We can say that every player who studies SNGs or poker tournaments has heard or seen the acronym ICM at some point. Independent Chip Model, a very useful and important mathematical part in poker, which seems scary at first, but becomes simple once you understand how it works.
Understanding ICM
To understand ICM, you need to know two things about poker: Pot odds and the mathematics behind it. When you start applying ICM, you will notice a big difference in your results at the end of the month of grinding.
There is a problem when calculating pot odds in tournaments. Chips do not have a fixed value. And how does this change our thinking? Chips have different values. If we compare the value of a player's last and only chip with the 10,000th chip in a 10K stack, the last chip is worth much more than the 10,000th, since if he loses the last one he will be eliminated from the tournament, while if you lose only this last chip, you will have 9,999 in chips left to play. Based on this thinking, we can understand that the amount of "money" used to calculate pot odds based on chips is not completely useful for analyzing our decisions in tournaments.
The idea behind ICM is that the amount of chips you have, compared to the total number of chips in the tournament, ultimately determines your probability of winning the tournament. You can calculate your probability of finishing in 2nd place, for example, based on the total number of chips in the tournament minus the chips of the 1st place finisher. This applies to all positions in the tournament. With this, you calculate how much you win by multiplying your probability of finishing in a specific position, arriving at a decimal number, which represents your expected share of the total prize pool, usually referred to as expected value (EV).
The math behind this may be complex, but the idea is simple and practical. There are several specialized calculators available to perform the calculations, such as the ICM Calculator. If you want to learn how to calculate manually, you can find several formulas available on the internet.
To continue the article, we recommend using an ICM calculator. Let's take the first example.
Example
There are three players left. The Button has 2,000 chips, you (BB) and the small blind (SB) each have 4,000 chips. This is a standard 10-handed SNG, which pays 50% to 1st, 30% to 2nd, and 20% to 3rd. The blinds are currently 150/300. Your hole cards are a nice pair of queens (QQ). The SB goes all-in, and from information gathered in the game, he knows that his opponent would only do so with AK. How do you calculate the math for this play?
In this case, we have three possible situations. The fold, the call that brings us victory and the call that brings us defeat and 3rd place. We will not consider a draw, since this would be very rare in this situation.
Let's start with the fold. The button would still have 2K chips and you would have 3.7K, while the SB would have 4.3K. With these numbers, the calculator gives us 0.3482. If the tournament had a buy-in of $10+$1, the expected value would be $34.82 with these three amounts of chips. In the long run, you will win $34.82 each time you face this situation. A good number.
Now, if you call and lose, you would have 0 chips and a 3rd place finish. The ICM would be 0.20000. Multiplying this by the long term, it is $20. If you call and win, you will have 8,000 chips, and the button will have 2,000. In the ICM calculator, the value will be $46 (0.4600).
What is the EV of calling? QQ will win approx. 56% of the time against AK.
This is a simple equity calculation that can be done with a program like PokerStove. Coming back to ICM, 56% of the time we will have an ICM of 0.46 and 44% of the time an ICM of 0.20. The average of this (0.56*0.46)+(0.44*0.2) is 0.3457!
Our expected value is very close, but lower! With the call we have 0.3457 and with the fold 0.3482. In this case, the best play in the long term will certainly be the fold. The difference between the two decisions financially would be $0.25. Although low, this value represents 2.3% of your ROI (Return on Investment).
Folding QQ may seem strange. Yes, it really is. In this example, we were certain that our opponent would only make such a play with AK. In a normal game, we could never be 100% sure of our opponent's hand, so we thought of a range of hands. In this situation, if we added some hands to our opponent's range, our QQ would certainly end up having a positive expected value, making the call worthwhile.
Conclusion
The main purpose of the ICM is to allow the calculation of what really matters in a tournament: the prize pool. You don't want to get into bad situations and risk losing large chunks of the prize pool without being the favorite to do so. The prize pool difference in a SNG may seem small, but in a larger tournament, the amounts jump drastically at the final table, so every wrong or right decision can cost you a small fortune, think about it.
Article adapted from: ICM – An Introduction
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Great post
We appreciate the compliment!