence of our kamma is that another birth takes place, and our little bundle of karmic pluses and minuses determines what kind of birth that will be.  This cycle is inevitable, and eternal, unless we are able to break free of this cycle via liberating ourselves from clinging to this world and become enlightened.

This cycle can be hard to conceptualise, so it’s often described using an analogy.  Imagine my life as a burning candle, with the flame representing my consciousness.  Right as the candle is running out, I use that flame to light the next candle.  The next candle lights up right as the old one burns out.  So my consciousness directly causes another, subsequent consciousness to arise in the next life, but my original consciousness burns out — the new one is a different consciousness, existing in a different body (which may or may not be human).  Kamma is what lifts the old candle to the new and causes the new one to light up.

Now there’s obviously a hell of a lot more to kamma, death and rebirth, but that’s the gist of it.  Rebirth is probably the hardest thing for Western Buddhists to get to grips with, and many people (including myself) choose to conceptualise rebirth largely as a reframing of the physical facts of death — so upon death, the matter of my body will inevitably become part of the environment and provide materials and energy for future beings, so in that sense I am ‘reborn’ and contribute to the arising of some future sentient being(s), and this then keeps happening over and over.  That framing is totally fine for many people, and still works alongside the importance of Buddhist ethics, meditational practice and kamma, so the whole edifice hangs together well enough.

Some then later go on to accept the whole picture of life, death and rebirth; personally I’m more willing to buy that picture than anything hinging on eternal souls, infinite punishments in Hell after death for finite crimes in this world, or various other things.  Buddhist rebirth also still accepts death as a real cessation of existence; only kamma continues to the next life, not the same consciousness and there’s no essential essence that transfers over.  But still it’s a pretty major leap.  Most people I’ve encountered online or elsewhere who properly believe in rebirth as Westerners came to that conclusion after years of meditative contemplation, so who knows, I may also decide such a thing a decade from now.

As a point of clarification — yes, the Buddha does say upon reaching enlightenment that he can see all his previous lives.  However, this is not because of direct recollection of those experiences through an eternal soul or directly transferred consciousness, but because he at that point attained perfect understanding of kamma and thus his own karmic history.  So he was able to see all that as an unfolding of karmic cause and effect across unimaginable aeons of time.  That’s the idea as I understand it, anyway.

And for the hell of it, an additional answer to an unasked question — what do I mean by ‘aeons’?  Well, Buddhism talks about a truly immense units of time called a kalpa.  How long is a kalpa?  Imagine a huge cube of granite, measuring 16 miles on a side.  Now imagine every 100 years, a man comes along and gently brushes a silk handkerchief against that mountain of rock.  A kalpa is how long it would take for the mountain to be completely worn away by that bit of silk.  So when Buddhists talk about long cycles of death and rebirth, they’re talking about really really long cycles.

Okay fine, so reincarnation isn’t a thing, it’s rebirth.  How do you explain the Dalai Lama, isn’t he supposed to be a reincarnation?

Well, we’re getting to the limitations of my knowledge here, but technically the Dalai Lama is not a reincarnation but is an emanation, specifically the 14th emanation of Avalokitesvara (Chenrezig in Tibetan, Kannon in Japanese Buddhism), the boddhisattva of compassion.  There’s a lot to explain here, much of which I don’t fully understand, so I won’t attempt to do all that.  I’ll do a bit of explanation, but bear in mind some of the details may be oversimplified or a bit ‘off’.

The gist of it is that Avalokitesvara is an enlightened being that can ’emanate’ into different physical existences.  So each Dalai Lama is essentially a physical manifestation of an enlightened Buddha, who put a bit of themselves into the Dalai Lama to hang about on the Earth and teach us Buddhist things.  After a Dalai Lama dies, the next one appears somewhere else, again as a manifestation of the same enlightened being.

