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

[pokeryogi]

Optimal play in a cash game is different than a tournament, even in winner take all. The main difference, the ability to rebuy in a cash game for your opponent as well as yourself. In a cash game you could rebuy and still bust em all. In a tournament, there is no such option. Once your out your always out. Pushing small edges, as you should in a cash game, is more dangerous in a tournament.
Still learning,
PY

[pzhon]

[ QUOTE ]
Pushing small edges, as you should in a cash game, is more dangerous in a tournament.

[/ QUOTE ]
If you make small error after small error, how do you win? Volume?

The idea that you may want to avoid a +EChip play in a tournament only applies in a very restricted context. People cite it far too frequently when it does not apply.

/images/graemlins/diamond.gif The gain in chips now has to be small.

/images/graemlins/diamond.gif The variance has to be high.

/images/graemlins/diamond.gif The variance must be higher after the aggressive play.

Sometimes the play with the higher EChips and variance is to smooth-call or slow-play or make a normal bet rather than to throw a lot of chips into the pot now when you won't be called.

/images/graemlins/diamond.gif You have to be sure you have a big skill advantage.

If you don't dominate ring games against the others in the tournament, you have no reason to sacrifice chips to avoid variance in a freezeout.

If the blinds are huge, you probably don't have a big skill advantage.

Somehow, the good idea that the very best players should make small adjustments gets warped into the misconception that all players should make substantial adjustments. Next, we get a stream of novices who are convinced that the way to become a world-class player is to be willing to fold AA preflop.