[0,1] game and tournament play?

[Aisthesis]

Does anyone have a simple example in which the [0,1] is applied to a tournament situation?

The simplest one I can think of may be so simple as to be completely trivial (I haven't managed to think it through completely yet):

A and B both buy in for $2 to a tournament which B is going to win most of the time. The rules are this: A always posts $1 blind, and B can call or fold. Initial stacks are $2, and last man standing wins.

B's best play here may well be to just maximize EV with just calling [1/2,1] every time. But he can obviously increase his probability of winning by playing tighter than that. The tighter he plays, the more often he'll win (he just needs to avoid losing both his first and his second hand), approaching 100% if he has the patience. But he has to play a lot of hands to win A's $2.

So, assuming that if B loses, he can just buy-in again under the same circumstances, let's define his "best play" as the hand selection which will maximize his winnings per tournament hand played. That will almost have to be the same way he plays in a "cash game"--namely calling on [1/2,1]. That's really going to have to give B a value of .25 for each tournament hand played (although he can obviously improve on his ROI% by playing tighter).

Or is the identity between best tournament strategy and best cash game strategy less clear than it seems on first glance? If they're the same in this case, does anyone have a (simple, please!!) tournament example where there is a clear difference?

I will say that in my ultra-simple example it could be advisable for B to tighten up on the second hand he plays if he has lost the first one. It seems less likely that he would want to loosen up on the second hand if he has won the first one (now he has $3 left to A's $1) ... but maybe that's also something to be considered.