This is why each new Dalai Lama is tested to see if they recall certain objects, places and people from their last incarnation — the idea as I understand it from the Dalai Lama’s own statements is that as an emanation of a higher-level being, that higher-level mindstream (another complicated Tibetan Buddhist concept) retains knowledge of experiences from their last go-round.  So the Dalai Lama’s existence is still compatible with Buddhist concepts of rebirth and not-self — he is not literally the same soul reincarnating around the place, but a manifestation of a larger being that creates different individuals in each emanation.  That larger being retains knowledge of the karmic processes of cause and effect that link each emanation, allowing the Dalai Lamas to remember things from previous incarnations.

Does that really make sense?  For me it’s pretty hard to swallow, perhaps because I’m viewing it from outside its original Tibetan context, where incarnate Lamas (tulku) are a major thing and have been for centuries.  Personally, viewed either way it doesn’t affect my opinion of the Dalai Lama himself, who I’ve had the great fortune to see speak in person at length for several days back in 2004.  He’s quite clearly an exceptional human being, and when he speaks about compassion I very much trust what he has to say, whether he’s an emanation of Avalokitesvara or not; his behaviour, knowledge and practice speak for themselves, independent of any other considerations.

OK fine, so I get that there’s no God, no soul, no self, and suffering is everywhere and we’re constantly reborn into that suffering forever, but honestly that sounds awful.  If all that’s true, then what’s the point of anything?  If we’re all doomed to just suffer and die over and over again, why bother with any actions at all?

This is a very good question, and a really common one.  It’s very easy to misconstrue Buddhist thought as being fundamentally nihilist.  The self is not real, there is no God, death is for-real death for the most part, and suffering is all we get.

But the Buddha very explicitly, and repeatedly, denies this interpretation.  He frames this debate as the idea that reality is absolute and real against nihilism, in which nothing exists.  Buddha’s way is called the Middle Way because it embraces neither sensual indulgence nor strict asceticism, and likewise here it straddles two extremes.  While everything is always changing and dependent on external causes and conditions to exist at all, that does not mean nothing exists; instead, it means that things — including ourselves — do not have an inherent, independent existence.

Imagine, for example, the chair you’re sitting on right now.  That chair was not always a chair, but was once bits of wood, which were once part of a tree, which grew out of some seeds, and so on.  The Buddhist might say that the chair is thus not an absolute, independently existent thing, but is instead the result of various causes and conditions that lead to its current existence as a chair.  What we call a chair is a product of conceptual thought, not absolute reality, because actually chairs are all differing composites of various other things and the events that caused them to exist.

Crucially, however, that does not mean the chair or the bits of wood or whatever don’t exist at all; it just means that we should avoid clinging to the chair as an independently-existing thing and instead accept it as a fundamentally impermanent agglomeration that will eventually decay and cease to exist in its present form.  So, things still exist in Buddhist thought, but are empty — not of existence as a whole, but of independent, absolute existence.  In relative terms — everyday terms — that chair still exists, as do we, and the causes and consequences of our actions every day.

To take it even further, because we ourselves are not-selves and are composed of the five skandhas roaming about the place, we are also interdependent on everything around us.  So in that sense, not-self and emptiness concepts mean we are less separate from the world than we are in traditions that hold we have a non-physical, eternal soul.  My existence is dependent upon, and intermingled with, the causes and conditions that also make up everything else, so in that context it’s extremely important I be mindful of my actions as I am also not absolutely existent independently, but am part and parcel of the swirling mess that is samsara.

OK right — I kind of get it.  Or maybe not.  But if I take it as read that stuff still exists, and things I do actually matter, then what do I do to avoid suffering?  If suffering is inevitable, as it sounds like it is, then what can I possibly do to not be miserable?

Now we reach the core of Buddhist actions, rather than just philosophising.  In his very first discourse after reaching enlightenment, Buddha laid down the core of Buddhist practice: the Four Noble Truths, and the Noble Eightfold Path.  The Four Noble Truths are (roughly) as follows:

  1. The Truth of Suffering — there is suffering (dukkha)and it is everywhere.
  2. The Truth of the Origin of Suffering — suffering comes from attachment, or grasping/clinging to sense-pleasures, desire for existence, or desire for non-existence.
  3. The Truth of the Cessation of Suffering — suffering can cease when we give up these attachments.
  4. The Truth of the Way Leading to the Cessation of Suffering — the way to end suffering is to follow the Noble Eightfold Path.

