Normality of winrates

[cwes]

In this (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=4015752&an=0&page=0#Post 4015752) thread the question whether poker winrates are normally distributed came up (as normality is often assumed for calculating ROR).

I ran my per hand winrates for 90k hands through every possible test for normality contained in the R software package (http://www.r-project.org/) and each test rejected normality pretty badly.

Even by looking at a histogram of my winrates I can tell they cannot be normally distributed (and it's not even close).

I would like to hear some comments from you guys.

[BruceZ]

[ QUOTE ]
In this (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=4015752&an=0&page=0#Post 4015752) thread the question whether poker winrates are normally distributed came up (as normality is often assumed for calculating ROR).

I ran my per hand winrates for 90k hands through every possible test for normality contained in the R software package (http://www.r-project.org/) and each test rejected normality pretty badly.

Even by looking at a histogram of my winrates I can tell they cannot be normally distributed (and it's not even close).

I would like to hear some comments from you guys.

[/ QUOTE ]

What time period did each data point represent? If you plot win rates per hand, or per hour, or even per session, these will not be normal; however, if each data point represents a sufficiently long period of time, and there haven't been any major changes to the playing conditions, then you should see that the data begins to be well-approximated by a normal distribution, as guaranteed by the central limit theorem.

[BillC]

I would be surprised if per hour win rates were far from being normal. I might even suspect that you are using the software incorrectly, or making some other error.

Bruce, why do you think hourly win rates are not (approximately) normal? This question has arisen many times on this site over the years, and never really addressed as far as I know.



[ QUOTE ]
[ QUOTE ]
In this (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=4015752&an=0&page=0#Post 4015752) thread the question whether poker winrates are normally distributed came up (as normality is often assumed for calculating ROR).

I ran my per hand winrates for 90k hands through every possible test for normality contained in the R software package (http://www.r-project.org/) and each test rejected normality pretty badly.

Even by looking at a histogram of my winrates I can tell they cannot be normally distributed (and it's not even close).

I would like to hear some comments from you guys.

[/ QUOTE ]

What time period did each data point represent? If you plot win rates per hand, or per hour, or even per session, these will not be normal; however, if each data point represents a sufficiently long period of time, and there haven't been any major changes to the playing conditions, then you should see that the data begins to be well-approximated by a normal distribution, as guaranteed by the central limit theorem.

[/ QUOTE ]

[cwes]

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I would be surprised if per hour win rates were far from being normal.

[/ QUOTE ]

I used per hand win rates. Bruce is most likely right.

[BruceZ]

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I would be surprised if per hour win rates were far from being normal.

[/ QUOTE ]

I used per hand win rates. Bruce is most likely right.

[/ QUOTE ]

Sorry, I didn't notice that you said "per hand". That is definitely the problem. Try per 30, 50, 100, 120... hands, and let us know at what point you get good normality. I just meant that the theory does not guarantee these will be normal until each data point represents a large enough number of hands. It's possible that you could get decent results sooner as BillC suggests. Even for fairly ugly skewed distributions, you don't have to add many points before the sum starts to follow a bell curve. Basically, each additional hand causes the distribution to be convolved again with the per hand distribution, which is a smoothing operation.

[Agthorr]

I've found that if you group hands into sets of 40, the result does not fail normality tests. The skew and kurtosis of this distribution are also close to zero. I'm working with relatively small datasets though (less than 10,000 hands), and I'd be interested to hear from anyone with larger datasets.

It would also be interesting to see how non-stationary the distribution is.