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Here I'm going to show a way to compare calling to folding using ICM, ignoring that there is an extremely short stack left in the tournament who is about to hit the blinds. The equivalent calculation for cash would just be a simple comparison of bet/(bet+pot) to our equity against our opponent's range, but here it's more complicated.
Let's assume for simplicity that if we call, either we win or we lose. Let the chance of winning (ie: our equity) be E.
Case 1: We call and win. Before blinds are posted in the next hand, we will have a stack of 10100 in the SB, another player will have 2400 in the BB, a player will have 100 in the CO, and a player will have 1000 in the BU. That gives us an equity in the tournament of 44.5% based on the ICM.
Case 2: We call and lose. Our equity in the tournament is now 0%.
Our total equity in the tournament for calling is then 0.445E + 0(1-E) which is just 0.445E.
If we fold, then before the blinds are posted in the next hand, we will have 4800 chips in the SB, the BU will have 1000 chips, the CO will have 100 chips, and the BB will have 7700 chips. In this case we have an equity of 35.38% in the tournament based on the ICM. Therefore, folding is better than calling when:
0.445E < 0.3538
E < 0.7951
So we need 79.51% equity to call here. Notice how much difference there is between this number and how much equity we would need to be able to call in a cash game.
Now we open PokerStove and look at some ranges for when we hold AA as follows:
Against QQ+, we have 79.305% equity.
Against PokerStove's top 2%, we have 79.887% equity.
Against PokerStove's top 5%, we have 83.043% equity.
Against PokerStove's top 8%, we have 84.197% equity.
Against PokerStove's top 11%, we have 84.678% equity.
Now the way I have presented this, we can figure out what range we should call with against any of our opponent's ranges. For example, if we have KK and our opponent is shoving {JJ+, AK} here, then we have 62.601% equity and should fold.
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