Poker News

Richard Burke

I signed up for a few games at our local poker room and then waited for a spot to open. Fred saw me, asked to be dealt out, and hustled over to my chair. He had found an on-line ICM calculator on a website and used it for Sit & Go tournaments, he told me, and he had some questions. How did it work? Why didn?t his ICM calculator work for more than ten players and five places paid? How could he use it to win tournaments?

The Independent Chip Model rests on the fundamental assumption that the players? win probabilities are directly proportional to their current stack sizes. Based on that, an ICM calculator uses Bayes Theorem to compute the probabilities of finishing in the money and sums them to find each player?s equity.

The table above shows stack sizes for a five-player, $20 Sit & Go after level 3. Bayes? theorem tells us how to compute the probability that Ann will place, given that Bob, Cal, Don, or Ed won. Ann?s place probability equals the sum of the four Bayesian expressions shown below.

The first expression yields a probability of 0.17143 that Ann will place given that Bob won. The second expression yields a probability of 0.10 that Ann will place, given that Cal won, etc. Their sum is the probability that Ann will place no matter who else won. Ann?s place equity equals $30*0.31587, or $9.48; her win equity equals $70*3000/7500, or $28.00, for a total equity of $37.48.

Those expressions looked straightforward, so Fred wanted to know why his ICM calculator didn?t provide for more than ten players and five paid places. For a ten-player table paying five places, a modern server takes one or two seconds to evaluate and sum the 31,600 Bayesian expressions needed to compute all the equities to four decimal places: for ten paid places, it would take that same sever two or more minutes to compute all the players? equities. For twenty players paying five places, it would take that same server ten or more minutes to evaluate and sum 2 million Bayesian expressions. Fred seemed disappointed. How then could he use the ICM to help win multi-table tournaments, he asked.

You mustn?t fret about the other tables, I told him. You must deal with the opponents at your table. If you consider your particular table similar to a Sit & Go, then the ICM calculator will show your equity. If you can keep your equity above zero, as the blinds and antes increase, as opponents come and go, then you will, eventually, arrive at the final table.

That?s where the ICM shines, I told Fred. The ICM calculator will display your and the others? equity before and after each hand. When your equity increases, your chance to win improves; when it decreases, your chance to win diminishes. You should use the ICM calculator to analyze situations that arise frequently. After you?ve analyzed a few dozen, you?ll develop a feel for the ICM and then adjudge similar situations correctly yourself.

How, exactly, could he use the ICM to analyze situations, he asked. I was called to my game before I could even start to explain. Next time, I told him.

See Also:

ICM Part 1

ICM Part 3

ICM Part 4

ICM Part 5

Filed under: Poker News