A Step-by-Step Guide to the Independent Chip Model (ICM) for Tournament Poker Players

A Step-by-Step Guide to the Independent Chip Model (ICM) for Tournament Poker Players

18-02-2014, 08:32

PokerOlymp's Arved Klöhn explains what this term means, how ICM is used in poker and why you should be familiar with it.

By Arved Klöhn

Let’s start with a very simple question:  

What’s a chip worth in a poker tournament?

To answer this question in a satisfying way is the whole purpose of ICM.

Why Should You Know the Value of Your Chips?

Let’s say you’re sitting in a poker tournament, have a comfortable stack and the bubble is approaching.

Wouldn’t you like to know how much money you can expect to win in the long run? What about doubling up?

Is it worth it to jeopardize your healthy stack right before the bubble? And how much would it hurt your expectation to lose half your stack?

The specific payout structure of poker tournaments makes all those questions quite tricky. Twice as many chips are not always twice as valuable.

Sometimes it's much more important to just survive the bubble (or the next payout jump) than to accumulate more chips.

Simply counting your chips will rarely help you to exactly evaluate your tournament situation. You have to know what your chips are worth.

Chips 2
The value of chips can increase enormously during a tournament.

What’s the value of a chip in a poker tournament?

Let’s take a very simple example. Say you’re playing a sit-and-go:

Buy-in: $10 # of players: 10 Payouts: 1st - $50, 2nd - $30, 3rd - $20 Initial stack: 1,000 Chips

Right at the beginning of this tournament 1,000 chips are obviously worth $10. But as the tournament progresses their value will change drastically.

Let’s assume you barely make it into the money and after seven players have busted you still have 1,000 chips. But now you’re guaranteed to receive at least third-place money.

Now your 1,000 chips are worth at least $20.

Even if you somehow made it into the money with just one single chip, this one chip would still be worth at least $20. The value of chips can increase enormously during a tournament.

But their value can also decrease. Let’s say you manage to win the sit-and-go. Then you will have all 10,000 chips, but only receive a $50 payout. So now 1,000 of your chips are only worth $5.

Over the years many brilliant poker players and theorists have tried to come up with a magic formula to assign an accurate value to the number of chips a player has. The book “Mathematics of Poker” even has a whole chapter dedicated to this subject.c

After a lot of hard work the poker community came up with the Independent Chip Model, which is now broadly used to attach precise monetary values to chip counts.

Every professional tournament player is familiar with this model and you should be too.

Bill Chen
Many brilliant poker players and theorists have tried to come up with a magic formula.

How ICM Works

The Independent Chip Model condenses the following two things into one value for each player:

The payout structure The stack sizes of all remaining players

Based on the stack sizes the ICM calculates for each player the probability of finishing 1st, 2nd, etc. and multiplies those probabilities with the payouts for each position.

To calculate the probability of a certain player finishing first it simply divides the number of his chips by the total amount of chips in play. The probabilities for finishing 2nd or lower are calculated in a similar but slightly more complex manner.

The calculations are in fact so complex that you usually need a computer. For 4 players one has to go though more than 20 steps of calculations. For 10 players you already need millions.

Fortunately many decent ICM calculators are freely available online.

One easy sample application of ICM

Lets go back to our previous sit-and-go example:

Buy-in: $10 # of players: 10 Payouts: 1st - $50, 2nd - $30, 3rd - $20 Initial stack: 1,000 Chips

Now lets assume after some time only 4 players are left and these are their stack sizes:

Player 1: 5,000 Chips Player 2: 2,000 Chips Player 3: 2,000 Chips Player 4: 1,000 Chips

Now what’s the value of those chips? Simply enter the stack sizes and payouts into an ICM calculator and you will get the following results:

Player 1: 5,000 Chips ≅ $37.18 Player 2: 2,000 Chips ≅ $24.33 Player 3: 2,000 Chips ≅ $24.33 Player 4: 1,000 Chips ≅ $14.17

If we assume all players are equally skilled, they can expect to win that much in the long run.

Player 1, holding 50% of all chips, will make considerably more than second-place money. Player 2 and 3 can expect to win a bit more than third-place money.