So all is not lost — yes, suffering is everywhere, and now we know that fundamentally suffering arises due to our desire to cling to aspects of existence even when existence is ultimately impermanent and constantly changing.  But we can end our suffering through the Noble Eightfold Path, which the Buddha conveniently lays down shortly after this:

  1. Right View — basically, accepting the Four Noble Truths, and believing that there’s a way out of all this.
  2. Right Resolve — renouncing material attachments and devoting oneself to a more contemplative life.
  3. Right Speech — don’t lie, don’t speak ill of other people, and don’t say things that are not of benefit to others.
  4. Right Action — don’t kill people, no stealing, no sexual misconduct.
  5. Right Livelihood — make your living without harming other sentient beings or doing other bad things.
  6. Right Effort — exert your will to avoid unwholesome states of mind that spawn ill will, desires for sense-pleasures, etc.
  7. Right Mindfulness — cultivate awareness of existence as being impermanent, full of suffering, and devoid of self (anicca, dukkha, anatta).
  8. Right Concentration — develop a ‘one-pointedness of mind’, or the centring of consciousness on a single object, without loss of focus.

So the way to end suffering is to lead an ethical life, refraining from absorbing ourselves in materialistic sense-pleasures and from causing harm to sentient beings, while also cultivating a concentrated, mindful consciousness.  In so doing we improve our kamma, reduce our attachment to the impermanent world around us, and develop experiential insight into the nature of mind and reality.  Eventually, if we do well enough, we can break the endless cycle of samsara and enter nirvana (nibbana), and we no longer suffer and instead experience unimaginable bliss.

I feel it’s important to note again here that in the context of the Buddha’s original sutras — called the Pali Canon and the core texts of Theravada Buddhism — the Buddha can’t help you with all this, as he’s not an interfering Christ figure or God.  Praying to him won’t do anything.  Ultimately the responsibility for your enlightenment — or lack thereof — rests with yourself and your own practices.  There are no supernatural authorities to reward or punish you; instead you simply reap the results of your good or bad actions through kamma.

This is not necessarily the case in Mahayana or Vajrayana Buddhism, where Buddhas and Boddhisattvas are seen as enlightened beings that do in fact try to help the rest of us mooks achieve enlightenment.  But even in the most ritual-laden Tibetan practices, still these ‘deities’ are seen as ultimately symbolic of qualities we wish to cultivate in ourselves, rather than as real gods/goddesses or beings that can intercede directly in our affairs.

Wow, finally — that Right Mindfulness/Right Concentration stuff sounds like meditation to me, at last!  You started all this off with that and haven’t given me any details at all yet.  So get to it.

Sorry about that.  I like talking about Buddhist philosophy so I got a bit caught up.

Right, so from the start here I should say I’m again focusing on the Pali Canon and the original sutras from the Buddha.  So essentially I’m talking about meditation as practiced in Theravada Buddhism, which are practices also core to every Buddhist tradition.  There’s tons of other types of meditation in Mahayana and Vajrayana (Tibetan) Buddhism, but they differ widely and would make this post even more ridiculously long than it already is.

Right Mindfulness in the context of the Noble Eightfold Path can be cultivated via what we now call insight meditation (vipassana).  Insight meditation is about developing awareness in ourselves of the three marks of existence: impermanence, suffering, and non-self.  The way this is done is deceptively simple, and it all starts with watching the breath.

This means that we sit in a comfortable, stable posture, and simply observe our breathing as it rises and falls.  Other thoughts will rise constantly, but rather than attend to them or explore them, we simply note their arrival and return to watching our breathing.  Physical pains may develop as we sit as well, and we do much the same: note the sensation, observe it as it rises and falls, don’t become involved, and allow it to pass.  As we do this over weeks, months and years, eventually we find it easier to redirect our attention away from the various thoughts and sensations that come and go, and we begin to understand that all mental phenomena — and indeed all phenomena — are like this.  Things come, and they go, and if we gently allow that to happen and return to focusing on the breath, we likewise train our minds to stop attending so much to impermanent, momentary thoughts and sensations.  In this way we develop mindfulness — a clear awareness of impermanence (anicca), direct experience of the way our mind clings and thus suffers (dukkha), and knowledge of not-self as we see our mind as it really is, composed of a mess of thoughts and sensations with no permanency or independent existence (anatta).

