Are Winrates Normally Distributed?

[stinkypete]

[ QUOTE ]

It is not at all useful. It tells us what we already know, but I think that Josh's method was flawed and led him to the wrong conclusion.

[/ QUOTE ]

while josh's method is flawed in a purely mathematical sense, i think his random variable, profit/hand (or profit/orbit if you prefer), is close enough to a random variable that his results will converge to something very close to a normal distribution for N>100, if he has enough hands.

the major problem here, as has been pointed out, is that the posted graphs aren't based on nearly enough hands.

[Shillx]

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 a near 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.

[stinkypete]

[ QUOTE ]
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.

[/ QUOTE ]

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.

[/ QUOTE ]

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?

[Justin A]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
It looks pretty close to normal here, but I think the way you did the sampling is not quite right.

You need to draw random samples from the total group of hands. Chopping them up into blocks is easier, but not appropriate. The way you have done it, we might find a different results using a different database.

[/ QUOTE ]

You probably want to draw largish random blocks of hands to randomize position as much as possible between the samples.

[/ QUOTE ]

OK, I figured out a way to do this in SPSS. I thought the data file would crash my computer but it doesn't

I have a data file with the amount I won/lost for 164,724 hands at 15/30. My win rate over these hands is a pitiful 1.13BB/100.

How large should the samples be and how many should I pull? I was thinking of selecting 10,000 samples of 1000 hands each.

Then I can I plot them and get the skewness, kurtosis, etc.

[/ QUOTE ]

I just ran 1000 samples of 1000 hands each from this list and from the graph and statistics, I am convinced that the win rates for these samples are normally distributed.

I can run a larger job overnight and then post some pretty pictures and stats for you.

[/ QUOTE ]

Max,
Can you do this with sets of 100 hands? I understand that once the sample sizes get large enough the sampling distribution will be about normal, but I'm wondering how close the bb/100 statistic gets us there.

[stinkypete]

[ QUOTE ]

Max,
Can you do this with sets of 100 hands? I understand that once the sample sizes get large enough the sampling distribution will be about normal, but I'm wondering how close the bb/100 statistic gets us there.

[/ QUOTE ]

this is a good suggestion.

[sfer]

[ QUOTE ]
[ QUOTE ]

Max,
Can you do this with sets of 100 hands? I understand that once the sample sizes get large enough the sampling distribution will be about normal, but I'm wondering how close the bb/100 statistic gets us there.

[/ QUOTE ]

this is a good suggestion.

[/ QUOTE ]

I don't think so. 100 hands is 10 orbits of full ring, and having a 100 hand block with 3 more button hands or 5 more Big Blind hands is very significant. I think you need large chunks in order to mitigate that.

[Justin A]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Max,
Can you do this with sets of 100 hands? I understand that once the sample sizes get large enough the sampling distribution will be about normal, but I'm wondering how close the bb/100 statistic gets us there.

[/ QUOTE ]

this is a good suggestion.

[/ QUOTE ]

I don't think so. 100 hands is 10 orbits of full ring, and having a 100 hand block with 3 more button hands or 5 more Big Blind hands is very significant. I think you need large chunks in order to mitigate that.

[/ QUOTE ]

You just made an argument for running the sims with 100 hand sets.

[stinkypete]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Max,
Can you do this with sets of 100 hands? I understand that once the sample sizes get large enough the sampling distribution will be about normal, but I'm wondering how close the bb/100 statistic gets us there.

[/ QUOTE ]

this is a good suggestion.

[/ QUOTE ]

I don't think so. 100 hands is 10 orbits of full ring, and having a 100 hand block with 3 more button hands or 5 more Big Blind hands is very significant. I think you need large chunks in order to mitigate that.

[/ QUOTE ]

that's a good point. rather than selecting hands at random, he could do something like filtering for 10-handed games only and selecting 10 hands from each position for each 100 hand sample. posting in the cutoff (or anywhere outside of the blinds) screws things up too, so those hands could be ignored. unfortunately that will get rid of a lot of the hands, since they're probably not nearly all at full 10-handed tables. there's a number of things similar to this that you could do to improve the approximation - this is probably the simplest, but as i said, you lose a bunch of data.