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match equity question

Posted By: Matt Cohn-Geier
Date: Tuesday, 14 October 2008, at 9:17 p.m.

In Response To: match equity question (Frank_N_Stein)

Since nobody has provided a really clear explanation, maybe I can try now that I'm fully awake.

Broader form:

Takepoint:

ME if you lose = 0% ME if you win = 100% ME if you drop = 9%

Most simply, TP = ME if you drop / (ME if you win - ME if you lose )--perhaps there is a better way of looking at this.

9 / 100-0 = 9/100 = 9%.

More generally, TP = risk / risk + gain. You are risking 9% (since if you drop you have 9% guaranteed, whereas if you take you could lose that 9% and go to 0%) to gain a potential 91%. So your risk is 9% and your gain is 91%. Risk + gain is 100%, so 9 / 100 = 9%.

Minimum doubling point:

Four ME numbers are relevant here, not just three. There is the D/Win, D/Lose, ND/Win, and ND/Lose scenario.

DW = risk / risk + gain. Your risk in this case is ND/Lose - D/Lose and your gain is D/Win - ND/Win. D/Win = 100%, ND/Win = 91%, so gain is 9%. D/Lose is 0%, ND/Lose is 65%, so risk is 65%. Risk / risk + gain = 65/74 = 88%. I don't have a simple way of looking at this.

Kit has written a number of articles about this on GU and in his comments in the OLM matches, but I am too lazy to go through them all.

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