Idependent Chip Model - What is ICM?
written by: John
The Independent Chip Model (ICM) is a mathematical approach to sit n go's and multi table tournaments. Chips are assigned a value based on the number of chips in play, the number of players left, stack distribution, the prize pool and payout distribution. Using all of this information, you can then determine how much equity in dollars you have in a tournament.
For example, my standard game is the 18-man turbos on PokerStars. The $6.50s have a prize pool of $108 and pays out at the rate of 40% for first, 30% for second, 20% for third and 10% for fourth. 27,000 chips are in play. Let's assume 5 players are left (bubble) and the chip leader has 14k in chips, 2nd place has 5k, 3rd has 4.5k, 4th has 3k and 5th has 500 chips. Here is each player's equity in the tournament based on all of this information.
1. 14k chips: $35.45
2. 5k chips: $25.09
3. 4.5k chips: $23.94
4. $3k chips: $19.53
5. 500 chips: $3.97
Now, equity is calculated on a hand-by-hand basis. In other words, if the chip leader were to pass $1k chips to the player in 5th place the next hand, then each player's equity in the tournament would shift as a result with the player's losing/winning the chips seeing the bulk of the changes.
How to Use ICM
Now, you don't need to be able to crunch the math behind the equity calculations above in order to become a profitable sit n go or multi table tournament player. In fact, I don't even know how and have no desire in trying to show you. There is software and calculators out there to do that for us. But you do want to have an understanding of what variables go into determining your equity in a tournament as the decisions you make in the later stages will have a drastic affect to these variables, thus affect your equity.
The proper way to use ICM is as if it was a risk versus reward model. In other words, you are often going to be faced with the decision of having to go all in and you will need to know if the hand you are holding is likely to increase your equity in the tournament or not. If it will, then you will more than likely take the chance and if not, you'll often fold. The most common situation where you'll be faced with this decision is on the bubble where one more player is left to bust before everyone else makes the money. At all costs, you do not want to be that "one more player" to bust and not make the money. Using ICM properly will help.
The first step to using ICM properly is putting your opponent's on a range of hands. This is the most important step and if you don't do this, than ICM is useless. You don't have to put your opponent on a single hand, but a range of hands will do just fine.
The next step is figuring out the equity your hand has versus your opponent's range. If you don't have these numbers memorized (don't worry, it takes time), then you can use a tool such as Poker Stove to do it for you.
Once you have this calculation, you will then need to determine your equity in the case that you win, fold and lose. You will then take your equity from the times you win and multiple it by the times your hand wins and then add that to the times you lose multiplied by your equity if you lose to get your new prize pool equity. The equation looks like this:
(win % * equity when you win) + (lose % * equity when you lose)
You will then take the outcome from this equation and compare it to your equity if you were to just fold. If in comparison you'll gain equity, then you will want to call/shove and if it's lower, then you'll want to fold.
If this is a bit confusing, don't worry. In Part II, I will have a real game example where I will explain this formula in a bit more detail.
Understanding cEV and $EV
Before I get started with my ICM example, I first wanted to explain the differences between cEV and $EV. This is another important concept to understand because each will have an impact on what hands you choose to play.
cEV stands for "chip EV" and is no different than playing in a cash game. In other words, the chips are worth their face value. So for example, if you were to get TT all in preflop versus a 25% hand range (66+, A2s+, A7o+,K6s+,K9s+,Q8s+,QTo+,J8s+,JTo+,T8s+), you would win 61.21% of the time. If you were getting in $100 stacks preflop, you could then expect to earn $122.42 over the long run.
$EV stands for "dollar ($) EV" and actually refers to how much money of the prize pool you stand to gain or lose with a given play. This is calculated using the formula I outlined above and then figuring out the difference in your equity between folding and calling.
It's important to realize that just because your hand is a +cEV play, it's not always going to be a +$EV play. In fact, in most cases the equity you risk is far more than the equity you hope to gain. What this means is that you'll actually want to be tighter in $EV situations in comparison to cEV situations.
Just so you're aware, all 9-man sit n go's will automatically be $EV while multi table tournaments will be cEV to start and progress to $EV once you make it to the final table. This is especially important to remember when reviewing your hands in a program like sit n go wizard because the hands you're told to push or fold will drastically be different between the two settings.
This concludes part I of the Independent Chip Model. In part II, I will cover a real hand example and explain how to use the formula outlined above. Additionally, I will cover a few tips that will show you how to further use ICM to your advantage to gain an edge over your opponents.