mathematical model for tournaments

[marv]

Hi,

I was thinking about how optimal play in one hand of a tournament in which only first place gets paid (like a headsup tournament) differs from a hand of cash game with the same ante/blind structure.

I seem to have convinced myself that there's no difference,
so an optimal cash player is an optimal tourney player in this case, but feel uncomforatble with this conclusion.

This is my argument:

My expected stack size at end of hand H (for H some very big number) is prob(I-win-the-tourney)*all-the-chips-in-the-game, since the tourney is bound to be over by hand H and at that point I've either got 0 or all the chips, so the aim of maximizing P(I-win-the-tourney) is the same as maximizing my expected wealth by hand H, which is achieved by maximizing my EV over each hand in the tourney separately. And this is exactly what an optimal cash-game player does.

Have I overlooked something?

This breaks down if more than one place gets paid, so my follow-up question is:

What is the current best known model for prob(I-eventually-win-the-tourney) as a function of the current stack sizes assuming optimal play by all players (for some realistic tournament structure)?

It must be non-linear or the argument I gave above will still apply, and tournaments would be must less interesting.

Marv