# KomiLowerBound

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# Ruling out a negative lower bound

Arno: I agree that 361 is an easy to prove upper bound, but how does the easy proof for 0 as lower bound look like? That assumes that having the first move is an advantage. How do you prove that? ^{[1]}

SAS: You don't have to prove that being Black is an advantage, only that it isn't a disadvantage. It isn't a disadvantage, because Black is allowed to pass his first move.

For simplicity I will assume that two consecutive passes end the game, but other rules should give the same result. Let's suppose that playing the first move (as opposed to merely passing) leads to an *n* point loss. First suppose the komi is 0. Then Black will pass and White will pass, and the position on the board is a jigo, and so the game is drawn. Now suppose the komi is -*n* (reverse komi of *n*). Then Black will pass. Now, a White pass will lose by the *n* reverse komi, but a White play will lose by the *n* reverse komi plus the *n* point disadvantage of first move. So either way, the -*n* komi (or any other negative komi) gives a win for Black.

[1] removed my "thinko" of negative komi. I was thinking along the lines of not being allowed to pass on the first move, which of course is not what go rules are about. -- Arno