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Every move, you flip 6 coins. If all 6 come up as heads, you swap seats and colors with your opponent.

This means that an advantageous board position is much less important, and it will be in both players favour to keep the board position very near evenly matched.

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Not always. A player that thinks he will lose a game that's tied in the last 8-ish moves will have an incentive to create a highly unbalanced game. That way, that player gets a 50% chance of winning.

Given that there's only one flip left and you need 6 heads, he has a 1/2^6 or 1/64 chance to win.

In go the last 8 moves is almost never going to make the difference (the last 20-40 moves in a game that doesn't end in resignation there are almost no mistakes in pro games).

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