8.7 KiB
Go
WIP
This article is about the game of go, for programming language see golang.
{ I am still learning the beautiful game of go, please excuse potential unintentional errors here. ~drummyfish }
Go is an old two-player board game that originated in Asia, one of the most beautiful, elegant, deep and popular games of this type in history, whose significance can be compared to that of chess, despite it largely remaining widely popular only in Asia. There however, especially in Japan, go is pretty big, it appears a lot in anime etc.
{ There is a nice site hosting everything related to go: Sensei's Library at https://senseis.xmp.net/. ~drummyfish }
Compared to chess the rules of go are much more simple -- which is part of the game's beauty (see easy to learn, hard to master) -- though the emergent complexity of those few rules is grandiose; so much so that to play the game well may be even harder than to play chess, as there are many more possibilities and mere calculation is not enough to be strong, one needs to develop a strong intuition; this is also the reason why it took 20 more years for computers to beat the best humans in go than in chess. Many say that go is yet deeper than chess and that it offers a unique experience that can't be found anywhere else. The spirit of go is also more zen-like and peaceful: while chess simulates war (something more aligned with western mentality), go is more about dividing territory, one could even see it not as a battle but rather a creation of beautiful patterns (something better aligned with eastern mentality).
From LRS point of view go is one of the best games ever, for similar reasons to chess (it's highly free, suckless, cheap, not owned by anyone, fun, mathematically deep, nice for programming while the game itself doesn't even require a computer etc.) plus yet greater simplicity and beauty.
TODO: rating, programming, stats, programs and sites for playing, 4x4 solved variant, ...
Rules
The rules of go vary a bit more than those of chess, they are not as much unified, but usually the details don't play as much of a role because e.g. different scoring systems still mostly result in the same outcome of games. Here we'll describe possibly the most common rule set.
The game's goal is basically to surround a bigger territory than the enemy player. The formal rules are pretty simple, though their implications are very complex.
Go is played by a black and white player, black plays first (unlike in chess) and then both players take turns placing stones of one's own color on squares -- a square is the INTERSECTION of the lines on the board, NOT the place between them. The stones are all the same (there are no different types of stones like in chess) and they cannot move; once a stone is placed, it stays on its position until the end of the game, or until it is captured by the enemy player. The board size is 19x19, but for for students and quick games 13x13 and 9x9 boards are also used. As black plays first, he has a slight advantage; for this white gets bonus points at the end of the game, so called komi, which is usually set to be 6.5 points (the half point eliminates the possibility of a draw). Komi may differ depending on board size or a specific scoring systems.
Any player can pass on his move, i.e. making a move isn't mandatory. However you basically always want to make a move, you one only passes when he feels there is nothing more to be gained and the game should end. If both player pass consecutively, the game ends.
The game considers 4-neighborhoods, NOT 8-neighborhood, i.e. squares that don't lie on board edges have 4 neighbors: up, right, bottom and left; diagonal squares are NOT neighbors.
Capturing: a player can capture a group of connected (through 4-neighborhoods) enemy player's stones by completely surrounding them, or more precisely by taking away all so called liberties of that group -- liberty is an empty square that's immediately neighboring with the group (note that liberties may lie even inside the group). If a player places his stone so that it removes the enemy group's last liberty, then the group is removed from the board and all its stones are taken as captured. It is possible to capture stones by a move that would otherwise be forbidden as suicide, if after the removal of the captured group the placed stone gains a liberty.
Suicide is forbidden: it is not allowed to place a stone so that it would immediately result in that stone (or a group it would join) being captured by enemy. I.e. if there is an enemy group with one empty square in the middle of it, you cannot put a stone there as that stone would simply have no liberties and would immediately die. Exception to this is the above mentioned taking of a group, i.e. if a suicidal move results in immediately taking enemy's group, it is allowed.
The ko rule states that one mustn't make a move that returns the board to the immediately previous state; this basically applies just to the situation in which the enemy takes your stone and you would just place it back, retaking his capturing stone. By the ko rule you cannot do this IMMEDIATELY, but you can still do this any further following round.
Territory: at any time any EMPTY square on the board belongs either to white (no black stone can be reached from it by traveling over neighbors), black (no white stone can be reached from it) or none (belongs to neither). Squares that have stone on them aren't normally considered to belong to anyone (though some scoring systems do), i.e. if you surround a territory as white, only the VACANT surrounded squares count as your territory. The size of territory plays a role in final scoring.
Prisoners are enemy's stones that are OBVIOUSLY in your territory and so are practically dead. I.e. they are inside what's clearly not their territory and with further play would clearly be captured. Obvious here is a matter of agreement between players -- if players disagree whether some stones are obvious prisoners, they simply keep playing and resolve the situation.
Scoring: there are multiple scoring systems, but the most common seems to be the following. At the end of the game we count the score for black as the size of black's territory PLUS one point for each stone black has captured PLUS one point for each white prisoner in black's territory. Score for black is computed analogously but we also add the komi compensation. The player with more points wins.
Handicaps: TODO.
Implications of rules and basic of strategy/tactics: life and death, eyes, atari, TODO.
Example: the following is an example of the end state of a beginner game on a 9x9 board:
_________________
9 |. # . . # # # O .|
8 |# . # . # O O . O|
7 |. . . # # O . O .|
6 |# . . # O . O . O|
5 |# . # O O O . . .|
4 |. # # # O O . . .|
3 |. . . # # O O . .|
2 |. . . . # # O # .|
1 |. . . . # O O O .|
'-----------------'
A B C D E F G H I
Here black's (#) territory is 23, and black made 9 captures during the game, giving together 32 points. White's (O) territory is 16 and he has one black prisoner (H2), giving 17 points; furthermore white made 6 captures during the game and gets 5.5 (smaller value due to only 9x9 board size) bonus points as komi, totalling 28.5 point. Therefore black wins.
TODO
Programming
See also https://senseis.xmp.net/?ComputerGoProgramming and https://www.chessprogramming.org/Go.
Board representation: a straightforward representation of the go board is as a simple array of squares; each square can be either empty, white or black, that's 3 values that can be stored with 2 bits, which allow storing 4 values, leaving one extra value to be used for some other purpose (e.g. marking illegal ko squares, estimated dead stones, marking last move etc.). 1 byte allows us to store 4 squares this way so we need only 91 bytes to represent the whole 19x19 board. On computers with enough RAM it may be considered to store 1 square in a single byte, making the board take more space but gaining speed (we don't need extra instructions for squeezing bit from/to a byte). Of course we furthermore have to keep track of extra things such as numbers of captured stones.
TODO
Stats
Some interesting stats about go follow.
There are 2.08168199382 * 10^170 legal positions on a 19x19 board, 3.72497923077 * 10^79 for 13x13 and 1.03919148791 * 10^38 for 9x9. The number of possible games is estimated from 10^10^100 to 10^10^171.
An average high-level game lasts about 150 moves. Average branching factor is 250 (compare to 35 in chess).