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Old 12-27-2005, 07:06 PM
Copernicus Copernicus is offline
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Join Date: Jun 2003
Posts: 1,018
Default Re: A Rebuy ? for Math Majors



BPA..I think the results of your request wouldnt be worth the effort.

Lets say in a freezeout with n runners, a starting stack of S per runner and a buy in (excluding vig) of b, your equity is (S/nS) x nb = b because everyones skill is equal. This is essentially an ICM value of the total prize pool, where your chances of each prize happens to be equal to everyone elses.

Now lets say because of your skill, you historical equity happens to be 3 buy ins.

The problem is that you can get to that increased equity in a lot of different ways...eg one player may be a survivalist who has an unusually high number of cashes where they are in the middle prize areas and never wins a first prize, or there may be a "win it all" player who has a small incremental advantage for the big prize, but never make it into the money if he doesnt win.

Now when you look at the equity of a rebuy for these 2 players the answers will be very different depending on the situation, despite their "equivalent skill" of 3b equity.

If the redistribution of chips is fairly even and the average is less than 3b, both players probably still have +EV.

However if the redistibution of chips is skewed, so that the majority are in a few players hands the "win it all" player will have a lower EV than the survivalist, because the ratio of the top stacks (that he has to surpass) to his new buyin is greater than the ratio of the average of the other stacks to the survivalists buyin.

In fact the survivalist may actually have increased EV in that situation...in the extreme say the top stack is equal to all of the rebuys plus his original stack plus the buy ins of 1/2 the field that have dropped out. The remaining players have exactly their original stack. The survivalist has 1/2 the field to get through to get to the same prizes he was contending for before, and a rebuy should be very +EV for him.

The win it all player on the other hand has more ground to cover to get to the same chip ratio to the other tcontenders.
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