Introduction

• Problems with the ICM
• How to improve the ICM
  
• Card removal effect
• Future game simulation
  

The Independent Chip Model (ICM) tells you how much your stack is worth in cash based on the payout structure of the tournament you are in. But can you blindly rely on this information? The answer is a definite no.

In order to understand why, you have to first understand why this mathematical model was developed in the first place.

You will often reach a point in the tournament, in which the few remaining players are deciding who gets which share of the payout. The blinds are too high for any one player to have an edge against the others.

A method was needed in order to determine how much of the prize pool belonged to each player based on his present stack size. After heavy discussion it was decided that the ICM was the best way to do this.

This approach is based on the assumption that a stack with the size 'n' is worth just as much as n stacks of 1, which relies upon conditional probabilities in order to be true.

According to "The Mathematics of Poker," the ICM formula used to day comes from horse racing. This model doesn't work as well with horse racing as it does with poker tournaments, however, since the horse that is favored to win rarely takes second when it fails to win. The reason for this: When a horse that is favored to win loses, it is usually injured.

Keep in mind that the ICM is not the same thing as the SNG Wizard (which uses the equity value estimated by the ICM to determine the equity of a push, for example).