Independent Chip Model Part 2 – Using The ICM Model

This is part 2 of a 3 part series detailing the specifics of the ICM model. The first part is an overview of the independent chip model. The 3rd part is a review of ICM calculators that will help with the complicated calculations in this article.The 2nd part of this series will show you how to use the ICM model to improve your chances of winning S&G tournaments and increase your ROI in the long run.

*Warning* This article is very math heavy. If you don’t care how to calculate ICM calculations, visit my review of the best ICM calculators to reap the rewards without doing the heavy math.

In the first part of this series we explained what the ICM model was. Now we’re going to go more in detail by explaining the calculation behind it and to do so we’ll use an example.

You are playing a $10+$1 6 player tournament at Full Tilt Poker with the following prize distribution:

Total Prize Pool: $60

1st: 50% – $40

2nd: 30% – $20

There are 4 players remaining with the following chip stacks:

Player 1: 4,500

Player 2: 3,000

Player 3: 1,500

Total: 9,000

In order to determine the equity of each player we need to establish each player’s odds of finishing in each of the two paid positions as well as the non-paid position. The calculations are fairly simple for this.

Player 1 finishes 1st – 4,500/9,000 = 50%

Player 2 finishes 2nd – 3,000/4500 = 66.67% *

Player 3 finishes 2nd – 33.33%

* Remember we assume player 1 will win, therefore the his 4,500 chips are not taken into account.

Player 2 finishes 1st – 3,000/9,000= 33.33%

Player 1 finishes 2nd – 4,500/6,000= 75%

Player 3 finishes 2nd – 25%

Player 3 finishes 1st – 1,500/9,000= 16.67%

Player 1 finishes 2nd – 4,500/7,500= 60%

Player 2 finishes 2nd – 40%

Player 1 will finish 2nd: 33.33% * 75% + 16.67% * 60% = 34.99% of the time

Player 2 will finish 2nd: 50% * 66.67% + 16.67% * 40% = 40% of the time

Player 3 will finish 2nd: 50% * 33.33% + 33.33% * 25% = 24.99% of the time

From these calculations we can now easily determine the probability of each player finishing in 3rd place.

Player 1 finishes 3rd: 100-(50+34.99) = 15.01%

Player 2 finishes 3rd: 100-(33.33+40) = 26.67%

Player 3 finishes 3rd: 100-(16.67+24.99) = 58.34%

Now let’s determine each player’s equity. The calculation is very straightforward:

(Probability of 1st)(Payout For 1st) + (Probability of 2nd)(Payout For 2nd) + (Probability of 3rd)* (Payout For 3rd)

Player 1 equity: (50% * $40) + (34.99% * $20) + (15.01% * $0) = $26.99

Player 2 equity: (33.33% * $40) + (40% * $20) + (26.67% * $0) = $21.33

Player 3 equity: (16.67% * $40) + (24.99% * $20) + (58.34% * $0) = $9.66

As you can see calculating the ICM manually is very time consuming and completely impractical when you are playing online poker with a 30 second timer. Fortunately there are several calculators available on the internet that will do the calculations in a fraction of a second. We will cover the most popular of these in the next part of this series. The purpose of this exercise was to show you how the numbers are calculated as a way of helping you understand what the numbers mean.

So now that you know how the numbers are calculated, let’s use a more practical example.

  • You are holding 10?-10? and you have 3,000 chips.
  • The blinds are at 300/600.
  • You are in the BB, player 1 is in the SB and player 3 is on button.
  • Player 3 moves all-in for 1,500 chips, the BB folds and now it’s up to you to act.

Now you need to analyze the three possible outcomes.

Outcome #1 – You call and win

Chip stack; 4,800

Probability of finishing 1st: 53.33%

Your equity: $30.32

You equity increased by $8.99 or 42% and now your chances of finishing 1st have increased by 20%.

Outcome #2 – You call and lose

Chip stack: 900

Probability of finishing 1st: 10%

Your equity: $7.33

Your equity has decreased by $14 or 65% and now you are in danger of finishing out of the money.

Outcome #3: You fold

Chip stack: 2,400

Probability of finishing 1st: 26.67%

Your equity: $16.96

Your equity has decreased by $4.37 or 20%

Again it’s important to reiterate that these numbers are completely meaningless unless you can effectively put your opponent on a specific range of hands. As you will see in the next section of this series several ICM calculators will ask you to enter a range of hands you expect your opponent would push all-in or calling an all-in. This is why it’s important to pay close attention and take notes on every player at the table.

Player 3 has 1,500 chips and with the blinds at 300/600 he only has approximately 3 BB left so the range of hands with which he could push all-in is very wide. Although throughout the tournament you have characterized this player as very tight and plays strong hands so it’s safe to assume he has something along the lines of A-K, A-Q or pocket pairs such as 10-10 or better. Let’s assume your opponent is holding A?-K?

10?-10? vs.A?-K? = 54.01% vs. 45.54%

Your average expected value if you call is (0.5401 * 0.5333) + (0,4599 * 0.1) = 33.4%

Compare this with the EV of folding which is 26.67%

Let’s put a dollar value to this equation and you get:

(0.334 – 0.2667) * $60 = $4

By calling the all-in everytime you will average an extra $4 in the long run therefore the decision is now very easy to make, you call the all-in.

Hopefully by now you have a clearer understanding of the Independent Chip Model and how it can be used to make calculated decisions that can improve your ROI in the long run. In the next section we will review some of the tools available online to simplify the process.

Click here for Part 3 – Reviews of the best ICM calculators