Are Winrates Normally Distributed?

[stinkypete]

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Hey,

MaxPower's post is the solution for all of the problems that we found with PT's sampling errors. It makes no difference how big your database is, because you can draw random 100 hand samples (picked one hand at a time) from it an infinate number of times. The old way you could only have 1000 x 100 hand samples if you played 100k hands. The new way, there are 100000 nCr 100 ways to draw 100 hands samples (this number is [censored] huge, 200 nCr 100 is like 10^58). If you take millions of these, you could both get a better picture of what the distribution looks like and also figure out what your true standard deviation with a very large level of confidence.

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how would this give you any new standard deviation data? i can't prove it off the top of my head, but i'm pretty sure this would give the same standard deviation PT would give you over the 100k hands.

EDIT: this assumes PT calculates SD on a per hand basis, which i believe it does, but i could be wrong.

[Shillx]

Well you can't calculate SD accurately on a per hand basis because the distribution isn't close to normal. You will have a lot of hands that will lose a small amount and then a long tail on the positive side (it will look more like an F-curve or even a chi square distribution). The reason why we do it in 100 hands blocks is to get a more normal distribution.

I always figured that PT did it by sessions (or tables played) and not by # of hands. I remember one time I put a couple big sessions (maybe 500 hands each) and it gave some error like "not enough sessions to calculate SD". So I deleted them and put in 5 or 6 small 30-50 hand sessions and it calculated an SD for me. So while I'm not certain, what it might be doing is finding the SD of the corse of the session and then normalizing it to a BB/100 value. This seems like a very poor way to figure out SD so I could be wrong (and hope I'm wrong quite honestly).

[stinkypete]

woops, my example sucked. deleted. fixing it. attempt 2 here:

[ QUOTE ]
Well you can't calculate SD accurately on a per hand basis because the distribution isn't close to normal.

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the definition of standard deviation doesn't rely on a normal distribution in any way. you can calculate the standard deviation of any distribution. its meaning obviously varies depending on the distribution though.

Example:

1 hand:
90% -1
10% +9

SDa = sqrt(0.9*1+0.1*9) = sqrt(1.8)

100 hands:
90% -1
100% +9
SDb = sqrt(90*1 + 10*9) = sqrt(180)


and SDb = sqrt(100)*SDa

so i ask, what is the problem with calculating the SD on a per hand basis?