An Introduction to The Independent Chip Model

Independent Chip Model (ICM) is a mathematical poker concept that attempts to put a value on each chip in a tournament. Figuring out the value of each chip can help you calculate your current equity in a tournament prize pool based on the stack sizes of the remaining players and the payout structure. ICM is far from perfect, based on a lot of assumptions, and debated a lot – but since many players use it, especially online, let’s present the basics of it here.

There is more value in playing a tournament than just getting first place. Every player with chips has a certain probability of coming in 2nd, 3rd, etc, and this is the same for all of the places that pay out. In ICM, a player’s chances of winning the tournament is equal to his/her share of the total chips. If you have half of the chips, your chance to win at that point in the tournament is 50%. If you possess 25% of the chips in play, you have 25% chance to win. If you have all of the chips, you win. Also, when your stack gets shorter, the value of each of your chips increases. A stack with 500 chips has more value in ICM than 25% of a 2000 chip stack. That is to say the standalone stack of 500 owns a bigger percentage of the total prize pool than 25% of a 2000 chip stack in ICM, even though the number of chips is exactly the same.

But ICM makes no assumptions about relative skill level, which is one of its major downfalls. It just assumes that your skill level is the same as the average skill level of all the players in the tournament.

To calculate your expected value based on your present number of chips, you take the probability of you finishing in each of the payout positions, multiply that by the corresponding prize 온라인 홀덤money, and add up all these pieces of equity. This is how you determine your expected value. Here is an example.

Pretend you are in a single table tournament. There is a $1000 prize pool, 2000 chips to start and there are 4 players at the bubble with 5000 chips each. The payout structure is the standard 50% for 1st, 30% for 2nd and 20% for 3rd (blinds are ignored to keep the math simple, and also because ICM does not adjust for blind amounts properly).

At this moment, each player has the same equity: $250.

Now pretend Player 1 is all in, and you are Player 2 and call. You win. So you now have 10000 chips, and Players 3 & 4 still have 5000 chips. So how did everyone’s equity change now that the bubble broke?

It follows that Player 1’s $250 of equity is going to be split amongst the remaining players in some kind of way; he is out of chips and wins nothing. And even though you now have a big chip lead, you are obviously not just guaranteed 1st place, so we know your equity will not be $500, but some amount that is less than that. It also stands to reason that your chip lead does give you more equity than the other two players. Using a basic ICM calculator, we see the new equity shares are as follows:

You: $383.30 (10,000 chips)

Player 3: $308.30 (5,000 chips)

Player 4: $308.30 (5,000 chips)

By calling Player 1, and winning, your equity increased $133.30. But to gain that extra equity, you had to put your entire $250 equity share at risk (if you called and lost, you win nothing). This means you laid almost 2-1 odds against yourself that you would break the bubble. Also, the moment you called, Player 3 and Player 4 gained $58.30 in equity, regardless of who won the all-in. They just sat there hoping you would call. This tells us that equity is gained by the other two players at the table who aren’t even in the hand. That equity had to come from somewhere. It came from the two players involved in the all-in.

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