[Aisthesis]

Thanks for the link! That's a very different table that can perhaps help me to better explain what I'm trying to do here.

The table you give shows how a hand holds up against random hands assuming the full table stays all the way to the river. I'm making almost diametrically opposite assumptions with my table: I'm assuming no one calls unless they have a hand that is favored over yours, and that they always call if they do have a better hand than you do.

The basic scenario is this: You are somewhat shortstacked in a tournament and have reached the point where you feel you have only two choices pre-flop: all-in or fold. The question is, what hands are good choices for the all-in?

My table here attempts to answer this question given two additional parameters: the number of people at the table and the size of your stack relative to the initial pot (before any cards are seen).

Some examples: Blinds are at 100/200 with no antes, and you have a stack of 1600 holding AJo UTG with 9 players (including yourself) at the table--a pretty good hand. Is this a hand where you might want to move all-in in the hope of a favorable coinflip?

According to the table, the answer is "no." The initial pot is 300, so your stack is 5.33 times this pot. Given the possibility of callers after you with superior hands, your stack-size would have to be at most 4.51 times the pot (1,353) to make moving in a +EV play on that hand.

But if you had AJs in the same position, moving in would have +EV up to a stack-size of 6.43 times the pot, so AJs WOULD be sufficient for the all-in move. If you do get a caller with a superior hand, AJs will hold up well enough that you are justified in taking the risk for the sake of winning the blinds (or doubling up).

Basically, with AJo in that situation, you will lose more total tournament dollars than you win if you move in, but with AJs, you will win more tournament dollars than you lose.

However, let's change the situation just a little: Same blind structure and same stack-size. But now you have AJo at UTG+2, and it's folded to you. So, there are now only 7 players, including yourself, in the hand. In this position, the table shows that moving in is +EV up to a stack-size of 6.55 (1,965 in this case). So, given the size of your stack, AJo is a good bet in this situation. You will now win more tournament dollars than you lose if you move in with AJo in this position.

Does this explanation help in explaining why I assume only a caller with a superior hand rather than everyone playing to the river? I felt that it was a more accurate reflection of practice to assume that either (1) you steal the blinds without a contest by moving in with these hands or (2) you get a caller with a superior hand.

For assumption (2) one of the main issues is just how often a superior hand to yours is going to occur at a table with n players. Actually, with AJo, more often than not you will have the best hand among 9 players, but when you don't, you lose so frequently that it is apparently not worth the risk.

Does this help at all in explaining where I'm trying to go with this?