# Forum for Infinitesimals Optimal Play

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# How long do "longer corridors" need to be? [#5683]

RickyDemer: How long do "longer corridors" need to be? (2018-05-10 12:06) [#11114]

How long do "longer corridors" need to be for Black attacking "longer corridors ending in minies" to necessarily come after Black playing minies?

"longer than a miny" is not enough, as can be seen from the following diagram.

Black to play

wins the chilled game and is the only way for Black to win the chilled game.

I do realize that the sentes are miai, and that the threat of Black's sente being at-all bigger than the threat of White's sente would make playing Black's sente into another way for Black to win the chilled game. Accordingly, it might be that one needs to ignore miai sentes like one needs to ignore even numbers of stars. However, it's not clear to me how one would show that, if that's indeed true.

107.210.159.110: ((no subject)) (2019-01-30 07:47) [#11312]

Bill: Good question!

Let's set up a difference game.

B Zero game

This is a zero position, OC. Now let's compare plays. Let Black play the miny and White play in the one space longer corridor, {0 | tiny}.

Difference game

Let Black play first in the difference game.

Black first wins

White gets the last play, but Black has one more point.
Now let White play first.

White first wins

White first gets the last play and wins by one point.
Now let's set up a difference game with the long corridor one space longer.

Difference game
Black first wins

Black wins by one point.

White first loses

If White plays the tiny first, Black makes a zero game.

White first loses (2)

If White starts in the longer corridor, Black wins by one point.
So the longer corridors have to be at least two points longer than a tiny or miny to be sure that the tiny or miny dominates.