Addendum to the Last Post -- Real Equity

In the comments for the last post, I claimed that I was going to evaluate how well my opponent will do by calling my all-in with A5o vs. the range {44+, A7s+, A8o+, KJs+, KJo+} and getting 1.86:1 pot odds. Let's suppose that the chip counts before the hand begins are as follows: SB - 55K, BB (me) - 21825, Button (A5o guy) - 73175. This is pretty close to exact for my chip count, and reasonably accurate for the other two guys.

We will use the independent chip modelling method to determine the value of tournament chips. Here is the pokerstove output of A5o vs. the range descibed above.

equity (%) win (%) tie (%)
Hand 1: 35.5566 % 32.82% 02.74% { A5o }
Hand 2: 64.4434 % 61.71% 02.74% { 44+, A7s+, KJs+, A8o+, KJo+ }

This means that 32.82% of the time, Button wins and eliminates the BB. The stack counts after the hand will then be: SB - 53575, BB (me) - 0, Button (A5o guy) - 96425. The handy ICM calculator in the link above tells us that the SB's stack is now worth $27.14 and the Button's stack is now worth $32.86.

2.74% of the time, there will be a chop between the BB and Button and the stacks (and stack values) after the hand will be: SB - 53575 ($22.48), BB - 22550 ($10.60), Button - 73875 ($26.92).

61.71% of the time, the BB wins the pot and the stacks (and values) are now: SB - 53575 ($21.07), BB - 45075 ($18.48), Button - 51350 ($20.44).

If the Button folds, the stacks (and values) will be: SB - 53575 ($21.90), BB - 28250 ($12.76), Button - 68175 ($23.34).

We are now able to calculate the "actual" difference in value between calling and folding in this spot. By folding, his equity is $23.34.

By calling, his equity is (0.3282)($32.86) + (0.0274)($26.92) + (0.6171)($20.44) = $10.78 + $0.74 + $12.61 = $24.13.

So I guess he makes $0.79 by calling there, which kind of surprises me. I really thought he was losing a lot of equity by calling in this situation.

Kudos again, brother! I now have to admit that the call was good.