Now, having success with vipassana also requires that we develop concentration, or the ability to focus on a single object within our minds.  This is the other main type of Buddhist meditation, called samatha (sometimes translated as ‘calm abiding’).  In samatha, conveniently, we also can use the breath as an object of focus, but instead of trying to develop insight into the arising and passing away of phenomena and observing this process, we focus on developing single-pointed concentration on the breath.  If other thoughts arise, we note them, immediately drop them, and return to the breath.  Over time, we can maintain this focus longer and longer, and enter states of deepening concentration known as the four jhanas.  I won’t go into these much but will just quote the Buddha here:

[i] Here, the monk, detached from sense-desires, detached from unwholesome states, enters and remains in the first jhana, in which there is applied and sustained thinking, together with joy and pleasure born of detachment;
[ii] And through the subsiding of applied and sustained thinking, with the gaining of inner stillness and oneness of mind, he enters and remains in the second jhana, which is without applied and sustained thinking, and in which there are joy and pleasure born of concentration;
[iii] And through the fading of joy, he remains equanimous, mindful and aware, and he experiences in his body the pleasure of which the Noble Ones say: “equanimous, mindful and dwelling in pleasure”, and thus he enters and remains in the third jhana;
[iv] And through the giving up of pleasure and pain, and through the previous disappearance of happiness and sadness, he enters and remains in the fourth jhana, which is without pleasure and pain, and in which there is pure equanimity and mindfulness.

Buddhism being Buddhism, of course, this is far from the end of the story.  There are four more jhanas beyond those, and the whole system is described differently in some Mahayana traditions and in Tibetan literature, so there’s tons more to discover on both main varieties of meditation.

Now these two meditation methods may seem rather closely related, or even hard to distinguish, and you’d be quite right — in fact in the early Buddhist canon the two seem to be intimately connected.  There’s a lot to talk about on this topic, which I won’t bore you with but instead will direct you to this free book on the close relationship between samatha and vipassanaA Swift Pair of Messengers.  Note however that this book assumes significant familiarity with meditational practices and Buddhist terminology, so it’s not recommended for beginners.

If you want to start practicing vipassana, again I’d direct you to Mindfulness in Plain English which is entirely about this kind of mindfulness meditation and is extremely clear and good.  Helpfully, the same author wrote a follow-up about samatha and the jhanas called Beyond Mindfulness in Plain English, which is equally excellent.

Right, so there are two main kinds of meditation, closely related but with different ultimate goals.  But aren’t they both, ultimately, about withdrawing from the world?  In meditation are we not just hiding from reality?

No, completely the opposite.  Mindfulness and meditation are about creating awareness of the world, how it functions and how our minds perceive it and relate to it.  In deep states of meditation, one understands how our normal states of mind are constantly polluted with unwanted thoughts, desires, and constant noise.  Buddhists call this the ‘monkey mind’ — the tendency of our minds to leap heedlessly from thought to thought, like monkeys cavorting in the jungle canopy.  We never settle, never allow ourselves to perceive anything in and of itself, but instead coat everything with conceptual thought and wallow in endless diversions.

When you start meditating, it won’t be long before you see this ‘monkey mind’ in action and realise that you are completely insane in a way you’ve never noticed before.  Focusing on the breath sounds simple, and turns out to be almost impossible.  Our brains leap from tree to tree, never allowing us a moment’s peace.  You might snap back to the breath and realise you’ve been stuck in a sexual fantasy for the last five minutes without even remembering how you got there.  Or you may try to count your breaths and never get past three as the distractions come so thick and so fast.  You may even discover — this is my problem — that you can have two or three independent, completely fleshed-out trains of thought going simultaneously, and it all seems like an unstoppable cacophony.

