ICM Calculator FAQ
How are the ranges calculated?
The algorithm is based on Fictitious Play.
Are the results real Nash Equilibria?
No, they are just approximations. The formal requirement for a Nash Equilibrium is that players must not be able to unilaterally improve their own equity by deviating from the Nash Equilibrium. For the vast majority of results produced by the calculator, this condition will not be met. But in most cases, players will not be able to improve their equity significantly when unilaterally deviating from the calculated ranges.
The results can be seen as a consistent set of player-ranges, where all players are using reasonable strategies, given the opponents ranges. That is, no player makes a big mistake by playing the calculated ranges, even under perfect knowledge of his opponents ranges.
Are side-pots/split-pots correctly considered?
Yes. All possible results from 2-way and 3-way pots are correctly handled.
Are card removal effects correctly considered?
"Direct" card removal effects are correctly handled. That is, the calling/over-calling players hand distribution is correctly modified given the pushers/callers range.
However, no modifications to starting-hand distributions are made due to folding. e.g.: If 3 players fold in front, the 4th player's starting hand distribution is still assumed to be perfectly random. In reality, the 4th player probably has significantly more Aces in this situation.
Why do the ranges for heads-up play differ from other published NE strategies?
If you own a copy of Chen/Ankenmans "Mathematics of Poker" (highly recommended, btw.), or SnGPT, you may have noticed that their heads-up NE push/fold solutions differ slightly from the ranges calculated here. To allow efficient calculation, the range construction is constrainted in this implementation.
While calculating heads-up NE solutions would be possible without constraints, the constraints are necessary to allow efficient calculation for multiple players. As the HU cases are calculated by the same algorithm, the range constraints still apply. This causes the minor differences to the MoP/SnGPT solutions.
Some calculated ranges are obviously bad, why?
There are many cases where the calculated ranges are in fact "bad plays". The algorithm optimizes ICM equity for the players. Weaknesses of ICM are therefore directly inherited by the calculator.
The most common flaws are related to ICM's non-awareness of future -EV rounds. e.g.: Shortstacks will usually blind themselves to death on the bubble, if they are optimizing their ICM equity every round.
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