# Using the Independent Chip Model

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The Independent Chip Model (ICM) is used to predict the likelihood of winning a Poker tournament based on the relative size of a player’s stack. Calculating the ICM yields a figure that represents a player’s equity in a tournament prize pool. It is most often applied to Sit-n-Go tournaments by players who reach the final table, and it is based on two important underlying assumptions.

First, ICM assumes that all players at the final table of a tournament are closely matched in terms of Poker skills and abilities. Second, it assumes that the probability of winning is proportional to each player’s chip stack. A deep-stacked player holding half the table’s chips has a 50% chance of winning, whereas a player with just one tenth of the chips has a 10% chance of winning.

Another key component of calculating the ICM is the tournament prize structure. In a typical Sit-n-Go, cash awards might be distributed to the top four finishers, with first place paying more than second, second paying more than third, etc. Let’s see how it works by using an example and doing some calculations.

## Making the ICM Calculation

Imagine four players remain in a tournament with four prizes totaling £zero up for grabs. Top prize is £100, second prize is £60, third gets $30, and fourth receives £10. The easiest calculation to make is for first place. If Player A has half the chips, his/her first prize equity is 50% x £100 = £50. If Player B has a quarter of the chips remaining, his/her equity is 25% x £100 = £25. Supposing the other two players are both short-stacked with roughly an eighth of the chips, they each have an equity of 12.5% x £100 = £12.50.

To calculate the equity for second prize, the participation of one of the players must be removed, because he/she will have won the top prize and is not eligible for second. If Player A is removed, so are half of the chips. Now Player B has 50% of the chips remaining and his/her second place equity is 50% x £60 = £30. The other two players each have a quarter of the chips, so their second prize equity is 25% x £60 = £15.

Of course, there is a possibility the player B will come in first, so Player A can also calculate his/her second place equity by removing Player B from the equation. This means Player A now has two thirds of the chips remaining or an equity of 67% x £60 = £40. Similar calculations can be made for scenarios where one of the short-stacked players takes top prize.

For third prize, two of the players must be removed. Assuming Player A and Player B take the top two places, the two remaining players will have a 50% probability of winning third, or 50% x £30 = £15. Fourth prize is guaranteed to the loser of the four players, or £10.

## Applying ICM to Play

Knowing the ICM calculation for each position can help players make decisions. Let’s suppose one of the short-stacked players goes all in pre-flop, hoping to steal the blinds or else double up. Should any player challenge him/her?

From a strictly ICM point of view, the answer is no. The other short-stacked player would be risking £15 in second-place equity plus £15 in third-place equity, to potentially gain £20, the difference between third and fourth place—a coin flip at best.

Player B would have to risk swapping places with the short-stacked player, giving up £15 equity for second place and £12.5 for first. If successful, Player B would still trail Player A in chips, so there isn’t much to gain. And Player A has even less reason to challenge; it would mean falling into a tie with Player B if unsuccessful and increasing equity only slightly otherwise.

As the example shows, sometimes the risk is simply not worth the potential gain. Even a big hand can be safely dropped to preserve equity, rather than lose what has already been gained. ICM is not the only criteria for decision-making in tournaments, of course, but it does add a unique perspective to play.

Published on: 30/12/2010

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