# The Independent Chip Model (ICM)

By Jennifear

Independent Chip Modeling (ICM) determines your equity share of the prize pool in a tournament based on the stack sizes of the remaining opponents and the probability of your finish. With these probabilities, a dollar value can be associated with your stack size.

ICM is usually much more prevalent in SNGs, but can also apply when there are large payout jumps at the final table of a tournament. Most experienced SNG players are very familiar with ICM and it’s use, but may not understand the mechanics behind it, or how to calculate it by hand.

The need for ICM stems from a non-linear value of tournament chips. In all SNGs that are not winner-take-all, or in the heads-up stage, the chips that you risk will be of a lesser value than the chips you stand to gain.

For example, in a 6-man \$20 SNG, with prizes of \$84 for first place, and \$36 for second place, you start with 1500 chips worth \$20. If you win you’ll finish with 6 times as many chips as you started with (9000), which are worth 4.2 times as much money as you started with (\$84). That may not seem fair, but all of the prize money is distributed at the end, so if you know how to use ICM as a weapon, you will end up with the lion’s share of the prize pool much more often than 1 in 6 times.

## The Mechanics behind Calculating ICM

Let’s look at the mechanics behind calculating ICM using an example situation:

• \$20 No Limit Hold’em SNG – 6-man.
• Prizes: \$84 / \$36
• Starting stacks: 1500 (total chips in play = 9000).
• Rick has 4500, Stu has 2700, and Mark has 1800.
• Blinds: 150/300.

The formula starts by calculating how much equity each player has in 1st place money, by looking at what percentage of the total chips a player has in play, and multiplying that by first prize (\$84).

From there, the formula has to determine how much equity each player has in second place money (\$36).This is a bit more complicated than determining first place equity, but it’s still doable by hand.

If Rick doesn’t win, there are a couple of ways he can take second place. His equity in second prize is the sum total of his equity for the times he doesn’t win, but he beats the remaining player. We will calculate the equity he has in second prize:

We should do the same for Stu:

and Mark:

…and if you add it up, this is what you get:

Armed with this information each player can use it to their advantage. Rick should know that he can shove on Stu’s big blind quite frequently. Stu will know he is risking \$38.70 when he calls, and will get barely half of that back when he wins, so he will have to win more than 60% of the time to make a call if Rick pushes on him, and since only some hands win that often against Rick’s wide pushing range, he will fold a lot. Mark will know that if the others are in a lot of pots together, he may end up getting second by default, which drives his equity up from \$27.09 to at least \$36 (second prize) on a hand where he folded before the flop!

## The Limitations of ICM

Independent Chip Modeling (ICM) is one of the most accurate ways to analyze the current value of your chip stack in a Sit & Go. But because it’s a purely math-based formula it misses some intangibles that the math doesn’t account for that should affect your decisions.

Lets look at some of these intangibles.

### ICM Underestimates the Chip Leader’s Value

This is by far the biggest limitation of ICM. If we’re playing a \$20 SNG with a total of 13,500 chips in play (9-man, 1,500 starting stacks), and the remaining stacks are as follows; 6750, 2250, 2250, 2250, then ICM calculates the equity of the 6,750 stack by assuming that since he has half of the chips in play (6750/13500 = 50%), then he will win half the time. However, even if these players are equally skilled, the 6,750 stack will be able to use his leverage to dominate the table, and perhaps win as often as 60-65% of the time. This means that being the chip leader is an advantage that ICM does not account for.

If you’re the chip leader, call a push less often than ICM would suggest that you do to protect your lead. If you’re a middle stack and calling would give you the chip lead, then call wider than ICM would suggest so that, should you win, you get to reap the benefits.

While a tight game is the cornerstone of early-game success, don’t over do it by making drastic changes to your ranges by playing much tighter than you would in a cash game or MTT. Simply play slightly tighter in a SNG than these other formats. By accumulating chips in the early going, you are setting yourself up to have the chip lead going into the bubble phase of the game, and you’ll enjoy this benefit.

### ICM and the Position of the Blinds

ICM doesn’t account for the position of the blinds. This is important to remember especially when the blinds get high, or when two players have very short stacks. Here is an example. Stacks 7100, 4900, 600, 400, with payouts of \$45 ,\$27, \$18. Blinds are 300-600. Here is the ICM calculation:

In this situation, with the blinds at 300-600, ICM shows that Mark’s stack is worth \$12.99 and Doyle’s is worth \$8.73. The truth of the matter is that the biggest consideration is which player will be in the big blind next. Should Mark have to play from the big blind before Doyle, then Doyle’s equity is higher than Mark’s because Doyle is facing elimination first.

If you are going to eat a big blind that is more than one-third of your stack soon, before anyone else will, then shove wider to protect your stack. You don’t want to be forced to call with a bad hand in the big blind.

If you’re short stacked but someone else will face elimination before you within the next few hands, play a very tight range.

### ICM Assumes Fixed Blinds

ICM assumes fixed blinds and does not account for blind increases, or fold equity. One of your largest weapons in poker, other than your chips and your cards, is your fold equity, which is your ability to win an uncontested pot when you push your chip stack. Your fold equity diminishes as your chip stack diminishes, but should you drop below 5 big blinds, your fold equity diminishes drastically, as your opponents will often be committed to call any push you make.

If you have 5-9BB or 8-12BB with the blinds about to increase, you are in a position where your stack will likely drop. In this situation you are in immediate danger of falling below this 5BB threshold. ICM calculates the number of chips you have divided by the number of chips in play to determine your equity, so it has no knowledge of this.

If you are using an ICM calculator to determine your pushing range and you are going to lose your fold equity if you do not push, then push wider than recommended.

If a solid player is in danger of losing their fold equity, and they push, realize they may be shoving a wider range, and call slightly wider than ICM recommends.

If the other effective stacks are dropping below 5BB as well, then do not push wider, because even if you gain chips, your fold equity is gone anyway, as your opponents with 4BB and less will call you with a similar range whether you have 4BB, 6BB, or 14BB.

### Conclusion

Understanding the concept of ICM fundamental to success in SNGs. You don’t need to be a math geek to understand ICM – just being aware of the concept is the most valuable knowledge a successful SNG player can possess. If you can find a hand history of your own, then take an example of two, and work through it yourself. Play around with ICM calculators and study situations away from the table. It’s a great way to learn.

As was said at the beginning of this lesson – due to the non-linear value of tournament chips, the chips that you risk will be of a lesser value than those you stand to gain. Therefore the most important thing to remember is that your last chip is always going to be your most valuable chip. If you’ve fully grasped this concept then you’ll know that your chips and the leverage they provide is your biggest weapon.

Jennifear is an online professional MTT and SNG player. She is a well-regarded, highly experienced and hugely popular poker coach who has taught hundreds of successful players.

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