But it’s important to be gentle with yourself, and simply allow these things to pass away, and say to yourself ‘OK I was distracted, that’s fine — now back to the breath’.  The simple act of redirecting your attention back to the meditation object is mindfulness!  You are being aware of your mind’s constant straying, and consciously moving back to moment-to-moment experience.  Keep doing that, keep redirecting yourself, and eventually that redirection will become easier and easier to achieve.  Each time you do it, you’re retraining your mind and developing a new habit: instead of getting lost in conceptual thought, retreating from the world and the realities of mind and life, you will redirect yourself back to experience.  Eventually, meditation will allow you to carry over this training into your everyday life, and your awareness of every moment of existence is enhanced.

So, ultimately meditation is not about retreating from reality.  Meditation is about being present in reality in a way we normally never are.  We train ourselves to experience moment-to-moment existence as it really is, observe the comings and goings of our thoughts and the world around us, and become more aware of our reality than before.

OK that sounds a bit more positive.  But what about compassion and loving-kindness and all the stuff the Dalai Lama talks about?  This all seems really inwardly-focused.

Well, I wouldn’t necessarily agree with that — cultivating insight in one’s own mind naturally helps us to perceive the impermanence and suffering present in the world for everyone else, too.  As we become aware of our own crazy ‘monkey minds’ we understand how everyone suffers the same thing, and over time that helps us build compassion.

But yes, there are meditation methods specifically oriented around metta, or loving-kindness.  This is a Buddhist vision of compassion in which we experience pure, unconditional kindness toward all sentient beings; it’s often described as similar to the love a mother feels for her child.  In developing metta within ourselves, we attempt to give that same love to any and all sentient beings on Earth, whether they are friends, enemies, business competitors, or whatever.  Tibetan Buddhists like to say that, in all the hugely long kalpas of the universe’s history, all beings have at some point been our mother, so we should treat them with the same unconditional love and respect we do for our current mothers.

I’m truly becoming a broken record at this point, but our good friend Bhante Gunaratana wrote another helpful book on metta meditation, which again I highly recommend: Loving-Kindness in Plain English: The Practice of Metta.  Again this is well worth picking up if you want a readable, approachable introduction to metta.

In essence, this kind of practice revolves around entering a calm, meditative state, and then beginning to imagine you are offering pure love and compassion to others, but always starting with yourself.  This can take different forms depending on the practitioner; you may mentally recite a series of well-wishing phrases to yourself, then to a close friend, then your whole family, then your enemies, then to the entire world, for example.  Or it may involve visualisations, like fondly remembering a moment of pure compassion and then imagining that radiating outward from your body to encompass the entire planet.  However you do it, the idea is to bring that genuine feeling of compassion into your mind, then imagine giving that out to the world.  Over time, this practice trains your mind to offer compassion as your default response to other people.

One kind of metta meditation I particularly like is tonglen, which is a Tibetan practice.  Tonglen, like many Tibetan practices, centres on visualisations which is a method that I find easier to focus on.  Again there are many variations, but a common method of tonglen is to imagine your own suffering as piping hot black smoke emanating your body and mind.  As you breathe in a deep breath, that black smoke enters your body and is transformed into cool, clear vapour.  Do this a few times, then imagine a wider group of people, like friends or family, and again take all their suffering into your lungs, and breathe out only cool, clear vapour.  Then you can expand further and encompass the suffering of all sentient beings.  In this way, tonglen is meant to help us face suffering in ourselves and others, and be willing to take it into ourselves and offer something positive in return.  Tibetans particularly endorse this practice for helping us deal with ill health, or even terminal illness in ourselves or others.  In a way it helps us ‘toughen up’ and develop the mental strength to absorb bad things selflessly and compassionately.  If our dearest friend is dying, we might do tonglen while imagining their terrible situation, in order to build our strength so we can face it with them.

Metta is a very positive meditation experience for most people, and in my experience can help us be more compassionate toward ourselves as well as others.  Some might find it easier to get started with than vipassana or samatha, as well, since it has a more emotional, everyday focus.

