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sthief09
09-27-2005, 05:08 PM
how do I figure out the odds of having an x bb downswing for a given winrate and stnadard deviation (and no, I'm not running bad, I just like the math behind the game)

I'm assuming it's a markov chain but I don't remember how to do that stuff, and I never want to open my stochastic models book ever again /images/graemlins/wink.gif

AaronBrown
09-27-2005, 06:04 PM
If W is your win rate per 100 hands and S is your standard deviation, then over N hands your expected profits are W*N/100 and the standard deviation of that number is S*(N/100)^0.5.

To get the probability of being behind by X or more after N hands, you need to use a Normal table or a spreadsheet (computing it by hand is impractical). The Excel formula is NormDist(-X,W*N/100,S*(N/100)^0.5,TRUE). That says, give me the probability that a Normal variate with mean W*N/100 and standard deviation S*(N/100)^0.5 has a value less than -X.

If you want to compute your probability of a downswing of X or more anytime during the N hands, it's more complicated. You either need to use an approximation, or add up a series of Excel computations, or write a short program.