The Independent Chip Model Explained

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Yawn.  I'm already bored.

But wait...this is worth knowing.  Being able to make even basic ICM calculations is a tool every tournament player should have in their toolbox.

The ICM model allows you to estimate the real world value of your chip stack at any given moment in a tournament.

The reason you should know a little about ICM is because it can, and should, affect some of your decisions in tournaments - especially at the later stages.

Why is ICM only used in tournaments?

In the case of a cash game, if you have $500 in chips in front of you then the real world value of those chips is....$500.  So, if you're facing an all in and you have more than 50% equity, it's going to be a profitable long term play to call off your chips. a tournament situation, even if you win every chip in play you still only win a portion of the prize pool.  Unlike a cash game, having 10% of the chips in play in a tournament doesn't mean your stack has a real world value of 10$ of the prize pool.

Your tournament chips real world value, and any given moment in a tournament, will depend on the following:

- Your percentage of the total chips in play
- The prize pool distribution
- The distribution of chips in other players stacks

There are times where chips can also be worth more or less depending on how likely you are to cash in the tournament.

cEV versus $EV

cEV stands for "chip expected value", and is what you're used to calculating in cash games.  You're facing a call, you calculate your pot odds, and if you have the right price you make the call.  By doing this, you're calculating cEV.

$EV ("expected value in dollars") only applies to tournaments and quantifies what your tournament chips are worth in real world dollars.  $EV will never be equal to cEV.

Now, the calculations for $EV are complicated, and basically impossible to calculate on the fly in a tournament.  But, getting exact numbers isn't really necessary.

By using ICM tools available online, and some basic knowledge of the concept of ICM, you can make reliable estimates and use that information to make better decisions at the table.  Also, the deeper you get in a tournament, the easier the calculations are to make - which is perfect because that's when they're the most important.

ICM Example

Let's say we're playing a 10 man SNG, and the buyin is $100 for a total prize pool of $1000.  There are four people left in the tournament, and the prizes are:

1st: $500
2nd: $300
3rd: $200

So, if the four remaining players each had exactly 25% of the chips in play, the calculation would be easy and everyones stack would be worth $250.

But...and this is the far more likely scenario, what if one player had 70% of the chips in play and the remaining three players collectively had 30%?  The largest stacks real world value can't be $700 because the largest prize amount is $500.  This is where the ICM magic happens.

We can't just say that the player with 70% of the chips will win the tournament every single time, so in reality his stack can't even be worth as much as the first place prize of $500.

With stacks sizes of 7,000 - 1,000 - 1,000 - 1,000 chips and the payouts above, here's what the real world value of each stack would be using an ICM Calculator:

7,000 is worth $431.67
1,000 is worth $189.44 each

Notice that while the short stacks only have 10% of the chips in play, their chips have a real world value much higher than 10% of the prize pool.

Why you should learn ICM

ICM is an especially valuable tool when you're on the bubble in a tournament where it's the difference between cashing or not, and on the final table where pay jumps can be huge.

Simply understanding how ICM work will help you make more informed decisions at the more important stages of a tournament.  It will also let you know when to put pressure on your opponents by shoving a wider range and force some folds due to ICM factors.

Today's article is just a brief overview of ICM.  Next time, we'll take a deeper look and look at some actual tournament situations and how ICM should influence your decisions.