Are Winrates Normally Distributed?

[MNpoker]

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i think a more realistic hand distribution would be much closer to approaching normality.

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Where's Capt obvious?

Mine was just for example purposes.

BOTH will move towards normalcy one will just be quicker than the other.

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lose 0sb with P1
lose 1sb with P2
lose .5sb with P3
lose 2 sbs with P4
lose 3sbs with P5
lose 4sbs with P6
lose 5sbs with P7
.
.
.
lose 12bbs with Pn

then the upside:
win 0 with Pa
win
.
.
.
win 55bbs with Pm


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This is the table I was recommending to be set up. Then run convolutions.

Just like we will never know our win rates to the .00001 per 100 we will never know exactly where the distribution becomes normal.
That's just part of statistics and the reason people use confidence intervals.

The defintion of 'enough' data is how much you have.

[MaxPower]

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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.

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

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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.

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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.

[sfer]

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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.

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I think 1K hand chunks is probably large enough.

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Josh's graph with (only?) 1500 datapoints suggests otherwise.

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Actually it doesn't suggest otherwise. It just doesn't suggest anything. If you look closely at the BB/100 graph you will see that it is much too granular to draw any sort of conclusion on convergence properties (how closely it approximates normal). There are only 38 different points on the x-axis each of which have having frequency values between 0 and 11. To even have a shot at drawing a reasonable conclusion we would need something more like the BB/10 granularity at the BB/100 level. This would require a 1.5 million hand DB instead of a 150k hand DB.

I do agree with you, however, that this is interesting and is worth looking into. And I think that Josh's method (looking at empirical data) is the best way to do it because we don't have an accurate theoretical model for a hold'em probability distribution.

[ScottyP431]

Max Power,

Isn't what you are describiing a sampling distribution of the mean? Doesn't that always produce a normal distribution even if the population distribution is not normal?

[stinkypete]

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Max Power,

Isn't what you are describiing a sampling distribution of the mean? Doesn't that always produce a normal distribution even if the population distribution is not normal?

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i don't know what it's called, but his method will produce a normal distribution regardless of what the data is, if the samples are large enough.

[jetsonsdogcanfly]

I don't think that tells you anything particularly usefull. A distribution of randomly sampled means will necessarily converge to normality, but doesn't give you any new volatility information.

[jetsonsdogcanfly]

I think a better way to do this would be to run some ARMA models with component GARCH disturbances. This should be run on the time series of bb/x blocked returns. The confidence interval can be computed using

with gamma1=skewness, gamma2=kurtosis, C(sub-alpha)=the standard normal Critical value corresponding to the confidence level.

Piece of Cake.

[mmbt0ne]

Josh, you have Arean open. I can see it. Save a huge text file, load it into input analyzer, and see what kind of p-values it gives you for all the different distributions it tests for.

FWIW, I tried to say this earlier and pete made me doubt it a little with his well-thought-out responses. However, I still want to do more tests on it.

[MaxPower]

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Max Power,

Isn't what you are describiing a sampling distribution of the mean? Doesn't that always produce a normal distribution even if the population distribution is not normal?

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You guys are correct. I just basically demonstrated the Central Limit Theorem.

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.

The sampling distribution of win rates is normally distributed and it is appropriate to use that distribution to calculate confidence intervals. This is just an empirical demonstration.