### ELI5: Independent Chip Model (ICM)

In a tournament your chips to not accurately represent actual \$-value.

Imagine you are in a normal 9-handed sit and go with a buyin of \$100 and 1000 chips each. Payouts are 50%/30%/20%

When you start the tournament 1,000 chips is clearly worth \$100 because that's what you paid to get them. BUT! When you win the tournament it is obvious they are worth less because 10,000 chips are now worth "only" \$500. The tournament chips are worth 50% of what they were when the tournament started.

ICM tries to better calculate the \$-value of tournament chips. It works like this:

1. You (player 1) have 50% of the chips? Cool, you have a 50% chance of winning the tournament.
2. Player 2 has 20% of the chips. Alright, he has 20% chance of winning.
3. Repeat step 2 for every remaining player. Now we know everyone's chance of winning.
4. Now we need to know everyone's chance of finishing in second place. This is done by "removing" first place and doing the above calculation again for every remaining player that didn't "win" the tournament.
5. This is repeated recursively for each prize in the prize pool.

The problem with ICM it becomes very complex and time consuming if there are a lot of players and a lot of prizes.

Very easy example where very player has the same amount of chips. When everyone has the same amount of chips you can just divide the prize pool among the players, but I will show how ICM arrives at the same number.

Player1: 3000 chips
Player2: 3000 chips
Player3: 3000 chips

1st: \$450
2nd: \$270
3rd: \$180

Player1 has a 33% chance of winning. This gives him \$450 * 0.33 = \$148.5 in equity

Player2 also has a 33% chance of winning. If Player2 wins then Player1 has a 50% chance of getting 2nd place (3000/6000 chips). \$270 * 0.33 * 0.5 = \$44,55 in equity

We repeat the last step for Player3 which gives Player1 another \$44,55 in equity

Player1 has a 100% chance of getting 3rd place if Player2 wins and Player3 gets 2nd place.

This gives us: 0.33 * 0.5 = \$29,7 in equity

Lastly we must add the last way Player1 can get 3rd place which is when Player3 wins and Player2 gets 2nd place: 0.33 * 0.5 = \$29,7 in equity

If we sum these up we get: 148.5 + 44.55 + 44.55 + 29.7 + 29.7 = \$297 in equity total

The real number is 300. We lost \$3 because we only used two decimals in our calculations.