In poker, the Independent Chip Model (ICM) is a mathematical model used to calculate a player's overall equity in a tournament. The model uses stack sizes alone to determine how often a player will finish in each position (1st, 2nd, etc.). A player's probability of finishing in each position is then multiplied by the prize amount for that position and those numbers are added together to determine the player's overall equity.^[1][2]

Beginning Sunday, the WSOP has built a hybrid model for the tournament where players will play online for a projected two days until the field has been whittled down to nine for the final table. ICM – is a mathematical model used to calculate player’s equity in the tournament according to a number of chips he is holding. Therefore, this model plays a huge role in effective poker tournament strategy. What Is The Independent Chip Model (ICM)? How to use ICM Easy-to-understand guides for the independent chip model (ICM) in poker are few and far between, so I'm going to try hard to keep this article as concise and relevant to improving your Sit and Go tournament game as possible. ICM stands for ‘Independent Chip Model’ and represents how the value of chips change over time as a tournament progresses. Unlike in cash games where the value of each chip is fixed, the value of a chip in a tournament reduces over time as nobody can win 100% of the prize pool even if you accumulate all the chips in play. How to Use Tournament as Part of Your Poker Strategy. Strategy approach to tournament games are notably different than strategy approach to cash games. For a start, not all chips are equal in tournaments. A technique known as ICM (independent chip model) needs to be employed in order to correctly assign chips a monetary value.

The term ICM is often misunderstood to mean a simulator that helps a player make decisions in a tournament. Such simulators often make use of the Independent Chip Model but are not strictly speaking ICM calculators. A true ICM calculator will have the chip counts of all players, as well as the payout structure of the tournament, as input and each player's equity as output.^[3]

The ICM can be applied to answer specific questions, such as:^[4][5]

• The range of hands that a player can move all in with, considering the action so far and the stack sizes of the other players still in the hand
• The range of hands that a player can call another player's all in with, and recommends either calling or moving all in over the top, considering all the stacks still in the hand
• When discussing a deal, how much money each player should get

References[edit]

1. ^Fast, Erik (2012-03-20). 'Poker Strategy -- Introduction To Independent Chip Model With Yevgeniy Timoshenko and David Sands'. cardplayer.com. Retrieved 12 September 2019.
2. ^'ICM Poker Introduction: What Is The Independent Chip Model?'. Upswing Poker. Retrieved 12 September 2019.
3. ^Walker, Greg. 'What Is The Independent Chip Model?'. thepokerbank.com. Retrieved 12 September 2019.
4. ^Selbrede, Steve (2019-08-27). 'Weighing Different Deal-Making Methods at a Final Table'. PokerNews. Retrieved 12 September 2019.
5. ^Card Player News Team (2014-12-28). 'Explain Poker Like I'm Five: Independent Chip Model (ICM)'. cardplayer.com. Retrieved 12 September 2019.

Further reading[edit]

• Harrington, Dan; Robertie, Bill (2014). Harrington On Modern Tournament Poker. Two Plus Two Publishing LLC. ISBN1-880685-56-6. Harrington discusses the ICM on pages 108-122.
• Collin Moshman (July 2007). Sit 'n Go Strategy: Expert Advice for Beating One-Table Poker Tournaments. Two Plus Two Publishing LLC. pp. 122–. ISBN978-1-880685-39-6.
• Jonathan Grotenstein; Storms Reback (15 January 2013). Ship It Holla Ballas!: How a Bunch of 19-Year-Old College Dropouts Used the Internet to Become Poker's Loudest, Craziest, and Richest Crew. St. Martin's Press. pp. 17–. ISBN978-1-250-00665-3.

ICM or “Independent Chip Model” is a term which will inevitably cross your way if you’re a poker tournament player. In this article we want to explain in detail what ICM means in poker and what this model is used for.

What is a chip worth in a poker tournament?

The background to ICM is a very simple question: What is a chip worth in a poker tournament?

For a poker player in a tournament it is important to know how much his chips are worth at each moment. The specific question is: How much prize money can a player expect to win with his chips in the long run?

