Problem diagram.
What is Black's best line of play on 2x2 Go?

Think the answer is trivial?
Think again!

Source:
Myron Souris

For 2 by 2 Go, the Japanese rules' concept of life is ill-defined, so assume the Situational SuperKo rule (no repeating a position with the same player to play), along with Chinese area scoring.

Assume no komi. Two consecutive passes ends the game.

Solution follows    (or click here to download SGF)

Node 1
Black 1 and White 2 are obvious even to a beginner. But what does Black do next?!

If Black passes, then White passes, and the game quickly ends in a tie.

But does Black 3 win?!

After Black 3, White cannot pass, because Black would then pass to give a 1 point Black win.

Node 2
So White 4 must capture the 2 Black stones. Next, Black 5 is the only winning move!

If Black 5 were in the lower right corner instead, White would capture the Black stone with 5. But then the SuperKo rule would prevent Black from recapturing in the lower right corner, because that would repeat the overall board position after Black's very first move. The game would end with White taking the entire board!

After Black 5 in the diagram, White has two continuations: pass or capture.
Continue below to see each possibility.

Node 3 (continuation from Node 2)
If White 6 is a pass, then Black captures 2 stones with 7. Then after White 8, Black passes! The SuperKo rule prevents White from capturing the 2 Black stones, because White would repeat the position after White 4 in the Node 2 diagram above.

So White has to pass, the game ends, and Black wins by 1 point.

Note that White cannot do better by playing 8 in the lower left corner instead. Black would pass, and White has the same problem as with White 8 in this diagram.

Node 4 (continuation from Node 2)
But what if White 6 captures the Black stone in the upper right?

Node 5
Black 7 re-captures the 3 White stones immediately. White 8 is forced. Then similar to what happened in the Node 3 diagram above, Black puts White on the spot with 9, i.e., SuperKo prevents White from playing a stone.

Black wins again by 1 point.

See the SGF for a complete analysis, but the conclusion is that on a 2x2 board, Black wins by 1 point!

If 2x2 Go is this tough, what chance do we have of understanding the 19x19 board?!

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