Even the short stacked Player 4 can expect to win some money.

Making Decisions Based on ICM

Call or fold? ICM will tell you.

Now we know what the chips are worth in the long run, but how does this knowledge help us make better decisions right now?

Let’s return to our example and, for simplicity'ss sake, let’s assume there are no blinds or ante in play and you are Player 3. The following situation comes up:

Player 1 (BU): 5,000 Chips Player 2 (SB): 2,000 Chips Player 3, you (BB): 2,000 Chips Player 4 (UTG): 1,000 Chips

Player 4 and Player 1 both fold and Player 2 goes all-in for 2,000 Chips. You hold Ace-Nine (unsuited) and …?

Should you call or should you fold?

Let’s further assume you know Player 2 pretty well because you play very often against him and you know he’s bluffing quite often in those situations. Overall you assume you will win the showdown six out 10 times if you call his all-in.

So you’re a favorite to win if you call but in tournaments it’s sometimes not enough to simply be the favorite. Let’s analyze the situation by using ICM.

Three things can happen after Player 2 goes all-in:

You fold (stack sizes stay the same) You call and win (now you have 4,000 chips and Player 2 is busted) You call and lose (now you are busted and Player 2 has 4,000 chips)

For all 3 situations we can now calculate the ICM values:

Stacks after fold ICM-EV Stacks after call and win ICM-EV Stacks after call and loss ICM-EV Player 1 5,000 $37.18 5,000 $38.89 5,000 $38.89 Player 2
2,000 $24.33 0 $0 4,000 $36.44 Player 3 (you)
2,000 $24.33 4,000 $36.44 0 $0 Player 4
1,000 $14.17 1,000 $24.67 1,000 $24.67

This means if you call and win you will have 4,000 chips and those chips will net $36.44 in the long run. But if you call and lose you will have zero chips and those will net you $0 in the long run.

We've already established that you win the showdown 60% of the time. So we can easily calculate your expected value (EV) for calling:

EV = 60% * $36.44 + 40% * $0 = $21.86

On average you can expect to win $21.86 if you call the all-in. Now let’s compare this number to your expected value if you simply fold: $24.33 – that’s over $2 more!

This means in this example the ICM advises a fold as the best play in the long run although you are a 60% favorite to win the hand!

ICM does the thinking for you.

But why is a fold the better option?

Simply put: Player 4, the short stack, forces you to fold although he isn’t even involved in the hand. It's much better for you to wait for him to bust than to jeopardize all your chips.

If you wait patiently he will probably bust before you do and you will have the third-place money guaranteed. But if you call the all-in, there is a very reasonable chance you will bust first yourself.

ICM takes those considerations into account and correctly advises you to fold.

How to Use ICM to Improve Your Tournament Game

Obviously you can’t run calculations like the one we just did on the fly at the table. You’re not going to calculate your expected ICM value during a poker game.

But ICM knowledge helps you tremendously to work on your game and to develop the right instincts for how to act and react in certain situations at the table.

Several ICM trainers are available online (unfortunately the good ones are not free), which guide you through many different tournament situations advising the best play.

It's a great start, but ICM isn't flawless.

Six Handy ICM Guidelines

ICM always advises to call with tighter ranges in tournaments than in cash games. The first chip you have is always the most valuable. Doubling your stack never doubles the value of your chips (it’s always less). Correct ICM play has the most impact during and before the bubble. Correct ICM play usually advises you to avoid narrow all-ins if there are players left with fewer chips than you. If you have a medium-sized stack during the bubble you should almost always avoid coin flips (or 60/40 all-ins) and fold instead. Big stacks should often threaten players with medium-sized stacks during the bubble because they can only call with very narrow ranges.

The Limitations of ICM

Currently the Independent Chip Model is the best-known method to value chips and evaluate tournament situations.

But although it's broadly used and acknowledged, ICM is not flawless. Some of the drawbacks are:

ICM does not consider the position of a player (a 4BB stack on the button is usually much more valuable than the same stack in first position) ICM does not take skill differences into account ICM does not consider potential future situations (sometimes it’s better to pass on small edges and wait for a larger edge).