Explanation of ICM

ICM stands for “independent chip model”. It’s a method of assigning tournament chips a monetary value in poker. But why would we do this? Can’t we simply count our tournament chips when making decisions?

The problem here is that an increase or decrease in out tournament stack is not directly proportional to monetary values. In other words; doubling the size of our chip stack does not necessarily double its real-world monetary value. In some cases, doubling our chip stack might only increase its monetary value very slightly. This changes the way we need to think about EV calculations and the profitability of various decisions.

The difference in number of chips vs monetary value  is related to the payout structure of whichever tournament we are playing. A certain number of chips might hence be more valuable or less valuable depending on whether we are playing a winner takes all tournament or a satellite tournament. 

Since running an ICM calculation by hand is somewhat complex, software is generally used. (There are a number of ICM calculators available for free online). We simply input the stack sizes of all remaining players along with the payout structure of the tournament. We are then told how much each individual tournament stack is worth in terms of real-world monetary values.

Example of ICM used in sentence -> Due to ICM considerations, we were forced to fold our pocket Queens preflop.

How to Use ICM as Part of Your Poker Strategy 

Let’s see a quick example of the type of results an ICM calculator will produce. Imagine the following tournament setup.

There are 10,000 chips in play and there are 5 players left in the tournament.

Player 1) 4,000 chips
Player 2) 2,500 chips
Player 3) 2,000 chips
Player 4) 1,000 chips
Player 5) 500 chips

It’s a satellite tournament and the top 4 finishers each receive a tournament ticket worth $25. Here are the ICM calculator’s results -

Player 1 - $24.50
Player 2 - $23.60
Player 3 - $22.80
Player 4 - $18.50
Player 5 - $10.51

Note that although player 1 has 8 times as many chips as player 5, his stack is only worth roughly 2.5 times as much.

Ignoring any blinds, let’s imagine that player 2 were to shove all-in preflop and player 3 was contemplating a call. If he is getting the pot-odds to make the call (50% equity or less required in this scenario), it would be a +EV decision with respect to tournament chips (we refer to this as chip-EV). However, such a call would very unlikely be correct with respect to $EV (where we take into account the monetary worth of each stack rather than the number of chips). Let’s see why not.

If player 3 wins the all-in, the monetary value of his stack increases to $25 (he wins a ticket). That’s a win of $2.20 over his current stack. If he loses the all-in, his stack is worth nothing and he is essentially losing $22.80. He is hence risking $22.80 to win $2.20, a call that would require a very large amount of equity, more than the equity he usually has. While in terms of chips it’s roughly an even money wager, in terms of dollars the risk:reward ratio is awful.

This is why even folding pocket Aces preflop might be reasonable in some tournament scenarios. Translated in a non-mathematical way, it’s more valuable for player 3 to try and hold on in the hope that one of the other players gets knocked out and blinded out. This way he’ll be able to win the $25 without putting his stack at risk. 

Chip EV

Using the same tournament chip data let’s imagine this is no longer a satellite tournament but a regular tournament which awards prizes to the top 3 finishers.

1st Place: $50
2nd Place: $30
3rd Place: $20

Re-inputting the data into the ICM calculator we get the following - 

Player 1) $32.82
Player 2) $25.68
Player 3) $22.29
Player 4) $12.60
Player 5) $6.60

Notice now that there is a much bigger difference between the ICM value of player 5’s stack and the ICM value of player 1’s stack. What can we learn from this?

The closer a tournament structure is to “winner takes all” structure, the closer $EV is to chip-EV. In a true “winner takes all” tournament, we can simply imagine that we are playing a cash game (since chip-EV and $EV are identical. At the opposite end of the spectrum, satellite style tournaments result in big discrepancies between chip-EV and $EV. Even very short stacks are proportionally valuable near the bubble in satellite tournaments, since they can be worth the full payout if someone busts before them.

See Also 

Tournament, Bubble, Structure, Sit and Go, Cash Game

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