OK great, thanks for that.  That’s quite enough for now.  Why did you write so much of this, anyway?

I felt maybe someone might find it interesting, I guess, but mainly it’s for me.  Buddhism is complex and studying it alone is difficult, so I felt the urge to get these core ideas down somewhere for my future reference.  As time passes and I get some more structured Buddhist experience and tuition, I’ll come back to this and adjust anything that doesn’t convey things well or introduces oversimplifications or mistakes.  Eventually I’ll probably write further posts in the future exploring some more detailed aspects of Buddhist thought.

In any case, I hope someone found this interesting, and perhaps even might be inspired to try some mindfulness/meditation practice.  As I said, even divorced from the Buddhist context these practices are often very helpful for people.  And if you try them and do find Buddhist philosophy intriguing, I hope this gives you a good idea of the basics.

So let’s say I read this and I do find it interesting, where do I go from here?

As I mentioned above I’ve focused on core ideas from the Pali Canon, the Buddha’s original teachings and the core texts of the Theravada Buddhist tradition.  This text alone is rather huge — you can find authoritative, complete translations by Bhikku Bodhi in hardcover in five exceedingly large volumes (one of them exceeds 2000 pages!).  There’s a ton to study there for a start.  If you want a great introduction to the Pali sutras with insightful commentary and a reasonable page count, pick up In the Buddha’s Words, also by Bhikku Bodhi.  If you decide to get deep into sutra study, you can follow Bhikku Bodhi’s extremely thorough lectures on all the Middle-Length Discourses here.

Update 29/12/17: For a bit more challenging reading on Theravada, check out this thorough translation of the Visuddimagga, The Path of Purification, in PDF format (853 pages!).  This is an extremely in-depth meditation manual and explanation of the Abhidhamma, often referred to as the core of ‘Buddhist Psychology’.  Highly recommended for philosophers, but it helps to have read the Pali Canon first.  If you’re feeling brave, throw in the Vimuttimagga, another manual on the Abhidhamma, available as a 433-page PDF and in numerous other formats.  Finally, if you’re feeling experienced enough in vipassana to tackle an 800+ page manual on the subject that digs deeply into the Pali Canon and related commentaries, you can try A Manual on Insight Meditation.

Beyond Theravada, there’s the Mahayana tradition, the ‘Greater Vehicle’, which embraces later teachings that focus much more on the ideal of the boddhisattva, or someone who reaches enlightenment but delays entering nirvana to help other sentient beings end their suffering.  Famous sutras to read in this tradition include the Heart Sutra, the Diamond Sutra and the Lotus Sutra.  The Lotus Sutra in particular presents a pretty major reconceptualisation of the Buddha(s), and is rather huge to boot, so should keep you busy for awhile, particularly if you dig into the nearly endless commentaries.  If you want to be a completist you can read English versions of the eighty-five volumes (!) of the Taisho Tripitaka.  For more approachable summaries of what Mahayana is about, Thich Nhat Hanh offers a well-written but still dense summary of his view on the tradition in his book The Heart of the Buddha’s Teaching.  The Dalai Lama’s books also cover some key concepts of the Mahayana tradition, particularly loving-kindness/metta.

Zen Buddhism is a Mahayana tradition, and probably one of Japan’s most famous exports.  It’s also the most popular form of Buddhism in the West.  Zen is known for its intense focus on zazen (sitting meditation), some rather crazy Zen masters, and mind-twisting koans that challenge the eager student’s perceptions of dharma.  If you want to read a classic of Zen thought, check out Dogen’s Shobogenzo, which is huge and dense but considered a masterpiece and the central text for Soto Zen.  For a more accessible intro to Zen, The Three Pillars of Zen is probably the best and most thorough.

Update 29/12/17:  Shasta Abbey Buddhist Monastery offers free PDFs of a number of books on Soto Zen practice here.  The page is helpfully laid out and suggests which books are best for beginners and for advanced practitioners.  The beginner books I’ve had a look at thus far (Zen is Eternal Life, Roar of the Tigress I, Serene Reflection Meditation) all seem to offer extensive introductions to both Soto Zen beliefs and practices, so do take advantage of these if you want a free intro to Zen thought.

