empirical equity study

[eastbay]

I finally coded up the icm comparison/validation I talked about doing awhile ago. The idea was to empirically determine my equity as a function of chip stack distribution and compare that to what ICM says.

A brief look at some bubble numbers:

Overall average equity on the bubble:

ICM: .232
Actual: .277

Looks pretty good. I've got about 4% more of the prize pool than ICM says I "deserved".

Breaking it down into situations where someone has more than half the chips:

stacks: actual equity, icm predicted equity, difference, standard error of sample, number of data points in this range
0,0,0,0: 0.282925; icm = 0.239223; delta = 0.0437015; std err=0.00508585; N=1265
0,0,0,1: 0.266667; icm = 0.195756; delta = 0.0709111; std err=0.0189215; N=90
0,0,1,0: 0.244944; icm = 0.203231; delta = 0.0417128; std err=0.0190025; N=89
0,1,0,0: 0.215385; icm = 0.18758; delta = 0.0278049; std err=0.0148834; N=117
1,0,0,0: 0.426316; icm = 0.393979; delta = 0.0323365; std err=0.0221329; N=19

0,0,0,0 means no one has more than half the chips.
0,1,0,0 means the guy to my immediate left does. etc.

This is kind of interesting, if it really holds up. You can see the increasing advantage of having the big stack further away to the left. This is an effect that is completely missing from the ICM, which takes no heed of position.

Another interesting fact is that the other players are playing the big stack at this phase of the game much more often than I am (N=19). And yet I have significant equity advantage over them on average.

Discuss. Probably more to come.

eastbay