[0,1]- all-in or fold two player tournament

[Siegmund]

My first guess - without getting out a pencil and paper - is that you're seeing something of an edge effect because of the short stack being right at 50% or 25% of the chips. Did you do the analysis when the stack sizes were at various other points in between? (Say every size from 10:10 to 19:1 in the 20-chip version?)

Intuitively, if I have more than 1/4 but less than 1/2 of the chips, I have to win twice to win, and lose once to lose. My winning chances should be very nearly constant at very nearly 1/3, for a range of stack sizes from about 30% to 45%. If the stacks were deep enough for the blinds to be 'small' compared to the stacks, I would expect a similar plateau of winning chances ~ 1/6 for stacks between 1/8 and 1/4.

When you are right on the knife-edge of having exactly half of the chips, you are in a situation where transferring a single chip causes a huge swing in your equity (moving you into either the 33% or 67% region) and the effect of who has to post which blind next (=can you win one or two chips if your opponent folds?) is going to show up as a significant equity difference.

I would guess that if you were in a situation where a swing of five chips didn't cross a big barrier (say there are 40 chips in play split 15-25) the difference from 33%/67% equity, and the difference between SB and BB, would be tiny.

Makes me wish I had a week to sit around and play with this problem myself. I did some work on [0,1] poker once upon a time, but never did consider a tournament. Great idea.