EV vs. risk, a simulation experiment idea

[eastbay]

A nagging question for tournament strategy is the eternal debate about "protecting your chips" vs. taking +EV when you can get it. We all know there is some truth in both sides of the debate, but it is always a matter of contention how much +EV you should give up to risk all your chips.

Here's an idea for a simulation experiment. The setup is this:

3-handed tournament. all-in or fold. Some "typical" (online) stack/blind structure, say 3300 chips apiece, blinds 150/300.

Each player does a modified Karlson-Sklansky calculation to figure out if he's going all-in or folding. The modified calculation has two new parts: first, it will consider two hands left to act (from the button), rather than just one, and as a result, the assumption of a call is based on positive edge, not +EV. Second, rather than choosing a criteria for EV>0, the criteria has a single parameter, say alpha, that is a fraction of his current stack. Each player has a pushing strategy with a fixed alpha.

If a player pushes in, he flips over his cards, and the SB calls if he has an edge. If the SB calls, the BB folds - there are no multiway pots in this model. If the SB folds, the BB calls if he has an edge. Cards are not shown if a player folds.

Assume payout of 50/30/20. Equity on first elimination is based on fraction of remaining chips. Play does not continue heads-up, but equity is simply calculated when the first player is eliminated.

The first question is then: If two players are playing alpha=0, what is the optimal alpha for the 3rd player?

Second more general question: If two players are playing alpha=alpha0, what is optimal countering alpha, for alpha 2,5,10,20%?

Comments?

(running the same thing for 4-handed bubble play would probably be even more interesting)

eastbay