How much is it worth doubling your stack, how catastrophic is it to lose half your stack? Such questions are essential for a tournament player. But the special nature of poker tournaments doesn’t make it easy to answer those questions. Having twice as many chips doesn’t mean you will win twice as much in the long run.

Often it’s more important to simply survive the bubble with a few chips than to have slightly more chips. Just by looking at the number of chips you have, you can’t tell exactly how well you’re doing in a tournament. You also need to know what these chips are worth.

Measuring the value of chips

Let’s examine the question “What is a chip worth in a poker tournament?” using an example:

Example Tournament

• Buy-In: $10
• Players: 10
• Payouts: 1. $50, 2. $30, 3. $20
• Initial stack: 1,000 chips

If every player gets 1,000 chips at the beginning, they are worth exactly 10 dollars before the first hand is dealt (we just ignore rake to make things easier). But as the game progresses, the value of these chips changes and 1,000 chips can be worth a lot more and a lot less than $10.

Poker Tournament Models 2019

• Chips can be worth more: Let’s say a specific player barely makes it through to the last three and still has only 1,000 chips, while his two opponents each have 4,500 chips. Then these 1,000 chips are obviously worth at least 20 dollars, because the prize money for third place is guaranteed. Even if a player made it to the last three with just one chip, that single chip would still be worth $20 – so the value of the chips can increase drastically during the tournament.
• Chips can be worth less: At the same time, the value of chips can also decrease: Whoever wins the Sit-And-Go at the end will have all 10,000 chips, but will only receive $50 prize money. So his chips will only have a value of $5 per 1,000 chips.

For a long time there were different models that tried to explain how much a chip is actually worth. In the excellent, albeit rather theoretical book Mathematics of Poker, various methods of assigning a definite monetary value tournament chips were discussed. In the end, the “Independent Chip Model”, or ICM for short, prevailed.

How does the ICM work?

The ICM considers the stacks of all players remaining in the tournament and the payout structure. With this information the ICM algorithm calculates the expected value for each remaining player. This algorithm is rather difficult, we give a brief explanation.

Here’s how the ICM algorithm works:

• Probability of finishing first: First the stack sizes are used to calculate the probability for each player to finish first. The model simply assumes that a player with X percent of all the chips also wins the tournament in X percent of all cases.
• Probability of finishing second, third, etc.: Then, in a similar way, the model calculates for each player how likely it is that he will come second, third, fourth, etc. However, these calculations are much more complicated. The probability that a player will finish second place is calculated by looking at all cases in which the player does not win. Then the stack of the winner is removed and the probability that the player will finish second is determined by the proportion of his chips to the remaining chips and all the probabilities weighted are added together. The same procedure is used for the other places.
• Expected Values: In the end the model multiplies the probabilities for each player’s finish distribution with the payouts, adds them together and gives an expected value for each player.

You can’t do such calculations in your head, because for 4 players you already need dozens of arithmetic steps. But fortunately there are a lot of ICM calculators online. For example try our advanced ICM Deal Calculator.

ICM in tournaments using an example

Let’s take the above example tournament again:

Example Tournament

• Buy-In: $10
• Players: 10
• Payouts: 1. $50, 2. $30, 3. $20
• Initial stack: 1,000 chips

Suppose there are still 4 players in the tournament and those are the chip counts:

Chip counts of the last 4 players

• Player 1: 5,000 chips
• Player 2: 2,000 chips
• Player 3: 2,000 chips
• Player 4: 1,000 chips

What are these chips worth according to the ICM model? We simply enter the data into an ICM calculator and obtain the following result:

ICM value of these stacks

• 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

This means that if all players are equally good, they will win those amounts of prize money in the long run. Player 1, with half of all chips, can expect much more than the prize money for second place, players 2 and 3 can expect a little more than the prize money for third place and even player 4, who has the fewest chips, can expect to win some prize money in the long run.

Making decisions with the help of ICM?

How can ICM help to make meaningful decisions in tournaments? Let’s go back to our example.

