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I'm looking for help to build a statistic in excel or just mathematically. What I want to figure is the chance of another player (villain) increase his stack with X BBs when I estimate his BB/100 to be Y against me, with the standard deviation BB/100 being Z and the maximum number of hands we play being A.

An example: I play HU and a player sits down. He's a fish so I estimate his BB/100 vs me to be -30BB/100. The problem is he will quit whenever he's 100BBs up. I know the standard dev to be 100BB/100 and we play a maximum of 200 hands. What is the chance of him reaching a 100BB increase vs me with these numbers?

I figured this was the community to post this in, please let me know if I rather should post this in a more general methematical community.

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    This is a rather unusual calculation, but poker does involve a lot of mathematics. So yes, you posted in the right place :)
    – Radu Murzea
    May 27, 2014 at 21:31
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    Good Q. I can't answer it, but I tweeted & Facebooked it ;)
    – Toby Booth
    May 27, 2014 at 22:08

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This is a fairly straightforward statistics question. You should look into the z-score for further details.

If we assume your results against this opponent follows a normal distribution, the Excel formula to answer your question would be:

=1-NORMDIST(X, Y * A / 100, Z * SQRT(A / 100), TRUE)

That's the probability your opponent will be ahead at least X BB's after A hands, asssuming Y and Z are in units of BB/100.

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