The key to using the Independent Chip Model (ICM) is making choices that have a positive expectation over time. In Part One, we went over the calculation of a player’s current chip stack as a dollar value. Now we can move forward and make decisions based on that information.
In the example used in Part One, we worked out the equity of five players remaining in an $11 nine-player sit-and-go:
Player 1: 1,740 chips = $15
Player 2: 835 chips = $8
Player 3: 1,585 chips = $14
Player 4: 2,590 chips = $20
Player 5: 6,750 chips = $33
Let’s say Player 5 eliminates Player 3 on the very next hand. Player 5 now has 8,335 chips and is in an ideal position on the bubble. The new equity values are as follows:
Player 1: 1740 chips = $19
Player 2: 835 chips = $10
Player 4: 2590 chips = $24
Player 5: 8335 chips = $37
Even though Player 5 collected all of Player 3’s chips, the equity of every player increases because the removal of one player at the table improves the chances of everyone making money.
With four players still alive and the top three places paying, it becomes a survival game for the short stacks. Thus, the big stack can take advantage by raising and applying pressure. This is the point in a sit-and-go where ICM becomes crucial. When should the big stack be raising? What range of holdings can the small stacks give the big stack and how often can they call?
If we are Player 1 in this example, our main goal is outlasting Player 2, the shortest stack at the table. All of our judgments can be made based on what our expected equity would be by raising, calling or folding.
Now let’s say we’re in the small blind on the next hand. Player 2 is in the big blind. Blinds are 75/150. Player 4 folds in the cutoff and Player 5, the big stack, moves all in from the button. We look at our hole cards and see Ace-Jack suited. What do we do?
The first objective is to assign a range of cards to Player 5. What could he make that move with? Given that he has almost all of the chips in play, and he’s been very aggressive throughout the tournament, we’re going to assume that Player 5 is moving all in with almost any two cards. He knows that we, along with Player 2, are merely trying to survive and finish in the top three. Therefore he can use his stack to bully us around.
The range we come up with for Player 5 is the top 90% of hands, which means he could be making this move with any pair, A2+, K2+, Q2+, J2+, T2+, 92+, 83o+, 82s+, 74o+, 72s+, 64o+, 62s+, 54o, 52s+ and 43s. Using an equity calculator program such as PokerStove, we can find that our AJ suited is a 3-2 favorite (almost 60% equity) against Player 5’s range.
In any other format, this would be an easy call for us. After all, there’s a 60% chance we’ll win the pot! But the variable in a sit-and-go is the stack sizes of your opponents, and we have to factor a short-stacked player into our decision. By making the call and winning the pot (assuming the big blind folds), our stack increases to 3,630, giving us $27 in equity. However, if we call and lose, we finish in fourth place and our equity is $0.
So if we ran this hand 1,000 times:
600 times we win and have $27 in equity. 600*27 = $16,200
400 times we lose and have $0 in equity. 400*0 = $0
At the end of 1,000 tries, our equity is $16,200/1,000, which equals $16.20. If we fold, we have 1,665 chips and $19 in equity, making this call a losing play in the long run.
In order to make a profitable call we need a hand with more than 70% equity against Player 5’s range. To be safe we should only be calling with pocket tens or better.
Not even Ace-King suited has enough value to make a call in this example. In fact, it has almost the same equity as our AJ suited against Player 5’s range. Overvaluing AK is a mistake seen often on the bubble of Sit & Gos. Hopefully this article will sway you from doing it in the future.
This is just one example of how useful the Independent Chip Model can be in Sit & Gos. They are a unique form of poker because there are many situations where folding is correct even when you know you have the best hand. Many top players stay away because of the mechanical math-related nature of the game, but when played correctly using ICM, Sit & Gos can be very rewarding to your bankroll.
