The Beauty of Go

I'm a casual chess player, as you might have guessed from my first gemlog post. I started playing chess as a child the same way quite many people do: I thought of my grandpa as the ultimate final boss of chess. At a later age I got a few times to try out Go in different events. I thought it was an interesting game, but sticked to chess as that was the game I knew. Now that I have started playing Go for myself I have found out that - even though I'm still clearly better at chess than at Go - it is in a certain way more beautiful than chess.

The rules of Go are very simple and minimal compared to chess. I learned the rules of Go simply by reading Wikipedia. When you compare the articles for the rules of chess and go, it's easy to notice that while the basic rules of chess need a whole section with subsections containing multiple paragraphs each, the bare minimum Go rules need just 9 rules as a list, maybe one sentence each (except for the fifth one, which is almost twice the length any other line, which reminds me of the Parallel Postulate in Euclidean geometry! Coincidence?).

Even though the rules of Go are simpler than the rules of chess, games of Go are far from simple. Even on the smallest common Go board, 9x9, there are 81 possible initial moves. The amount of possible initial moves in chess is 12, by contrast: eight for the pawns and two for each horse. This means that openings in Go are less regular and opening theory doesn't have an as big role because of that. The reduced amount of opening theory sparkles more creativity - that's why the Fischer random chess was developed! [1]

Assume the width of a Go board to be `w`. As the game goes on, Go has `(w²)!` possible games if we assume that stones are not played in places where captures have already happened and ignore passes. This translates to approximately 6e120, 4e304 and 1e768 possible games for the most popular 9x9, 13x13 and 19x19 boards respectively. In contrast, Claude Shannon has approximated the number of possible chess games to be in the league of 1e120, which is in light of these calculations just about in the ballpark of Go games played with the smallest frequently used board. Go is indeed generally considered to be computationally more complex than chess, which is certainly part of the reason Go was conquered almost twenty years after chess. [2]

Reasoning in Go and chess are quite different. Chess pieces seem to move in a natural way that's easy to argue about. It's easy to think "My opponent might next move there and then queen takes and takes, takes, takes, check, takes...". In one sense it is more crude compared to trying to find the optimal place to put your stone in Go. Go's open board leads to more strategical pondering. Successful play requires intuition about how different parts of the board may evolve and connect many moves in the future.

Tactics have also their place luckily, for example in different life and death situations. An unexpected placement of a stone is kind of more prone to lead to deadly outcomes such as in many tesuji [3], which invites the player to think out of the box such as when searching for a brilliant move in chess. Obviously both games have brilliance - fun has been optimised out of both long since, but I haven't done it myself for Go yet.

As an interesting side note, the difference between chess and Go somehow resembles a difference between Western and Asian culture. We often think in tactically efficient quarters and go for short-term results meanwhile Japanese businesses plan for centuries onward [4, 5] and China makes strategically planned mobile apps to cause brainrot in the west.

It is amazing how so complex patterns can arise from very simple rules. Go has got nine rules (at simplest) and still it is probably the most complex commonly played board game. It's not hard to get fascinated just by the beautiful stone patterns that arise from clever (or even not so clever) play. The way this complexity, strategy, tactics and beautiful patterns arise from simple rules reminds me of mathematics and especially Conways Game of Life [6, 7]. It feels very coincidental but even more fitting that Go has got *games of life* and death.

[1] Fischer random chess on Wikipedia

[2] AlphaGo vs. Lee Sedol on Wikipedia

[3] Tesuji at senseis.xmp.net

[4] A podcast in Finnish about Japanese businesses

[5] Nishiyama Onsen Keiunkan on Wikipedia

[6] Conways Game of Life on Wikipedia

[7] Play game of life online at playgameoflife.com