Thank you NOTI. For me this post was one of the most informative I've ever read on vpFREE.
My math skills are rusty and never really extended broader or deeper than mid-level calculus and algebra. Your explanation was easily understood. It also gave substance to a nagging feeling on my part that high variance has a hidden cost separate from bankroll considerations.
Well done!
G'luck all,
Gamb00ler
nightoftheiguana2000 wrote :
Given an infinite sample size, the net average result is greater than the net standard deviation for a positive per hand EV. Of course it would seem unreasonable to assume an infinite sample size, what with the unlikelihood of casinos in the afterlife and what not. Fortunately, one can use math to solve for the sample size at which the average result is equal to the standard deviation. And that formula is variance/edge/edge which has also been called the Nzero point. So, for example, FPDW for one hand has an average result of +.76% and a standard deviation of 5.08 (sd=sqrt(var)). That's in units of bets, so if you were playing for 5 quarters, the average would be .0076 x $1.25 = $.01 and the standard deviation would be 5.08 x $1.25 = $6.31 . So you can clearly see that at one hand the standard deviation just swamps that tiny average result. But, fortunately, the Nzero is a reasonable (compared to infinite) 25.84/.0076/.0076= 447,368 hands. The question arises as to how long you have to get to the Nzero point, is it your entire gambling lifetime? I would say no, the IRS wants you to report your gambling results on an annual basis and they don't allow carry forward of losses, so you'd better get to Nzero before the end of the tax year or you'll be paying a penalty if your result is a loss due to variance. Alternately if you are already ahead this tax year, you have a buffer, as the tax problem is only a problem is you show a loss for the tax year. But the problem is very real, the penalty is approximately your marginal tax rate on a winning year times your loss on a losing year. You pay the penalty on the winning year so it is somewhat hidden.
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Posted by: gamb00ler@yahoo.com
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