Liberties, territory, and how to finish a game cleanly
Go — Weiqi in Chinese, Baduk in Korean, Igo in Japanese — is a territory game that originated in China more than two thousand years ago and is still played under essentially the same rules today. Two players take turns placing stones on the intersections of a grid. Stones never move once placed, but they can be captured, and at the end the player who has walled off more of the board wins.
The rules fit on an index card, yet the game is famous for its depth: on the full 19x19 board there are 361 points and the opening alone offers a near-limitless choice of plans. Smaller boards keep the same rules but make games shorter and more tactical, which is why beginners are usually pointed toward 9x9 first.
Dead stones are removed automatically at the end. The game plays a few hundred quick random continuations from the final position, and a group that is captured in most of them and lacks two clear eyes is crossed out and counted for the surrounding player. It can misjudge unusual shapes such as seki, so capture anything you are unsure about. The AI passes when nothing useful is left: when the remaining areas are settled, or when you have passed and its count says it is ahead.
Every fight in Go is a liberty race. A lone stone in the open has four liberties, on the edge three, in the corner two. When your group and an enemy group surround each other, whoever runs out first is captured, so before you start a fight, count both groups. A group reduced to one liberty is in atari. Joining stones solidly pools their liberties, which is why a connected wall is much harder to kill than scattered stones.
Put a stone in atari and it can extend to gain a liberty — but if the extension leaves it with only two, you can atari it again from the other side. Repeat, and the chain zigzags diagonally across the board until it hits the edge and dies. This is a ladder. Before you start one, trace the diagonal: if a friendly stone of the fleeing side sits in its path, the chain escapes and your ladder stones become weaknesses. On Easy the AI flees atari by reflex; on Medium and Hard it reads the ladder first and starts ladders of its own.
Territory is about efficiency. In a corner, two board edges do most of the enclosing, so a handful of stones secures a dozen points. On an edge you have one wall for free. In the centre you have to build all four sides yourself. On 9x9 the board is small enough that the centre point and the 3-3 or 3-4 points are all common openings; on 13x13 and 19x19 the 3-4 and 4-4 points near each corner are the standard first moves. The AI also favours the third and fourth lines early, so expect a contest for the corners.
An eye is an empty point enclosed by your stones. The opponent cannot play into it, because the stone would have no liberties — unless doing so captures you, which happens when it is your last liberty. A group with only one eye can therefore be captured; a group with two separate eyes never can. When a group is under attack, look for room to form two eyes. A straight line of three empty points inside your group is the classic critical shape: if you play its middle point you make two eyes and live, and if your opponent plays it first the group dies.
Under area scoring the last phase is about borders and neutral points. Close every gap in your walls, including the edge points where a wall meets the side of the board. Every neutral point between the two positions is worth a point to whoever fills it, so do not pass while any remain. Playing inside your own territory costs nothing here, so capturing a hopeless invader removes all doubt. A worked example on 9x9: you have 26 stones and 18 points of territory, scoring 44. The AI has 22 stones and 14 points, scoring 36 + 7.5 = 43.5, and one neutral point is left. If you fill it, you win 45 to 43.5; if you pass and the AI fills it, it wins 44.5 to 44.
Every level filters its moves first: it never fills its own eyes, avoids self-atari with groups of two or more stones, and ignores small sealed areas unless a capture is involved. Easy and Medium then score each candidate once, rewarding captures, rescues, ataris, liberties and good opening lines. Hard plays out hundreds or thousands of quick random games from its best candidates and picks the one that wins most often, which gives it a real feel for territory and life and death, most of all on 9x9.
| Difficulty | What to expect |
|---|---|
| Easy | One-move scoring with plenty of randomness and no ladder reading. Often picks any of its top few moves. |
| Medium | The same scoring, but it reads ladders and simple chases before running or attacking, and plays its best candidate. |
| Hard | Monte Carlo playouts for about a second per move. Clearly stronger than Medium on 9x9 and 13x13; on 19x19 it plays at roughly Medium strength. |
| AI Training | A longer budget of about 1.35 seconds a move, more candidate moves, and all-moves-as-first statistics from every playout, which sharpen its estimates when playouts are scarce. In testing it beat Hard 32-16 on 9x9 and 10-2 on 13x13. On 19x19 the extra time still has to be spread thinly. |
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