Read "Harrington on Modern Tournament Poker" a while back, and it contains the following quote:
"ICM incorporates a sort of 'random walk' hypothesis. When we say that a stack's chance of winning the tournament is directly proportional to its percentage of the available chips, we're assuming that the stacks are moving up or down in small random movements over the course of the tournament."
I have some experience with random walk models, and was suspicious that ICM and random walk gave the same results. Random walk results are rarely linear. So, I ran a series of heads-up simulations in which the two players had varying starting fractions of a 2000 chip total. Then, based on a random number, one chip went from one stack to the other. Simulations ended when one player got to zero or if it got to a million hands, the program gave up. Here are the results:
The blue line would be the result if winning fraction was equal to the starting fraction of chips (ICM) while the red curve is the random walk output. ICM and random walk don't seem to be the same thing even if they're not outrageously different. It shouldn't be that surprising that a higher starting fraction yields a winning fraction that's even bigger, as you can survive larger amounts of noise. The implications for splits/ev aren't obvious (esp. when blinds are big), but it does suggest that splits among equal players based on ICM aren't necessarily ev neutral.
"ICM incorporates a sort of 'random walk' hypothesis. When we say that a stack's chance of winning the tournament is directly proportional to its percentage of the available chips, we're assuming that the stacks are moving up or down in small random movements over the course of the tournament."
I have some experience with random walk models, and was suspicious that ICM and random walk gave the same results. Random walk results are rarely linear. So, I ran a series of heads-up simulations in which the two players had varying starting fractions of a 2000 chip total. Then, based on a random number, one chip went from one stack to the other. Simulations ended when one player got to zero or if it got to a million hands, the program gave up. Here are the results:
The blue line would be the result if winning fraction was equal to the starting fraction of chips (ICM) while the red curve is the random walk output. ICM and random walk don't seem to be the same thing even if they're not outrageously different. It shouldn't be that surprising that a higher starting fraction yields a winning fraction that's even bigger, as you can survive larger amounts of noise. The implications for splits/ev aren't obvious (esp. when blinds are big), but it does suggest that splits among equal players based on ICM aren't necessarily ev neutral.
