# What is ICM

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14 November 2011
by Q.

## What is ICM??! This question is very popular and is asked by most novice poker tournament players. In this article I will try to shed some light on this topic.

In poker ICM stands for independent chip model. Now that definition is already interesting. Independent model - it is independent from what exactly? Actually model is independent from many things: player skill level, actual poker situation, blinds level, game dynamics, and this list can be continued. ICM is only important in context of tournament poker.

Now tournament poker is different from cash game in a simple way : your chips don’t really represent dollars, they are a currency that has some kind of exchange rate into dollars. This exchange rate is best known and understood at beginning of tournament – say you buy 1500 chips for 110$, and 10$ of that goes to rake. So if it was a hypothetical tournament with 1 player your 1500 chips would be worth 100$, and it wouldn’t make much sense to participate in such organized theft. In reality though tournaments have several players, and lets ignore HU sit and goes and extravagant 4-max tournaments, our minimum players tournaments generally start at 5-max games in OnGame for example. Here players can have 1500 stacks and if buy in was 100$+10$ 1500*5 =7500 chips will be representing a total prize pool of 100$*5= 500$. So at the start of tournament we can quickly evaluate chip value without any modeling stuff: its 500$/7500chips = 1/15$ for chip.

Now let’s get back to initial example with tournament and 1 participant. If tournament was to stop right now each player would receive 100$ and lose 10$ in rake. Again few would participate in this. So our quick conclusion is, in order to make money after paying 110$ our chip stack has to increase to some bigger value than initial 1500$ to become worth our initial buy in which was 110$. If we apply some naïve formulas it would mean that we need at least 150 chips so at stack of 1650 chips we will be worth 110$. Notice that this means that we gain those 150 chips from other players, and if we plan to play sit and goes on regular basis that will usually be expected from playing better than them.

I call this naïve because there is a little problem, once we have 1650 chips we aren’t guaranteed a payment, unless we happen to cash in tournament. We cash in Sit and Go after enough players have busted, and we get a prize that is specified by tournament payout structure according to our finish position. So in most tournaments there is no direct translation from chips to dollars. Actually in most poker tournaments only zero chips OR all chips of tournament get directly translated into dollars. And this translation is not done according to ICM, it is done according to payout structure. Player with all chips gets first prize of tournament, and players with zero chips get the rest prizes.

So zero chips get dollars, and players with chips aren’t getting money unless that’s all chips of tournament. This is when ICM comes into play. ICM or a model that is used to translate chip stack into expected dollar value does that by predicting that player will finish on given place with a calculated probability. Most ICM models that will convert chips into dollars will try to predict probability for each possible paid position. Once we know probabilities for respective finish positions we can quickly finish ICM calculation, and convert chips into dollars using following formula:

ICM EV$ = ProbabilityFinish1st * FirstPrize$ + ProbabilityFinish2nd * SecondPrize$ + … +ProbabilityFinishNth * NthPrize$

Now more specifically what ICM does: ICM assigns a dollar value to any static stack distribution in poker tournament. Notice word static, ICM deals with static situations. Now what is a poker ICM based decision? We evaluate probabilities of certain static stack distributions and calculate ICM equity for them. Next we calculate ICM equities and situation probabilities to get final ICM equity of situations. By situations I am referring to any poker hand outcome: our lost hand, our split pot, or victory or situation when we fold and someone pushes kings into someone’s aces and we get unexpected payday because it was bubble and we were a super short stack.

ICM is basically a function with 3 inputs, array of stacks, payout structure, and stack of interest. Given that, it returns ICM EV for stack of interest. Like in some situation stacks will be distributed as 3000, 3000, 1500 (chips), and we are interested in ICM equity of 1500 stack. ICM can answer such question with a dollar value answer.

Notice the word model. ICM is a model, it models actual poker situations which lead to players losing or winning with simplified mechanics which work alike real poker. ICM isn’t dealing with pocket cards, flops and rivers. Previously mentioned 3 inputs is everything ICM takes into consideration. As you can see 3 inputs aren’t including player positions, future hand possibilities, big blind values, antes or disconnected players. It also doesn’t include value of busting best player from tournament where the rest have no idea what to do with their cards or chips, each stack is only as valuable as chips in it.

This is our part 1 article on vast poker ICM topic.