Re: Why is 10,000 hands too small?
 

A while ago, I posted this. It is based on a standard deviation of 16 BB/100. If you are a tight player, these numbers are a bit high, if you're loose, they're a bit on the low side.

--GH

Re: Why is 10,000 hands too small?
 

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And since you were picky about me using a 2-sided t-test (my range, btw, was from a 1-sided t-test but I used a conservative 20BB estimate just to impose more restriction),

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I actually figured out that was probably what you did after it was too late to take down my post. Many people fail to make this adjustment correctly, and for them this isn't picky. It is fundamental and significant.


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I will be picky about you referring to it as my 1-sided Confidence Interval. T tests might have a nice CI representation but the test itself is against a 5% upper tail critical region.

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There is a fundamental equivalence between hypothesis testing and confidence intervals (DeGroot p. 482). The null hypothesis that the win rate is negative is called a 1-sided alternative, as opposed to a null hypothesis that the win rate lies between two bounds, which would be a 2-sided alternative. Rejecting the 1-sided hypothesis at the 5% level is equivalent to saying that the interval from 0 to +infinity is a 95% confidence interval for the win rate. This is what I meant by 1-sided confidence interval, so that 0 corresponds to 1.65 SD below the mean, and 95% corresponds to the area under the bell curve from 1.65 SD below the mean to +infinity, instead of the mean +/- 2 SD for a 2-sided alternative.

Re: Why is 10,000 hands too small?
 

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A while ago, I posted this. It is based on a standard deviation of 16 BB/100. If you are a tight player, these numbers are a bit high, if you're loose, they're a bit on the low side.

--GH

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Just curious, why is it 6200 and not 6400? And why do you keep subtracting 200 after quadrupling?

Re: Why is 10,000 hands too small?
 

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A while ago, I posted this. It is based on a standard deviation of 16 BB/100. If you are a tight player, these numbers are a bit high, if you're loose, they're a bit on the low side.

--GH

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Just curious, why is it 6200 and not 6400? And why do you keep subtracting 200 after quadrupling?

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I dunno. I came up with these numbers by running a python script.

Edit: Now that I think about it, it probably has to do with the 95% accuracy, which is only 1.96 Standard Devations. Using two SDs (97% accuracy), you do get the expected 6400.

Re: Why is 10,000 hands too small?
 

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There is a fundamental equivalence between hypothesis testing and confidence intervals (DeGroot p. 482)


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Hehe. True, and you win. I personally find it easier to think of it purely in terms of critical regions and p-values since not every test has a easily constructed CI lying around.

This is a funny topic of sorts for me right now. My Math Stat course is currently on hypothesis testing. One of our homework problems is to prove the relationship between a LRT involving normals and the t-test, so this topic is very relevant to me right now.