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Old 12-07-2005, 07:58 PM
SrGuapo SrGuapo is offline
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Join Date: Sep 2004
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Default Theoretical stats question re standard deviation

Say I offer you a coin flipping game, and you profit 1 if you flip heads, and 0 if you flip tails. Your expected win is .5, and the standard deviation is .5 (I think I am right so far).

Now, say I offer you a game that now involves two flips. If you flip heads twice, you profit 2. Otherwise, all other combos (TT, HT, TH) you profit 0. So, your expected profit is still .5, but what is your standard deviation?

I made a spread sheet where I ran this a thousand times, and the answer comes out to around .86 (plus or minus, not enough trials to get accurate). How does one arrive at this number via a calculation?

How this relates to poker is take a SnG, where a generally accepted standard deviation seems to be 1.7 buyins, and say you cash 40% of the time, and let's say you expect the average profit to be $2.50 (when you cash). Now, let's say you are playing some wacky double shootout step tournament where you have to cash in a second SnG to cash out, and you still expect to cash 40% of the time, but the expected profit when you cash is $6.25. So, in the double shootout tournament you expect to win .4*.4*6.25=1, which is the same as the single SnG (.4*2.5=1). However, if the standard deviation of the single SnG is 1.7, what is it for the double shootout step tourney?

I hope my question is clear. Thanks for your help.
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