Basic Normal Distribution Question

[Munga30]

In a small stakes thread, a poster asks whether his breakeven first 10K hands at 2/4 is just a downswing. Several posts shouting "meaningless" and "sample size" ensue. Gaming Mouse says it's not meaningless, just inconclusive. He says a player with a true win rate of 1.5 BB/100 has a X% probability of breaking even (or worse) after 10K hands and a 2 BB/100 player has a Y% probability of the same. (FWIW, I think X was about 16 and Y was about 9).

How were these probabilities calculated? I *think* if I choose a confidence interval where the lower limit is zero, the answer is just 1 minus that CI. Terminology may be a bit off, but is that about it? Please instruct. Thanks.

[gaming_mouse]

I assumed an SD of 15, which is close enough. Actual SD's can vary between around 14 and 18, but most I've seen are 15 or 16.

Anyway, say you win at 1.5BB/100.

Over 10000 hands, your SE (the SD of the normal distribution in question) is SD/(sqrt(100)). 100 because 10K has 100 samples of size 100.

So if your SD is 15, then the amount you've won after 10K hands has a normal distribution with mean 1.5 and SD 1.5. Now you find the area under such a normal distribution from -infinity to 0 using a normal distribution calculator -- you can find one on google.

HTH,
gm

[sethypooh21]

Someone also came up with a simple little excel sheet which allows you to plug in your "winrate" and SD and gives you the upper and lower range for various confidence intervals. I'm sorry to say I don't remember the poster's name or even which forum it was in, but I can email it to you if you PM me...

[gaming_mouse]

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Someone also came up with a simple little excel sheet which allows you to plug in your "winrate" and SD and gives you the upper and lower range for various confidence intervals. I'm sorry to say I don't remember the poster's name or even which forum it was in, but I can email it to you if you PM me...

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I think it's really kind of ridiculous that pokertracker does not do this for you automatically. Your win rate is basically meaningless without it.

[sethypooh21]

[ QUOTE ]
[ QUOTE ]
Someone also came up with a simple little excel sheet which allows you to plug in your "winrate" and SD and gives you the upper and lower range for various confidence intervals. I'm sorry to say I don't remember the poster's name or even which forum it was in, but I can email it to you if you PM me...

[/ QUOTE ]

I think it's really kind of ridiculous that pokertracker does not do this for you automatically. Your win rate is basically meaningless without it.

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Completely agree.