After Mahayana comes Vajrayana, Tibet’s unique mixture of Mahayana Buddhism and yoga tantra.  Tantra came to Tibet back in the 8th century or so and melded with Mahayana practices and native Tibetan Bon shamanistic practices to produce a ritual-heavy esoteric tradition, characterised by heavy use of mantras, tons of ritual objects, and lengthy, complex tantric practices featuring detailed visualisations.  Vajrayana can be tough to get a grip on as it’s an esoteric tradition, meaning practitioners aren’t really supposed to talk about the tantric practices with non-practitioners, and you won’t normally be taught any of them unless you’ve received an initiation from a lama.  In order to be initiated you may be asked to complete the ngondro preliminary practices, which consist of things like 100,000 prostrations, 100,000 mantra repetitions, and 100,000 of other stuff besides, although from what I understand you can sometimes start with tantra immediately once you start doing ngondro.

However, you can get a great historical summary of Tibetan Buddhism and a detailed survey of practices in the four major Tibetan traditions in Introduction to Tibetan Buddhism by John Powers.  Tibetan Buddhism is also gaining lots of Western adherents these days, largely thanks to the global adoration for the Dalai Lama, so various cities around the US and Europe actually have proper Tibetan monasteries now.  Like any Buddhist group they’ll be more than happy to have you join in, so if you read Powers’ book and find it interesting, look up your local Tibetan group, ring them up and ask to join a meditation or puja.  Some Tibetan sects also offer teachings online, or even tantric initiations/empowerments via webcam.

That basic idea works for any tradition, really — if you like what you read and want to try meditation under proper instruction and with encouragement from a group, find one in your area and give them a ring.  Just be careful to mind how you go, as some unscrupulous types do take advantage of new maybe-Buddhists seeking answers and try to suck them into some cultish stuff (looking at you, New Kadampa Tradition and Diamond Way Buddhism — don’t join these folks).  Remember that Buddhist Dharma teachings should be offered free or at cost, and Buddhists aren’t really into converting people and should welcome you to just sit and meditate in peace, whether you’re interested in Buddhist practices or not.  Retreats might cost more money, generally to cover accommodation and food, and the attendance of the teacher who may be travelling quite some distance.

A few things to remember, if you do go to a group — if you borrow or are given any Buddhist literature while you’re there, don’t leave it on the floor, step over it, or put things on top of it, this is disrespectful.  Put it on a table or shelf with nothing resting on top of it.  In Tibetan practices, don’t point your feet towards the altar or the lama either — be mindful of this if you need to shift positions while meditating, for example.  And of course, try not to disturb anyone who’s meditating, and please turn off your phone!

If you ultimately decide you want to be a Buddhist and do something ‘proper’ to mark that commitment, you can do what’s called ‘taking refuge’.  In doing this you pledge yourself to take refuge in the Three Jewels — the Buddha, the dharma (the Buddha’s teachings), and the sangha (the monastic community).  Most traditions will have some kind of ceremony for this.  This means you decide to trust that you can reach enlightenment as the Buddha did; that you understand the Four Noble Truths and will follow the Noble Eightfold Path; and that you will trust in those already following that path.  As usual, if you do this and then don’t practice or fall out of Buddhism, there aren’t any supernatural judgments awaiting you — it’s up to you to make good on that promise, or not.

It’s worth noting that major Buddhist figures like Thich Nhat Hanh and the Dalai Lama have stressed that it’s not really important to ‘convert’ to Buddhism.  You’re a Buddhist once you start following Buddhist practices and teachings, you don’t have to prove that to anyone, since no god or gods are watching or judging you anyway.  You can even be a Buddhist while following other religions, though bear in mind some fundamental Buddhist concepts are quite at odds with certain religions (might be hard to still be a Christian if you don’t believe in a creator God or an eternal soul, for example).

Anyway, that’s more than enough for now.  If any of you decide to try meditation, good luck, and if any of the Buddhist philosophy stuff appeals to you, I hope you find some of these links and books interesting.

Tagged , ,