[Aisthesis]

In this extremely simplistic tournament, just assuming that B keeps the obvious calling criteria of 1/2 for small, medium, or big stack, I come up with some strange results that then turn out to be much less strange:

First, the average number of hands played in this tournament is 32/5 = 6.4 (at least the way I did it, this required summing an infinite series that wasn't nearly as bad as it might seem).

Moreover, B wins the tournament exactly 90% of the time!! Basically, whenever he calls he will on average win 3/4 of the time. And it takes 2 wins in a row or 2 losses in a row for the tournament to end. The probability of B winning twice in a row is hence (3/4)(3/4) = 9/16, and the probability of A winning twice in a row is (1/4)(1/4) = 1/16. So for every time A wins, B wins 9 for a 90% win-rate.

I at first thought that this would mean that B was beating his results in the cash game version. But this isn't the case. His ROI is 2*(9/10) - 2*(1/10) = 8/5. Each tourney lasts 32/5 hands. So his average winnings per hand are (8/5)*(5/32) = 1/4. Same as in the cash game.

So, it seems quite likely that B's tournament play here will be identical with his cash game play. But I still don't really see any objective reason why B might not want to have different calling criteria here in the small, medium, and big stacks in order to maximize EV/hand in tournament play.