Thursday, April 30, 2009

A theory post....ICM (part 1)

I occasionally remember that a blog should be about more than just whining about some donkey sucking out on you, so here's the first in a series on...

ICM (independent chip model) assumes that the chances of any player winning a tournament at any given point depends on how many chips he has relative to the total amount of chips in play. For example, a player with 10% of the chips has a 10% chance of winning.
A simple example
Four players remain in a satellite with three $10K packages. ICM can be used to calculate the players expectation at this point:
Each player has a 25% chance of finishing first and winning $10K, for an expectation of $2500
Each player has a 25% chance of finishing second and winning $10K, for an expectation of $2500
Each player has a 25% chance of finishing third and winning $10K, for an expectation of $2500
Each player has a 25% chance of finishing fourth and winning nothing, for an expectation of $0
Total current expectation (tournament equity) for each player is therefore $7500.
So what?
Apart from determining what a fair deal would be if the players decide to deal, does this matter?
Yes. It does. A lot.
Consider what happens if one player moves all in, and another wakes up with a hand big enough to consider calling. Under normal circumstances (early in a tournament, or in a cash game), the second player should call if he believed his hand to have more than 50% equity against the shoving player’s range.
However, in this case, he needs significantly more than 50% to correctly call. To investigate how much more, let’s look at what happens to the tournament equity of the four players if Player A moves all in from the SB, player B calls in the BB, after players C and D folded, and when the hands are turned over, it’s a true 50/50.
Before the hand, all four players had $7500 equity.
Once the call is made, ignoring the unlikely case of a chop, players C and D’s equity increases by $2500 to $10000 (as they are now guaranteed a seat).
Players A and B now have only a 50% chance of winning $10K, so their equity drops $2500 to $5000.
Therefore, when he makes the call, Player D is risking $7500 in equity to win only $2500, so he needs odds of 3 to 1 against the shover’s range to call correctly (in other words, he needs 75% equity).


Good post Dara. Well explained.


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