In poker, ICM is short for Independent Chip Model. It’s a mathematical model used to calculate the equity of each player’s stack in a tournament situation.
In other words, it helps you to determine how much each chip is worth in relation to the chips of other players and the prize pool. .
The most important thing to remember about ICM is that it only applies in tournaments with a prize pool. In cash games and Sit & Gos, the value of each chip is always the same – one big blind.
But in tournaments, the value of each chip fluctuates based on your position in the tournament, your stack size, and the number of remaining players.
To use ICM, you first need to understand two concepts: tournament equity and push/fold equity.
Tournament equity is your share of the prize pool if the tournament ended right now. For example, if there are 10 players remaining in a tournament with a $1,000 prize pool, and you have 5,000 chips while the average stack size is 10,000 chips, your tournament equity would be $500 (5% of the prize pool).
Push/fold equity is your equity when you’re either all-in or fold. In other words, it’s what you expect to win on average when you’re either pushing with a hand or folding everything except for the very best hands.
You can use ICM to make better decisions in two situations: when you’re short-stacked and need to decide whether to push or fold, and when you’re faced with an all-in situation from another player.
If you’re short-stacked and considering pushing, you need to determine whether your push/fold equity is higher than your tournament equity. If it is, then pushing is +EV (positive expected value). For example, let’s say you have 1,000 chips and the blinds are 100/200.
You’re considering pushing with A♣Q♣ but you’re not sure if it’s +EV. To find out, you first need to calculate your push/fold equity and tournament equity.
Your push/fold equity would be: (probability of winning) x (prize pool) + (probability of tying) x (prize pool divided by 2) – (probability of losing) x (your stake). In this case:
[0.45 x ($1,000)] + [0.09 x ($1,000/2)] – [0.46 x $1,000] = $480.
Your tournament equity would be:
0.5 x $1,000 = $500
Since your push/fold equity ($480) is higher than your tournament equity ($500), pushing with A♣Q♣ here would be +EV.
Now let’s say you’re not short-stacked but another player goes all-in for their last 5 big blinds (10k). You have 20 big blinds (40k) and are currently sitting in second place out of 10 players remaining.
The player who just went all-in has A♦K♦ and needs help to stay alive. You look down at J♦J♥. What should you do?
In this case, we need to compare our ICM value with calling to our ICM value with folding: .
EV(call) = [Prob(win)*(Final Pot)] – [Prob(lose)*(Your investment)]
EV(fold) = [Prob(continue)*(Your investment)] – [Prob(lose)*(Your investment)]
where: Prob(win) = Your chance to win the hand; Prob(lose) = Your chance to lose the hand; Prob(continue) = Your chance continuing in the game by folding (1 – Prob(lose)).
We also know that: Pot = Total amount put into pot by all players; Final Pot = Pot + All-In Player’s investment; Your investment = Amount needed to call All-In Player’s bet; Total amount put into pot by all players before All-In Player’s bet = Pot Before All-In Player’s Bet
Plugging everything into our equations:
EV(call) = [Prob(win)*(Pot Before All-In Player’s Bet + All-In Player’s investment)] – [Prob(lose)*(Your investment)]
EV(fold) = [(1 – Prob(lose))*(Your investment)] – [Prob(lose)*(Your investment)]
where: Prob(win)= 0.77 from Table #2 below; Prob probabilities from Table #1 below; All values from Table #3 below
Our final equation becomes:
EV(call) = [(0.77)($5400 + $10000] – [(0)($10000]
EV($5400 – $10000]
EV($14400]
EV($10000]
EV($24400]
And finally we solve for FOLDING being optimal by setting these two values equal since we want to find out when FOLDING becomes optimal over CALLING…when they have equal value:
$14400=$24400 —> $10000=$16667 —> $16667 FOLD!.