For the sake of simplicity, we will pretend that there are no blinds and examine a specific tournament situation:

Example situation in a tournament

• Player 1: BU – 5,000 chips
• Player 2: SB – 2,000 chips
• Player 3 (Hero): BB – 2,000 chips – holds A♥ 9♦
• Player 4: UTG – 1,000 chips

Action: Player 4 folds, player 1 folds, player 2 goes all-in (2,000 chips), player 3 … ?

Player 3 is exposed to an all-in and what should he do now? Let’s say he knows his opponent, player 2, very well and estimates that he bluffs quite often and only sometimes has a better hand. Overall, player 3 expects to win the showdown in 60 percent of all cases when he calls.

So should he call the all-in?

Three things can happen now:

• 1. Player 3 folds (all chip stacks remain the same).
• 2. Player 3 calls and wins (player 3 now has 4,000 chips, player 2 is out).
• 3. Player 3 calls and loses (player 2 now has 4,000 chips, player 3 is out).

For each of these potential chip constellations we can calculate the ICM expectation:

ICM expectations after fold and ICM expectations after call

The table shows, if player 3 calls and wins, his 4,000 chips have an expected value of $36.44. But if he calls and loses, he has no more chips and his expected value for the tournament is $0.

Since player 3 can estimate how often he wins the showdown (60 percent), you can simply calculate his expected value for a call:

On average, a call is worth $21.86. If Player 3 folds, however, his chips have an expected value of $24.33 – around $2.47 more.

This means: in this specific example situation, the ICM advises a fold although the player has on average a much better hand than his opponent.

Why is a fold better in this situation when the player is the clear favourite in the hand?

Simply put: the short stack, player 4, is to blame. For player 3, it is much more profitable to wait for him to bust, rather than endangering all his chips. If player 3 simply waits, he will most likely at least secure the prize money for third place, but if player 3 gets involved in an all-in, there is a very realistic chance that he will be eliminated without a payout.

The ICM takes this into account and advises him to fold.

Quick ICM Poker tips

Now you can’t just do such ICM calculations at the table, but there are numerous ICM trainers on the net which can help you play through such scenarios using example situations. Here are a few tips on how to play correctly according to ICM:

• Call tighter: The ICM always advises that you should call tighter in tournaments than in cash games.
• More chips, less value: According to ICM, the first chip you have is always the most valuable. Doubling the stack is always less than twice as valuable.
• Impact before the bubble: The ICM has the strongest impact just before the bubble and around prize money jumps in the tournament.
• Avoid narrow All-Ins: According to the ICM, you should avoid narrow All-Ins when there are players with fewer chips in the tournament.
• Caution with medium sized stacks: Coinflips or All-Ins where you are only a narrow favorite should be avoided with a medium sized stack before or at bubble and you should prefer to fold.
• Play reckless as the big stack: Players with large stacks should very often threaten players with medium stacks with All-Ins, because according to ICM they can only call with very few hands.
• Threaten tight players: If the opponents have an understanding of ICM (or generally play very tightly), you should threaten them with All-Ins particularly frequently.
• Leave loose players alone: If the opponents do not have an understanding of ICM (or call very loose in general), you should also play much tighter yourself.

The Limits of ICM in Poker

Poker Tournament Software

The Independent Chip Model is currently the best known method for accurately measuring the value of chips in poker tournaments. But ICM is also not free of disadvantages. Some of these are:

• No position: The ICM does not consider a player’s position (a 4 big blind stack on the button is generally worth much more than a 4 big blind stack in first position).
• No skill: The ICM does not consider the players’ skills.
• No future: The ICM does not take into account possible future developments (sometimes it is better to avoid a narrowly profitable situation, since better ones might open up later).

Poker Tournament Structure

Very often ICM is used when calculating deals in tournaments, because it is the fairest model to give the stacks of the players a concrete value. So if you ever get into the situation of wanting to negotiate a deal in a tournament, an ICM calculator is recommended.

Relevant Resources

• Advanced ICM Calculator
• Introduction to ICM Poker (Upswing Poker)
• Mathematics of Poker (Amazon)
• Ben Sulsky, Quick ICM Intro (Run It Once Video)

Poker Tournament Simulator

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