You’ve made it to the final 3 in a WPT event, the Doyle Brunson North American Poker Championship. First place pays $1,000,000, second gives about $500,000 and third is about $250,000. You are the middle stack with about 1.6 million in chips, David “The Dragon” Pham is on your left with about 100,000 chips and chip leader Carlos Mortensen is on your right with about 4.5 million. The blinds are at $50,000/$100,000; you are in the big blind and David Pham folds on the button. Carlos now goes all in and you look down at pocket tens. Do you call or fold? Given that Carlos could be making this move with a wide-range of hands, it is tempting to call, but the correct answer is fold. What if after he went all-in, Carlos showed you that he has A-5 offsuit and you know you are about a 70-30 favorite? Do you call now? Actually you should still fold even though you know you are a 70-30 favorite.

The reason is that David is so short-stacked that he is likely to bust out in the next few hands. Even though calling will double you up 70% of the time, 30% of the time you will be out with only $250,000 in prize money. If you fold your tens, you can practically guarantee second place and at least $500,000. There are models that can estimate what your expected value (EV) of prize money will be based on the size of your chip stack and the other players’ stacks as well. If you make certain assumptions such as all the players are equally skilled, then you can use these models to see why folding is correct in the example above.

Most tournament players know that their chance of winning a tournament is equal to the percentage of the total chips that they have. If you have 20% of the chips in play you should win about 20% of the time. Your chances of coming in a place other than first place are a little more complicated to figure out and depend on other people’s stack sizes, not just your own. One model I like to use is called the Independent Chip Model (ICM) that assumes that after you figure out each person’s chance at first place, you can assign second place proportionally to the remaining players. Let’s say there are 3 people left in a tournament with 60/30/10% chip stacks. If you are the middle stack, there is a 60% chance that the chip leader will win. If that happens you should take second 3/4 of the time (since you have 3/4 of the chips outside of the winner). Similarly, the 10% of the time that the short-stack wins, you should take second 1/3 of the time (since you have 1/3 of the chips outside of the winner). Overall, your chances of coming in second are:

(60%) x (3/4) + (10%) x (1/3) = 48%

You can use similar logic to figure out additional places once you have second place figured out. Let’s use this model to look at the WPT problem above.

If you fold your tens, then the chip stacks (in millions) will be:

0.1
1.5 (you)
4.6

and your winning chances are:

1st 24%
2nd 70%
3rd 6%

giving you a prize pool expectation of about $606,000. If you call with your pocket tens and win, the chip stacks will be:

0.1
3.2 (you)
2.9

and your winning chances are:

1st 52%
2nd 46%
3rd 2%

giving you a prize pool expectation of about $753,000. However, there is only a 70% of winning with your tens and a 30% chance of busting out and taking home $250,000. So your prize EV of calling with your tens is

70% x $753,000 + 30% x $250,000 = $602,000

Since folding had an expectation of $606,000, calling will cost you an average of $4,000. While that seems pretty close, remember we’re talking about the situation where Carlos shows us the A-5 and we know we’re a 70-30 favorite. Against the unknown range Carlos could push, there is no way we can be a consistent 70-30 favorite and a fold is a clear winner.

This phenomenon of correctly folding a significant favorite occurs because tournament chips usually do not have a consistent value. In a ring game or winner-take-all tournament then the chips have a set value. But in a tournament with multiple payouts, chips change value as other players can bust out and you can gain money without gaining any chips. The result is that chips are more valuable to short stacks than they are to big stacks. 800 chips are more valuable to a stack of 1000 than to a stack of 6000.

A good tournament player always takes this into consideration. When there are short-stacks at the table, you sometimes need a lot bigger pot odds than you are used to in order to gamble with other stacks. Most players know that you will need better odds than normal, but it may be surprising exactly how much more you will really need.

Any serious player of single-table tournaments needs to have a good understanding of how ICM works. There are some free calculators available on the web, such as at www.chillin411.com/icmcalc.php. I also recommend that everyone get a copy of Sit-n-Go Power Tools at http://sitngo-analyzer.com/ SNGPT is a program that allows you to analyze your own hand histories and do lots of cool things with ICM.

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