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ICM: Independent Chip Model

ICM in Poker - Independent Chip Model - Poker Tournament Math

The independent chip model (ICM) is a formulaic method of determining what a player's current chip stack in a poker tournament is worth in real money.

To simplify, ICM helps figure out how much a player will earn on average depending on how many chips he or she has in the tournament at a given time.

Using ICM, players will be able to answer important questions in regards to their tournament play.

These could include which hands would be profitable to call all-ins with, which hands you can open push all-in with, and in which spots being the aggressor would be the better play.

Calculating ICM

Although it would be nice if there were a simple equation to determine the cash value of a player's stack on the fly, the reality of ICM is that it includes an immense amount of calculations. That being the case, it is highly recommended that players looking to find their prize pool equity use ICM calculators.

Still, let's look at ICM with simplified numbers:

Consider four players are left at a $10 Sit & Go table that started with ten players and each player started with 1000 chips. The payouts are the standard $50, $30 and $20 for first, second and third, respectively. If each of the four players has 2,500 chips, their chip value in regards to ICM would be $25 each. However, that congruency among players is rarely the case, so let's distribute the chips a little less evenly, as such:

  • Player 1 has 4,500
  • Player 2 has 2,500
  • Player 3 has 2,000
  • Player 4 has 1,000

Upon entering these figures into an ICM calculator, we can see each player's cash equity:

  • 4,500 chips are worth $35.44
  • 2,500 chips are worth $27.09
  • 2,000 chips are worth $23.85
  • 1,000 chips are worth $13.61

What this means is that on average and assuming equal skill level, each of these players will make the amount of money that the ICM calculator has determined their stacks to be worth.

Using ICM to Make Moves

The majority of ICM-based decisions end up happening on the bubble since, at that point in the competition, players simply want to reach a payout. ICM figures combined with equity value (EV) estimates can help make smarter moves to more often reach the money.

If you are player three from the previous example and have 2,000 chips, pushing all in with any two cards against player four with 1,000 chips will still leave you with a chip stack that's actually worth something.

However, if you're against player one or two, risking your poker tournament ICM calculated value can be a bad decision, even in cases where you begin the hand as a 60 percent favorite with something like A♣T♣ or J♦J♠.

When ICM Trumps Positive EV Moves

Though many players treat +EV plays as the ultimate deciding factor, situations arise where ICM figures are more important. As discussed before, these happen specifically around the bubble.

Consider you have the aforementioned hand A♣T♣ and are against player one who's a wild player. If he or she makes a bet that puts you all-in at the bubble with your current hand, ICM determines that you should still fold even though 60 percent win rate means you have positive EV for that hand.

If you win the hand

The table ICM will look like this:

  • 2,500 chips are worth $26.70
  • 2,500 chips are worth $26.70
  • You - 4,000 chips are worth $33.50
  • 1,000 chips are worth $13.09

Also take note that since this play made the top three players closer in chip stacks, the equity value of player four dropped slightly from $13.61 to $13.09.

If you lose the hand

The table ICM will look like:

  • 6,500 chips are worth $42.39
  • 2,500 chips are worth $32.42
  • 1,000 chips are worth $25.19
  • You - 0 chips are worth $0

So, with your 60 percent favored hand, there are two outcomes from an ICM simulator. In the winning situation, your value has raised $9.65 to $33.50. In the losing situation, your value has dropped from $23.85 to zero. This means that calling the all in from the big stack is, though a +EV move, bad ICM poker strategy since you are risking $23.85 to earn $9.65.

Full Tilt Poker gives MTT & SNG players the option to chop heads up according to ICM.

ICM Calculators

Chimp v1.0 (Desktop Program)

ICMIZER (Web-Based App)

ICM Nash Calculator (Web-Based App, Detailed Explanations on Push/Fold Scenarios)