The Independent Chip Model (ICM) is a game theory application that has become essential in sit-and-gos. It is best defined as a way to calculate your equity in relation to the prize pool based on the stack sizes of the remaining players in the tournament. Simply put, ICM is a way of analyzing how much your current chip stack is worth as a dollar value.
At the beginning of a sit-and-go (SNG), every player begins with the same amount of chips. An $11 nine-player SNG on PokerStars has a prize pool of $90; therefore everyone at the table has a starting equity of $10. As the tournament winds down and players are eliminated, every player’s equity is different. With the payout distribution at 50/30/20% for the top three finishers, knowing how much your stack is worth is crucial in determining your action during every hand.
Let’s say there are five players remaining in the $11 SNG mentioned above. In order to calculate the equity of each player at the table, you need to know A) their chip count and B) the payout scale of the tournament. Here’s an example:
Player 1: 1740 chips
Player 2: 835 chips
Player 3: 1585 chips
Player 4: 2590 chips
Player 5: 6750 chips
1st Place: $45
2nd Place: $27
3rd Place: $18
With 13,500 chips in play, Player 5 has exactly half the chips at the table. If the tournament was a winner-take-all format, Player 5’s equity would be 50% of the total prize pool or (0.5 * $90), which would equal $45. Player 4 has 19% of the chips, therefore Player 4’s equity would be (.19 * $90), the equivalent of $17. And so on.
However, with three places being paid the calculation becomes more complicated. There’s no need to work it out by hand. With several ICM calculators available online, such as SNG Wizard or SnG Power Tools, you can come to find that Player 5 has a 29.6% chance of finishing 2nd and 14.4% chance of finishing 3rd. To compute Player 5’s overall equity, add his equity for all three paid places:
(0.5 * $45) + (0.296 * $27) + (0.144 * $18) = $33
Using the same equation for the other four players, we can calculate the equity for everyone remaining in the tournament:
Player 1: 1740 chips = $15
Player 2: 835 chips = $8
Player 3: 1585 chips = $14
Player 4: 2590 chips = $20
Player 5: 6750 chips = $33
Keep in mind: This function does not take into account a player’s skill. The numbers are merely a way of finding out how much a player’s chip stack is worth.
So, what do we do with this information? The next step is determining whether a raise, fold or call is profitable depending on our stack and the stacks of everyone at the table. You either gain or lose equity by taking one of these actions. Near the bubble of an SNG your options are usually either moving all in or calling an all-in, since the blinds have increased to the point where these are the only plays left to make.
In order to make decisions with a positive expectation value, it is imperative to be able to put opponents on a range of hands that they will move all in or call with. We’ll go into that further in Part 2 of my ICM series: The bubble!
