Sample Size and Stats Convergency - Gambling and Probability

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Sample Size and Stats Convergency

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05-04-2015 , 05:02 PM

onlinepokerwiz

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Curious about how big of a sample do i need on a specific stat like 3bet vs HERO%, or call vs BB 3bet after raising from the BTN, etc., for it to be actually usefull in practice and/or can be used as baseline to support/justify certain decission...Cheers.

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05-05-2015 , 10:19 PM

Cranberry Tea

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A rigorous answer would depend on how much certainty you want. More certain --> bigger sample size.

As a practical matter, you can sometime make reasonable inferences from small sample sizes. Like, if some guy's been 3betting every hand for 50 hands, you can be reasonably sure he's not a nit even though we only have a 50-hand sample size. ofc, there's some chance he's been getting premium hands 50 times in a row, but you can make a reasonable bet that usually isn't the case.

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05-06-2015 , 09:55 AM

onlinepokerwiz

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Thanks for steping in and reply very much apriciated, i understand what you say and i have some knowledge about statistics but this its a bit out of my league so, how do i calculate that asuming a solid level of certaintity? are we talking about confident interval? can we use .95 or .99? Do all stats have the same sample size:certainty:level of convergency ratios? I mean, do some stats need a bigger sample than other for it to converge?

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05-06-2015 , 09:59 AM

onlinepokerwiz

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I found this calculator online, is it practical for what im asking/need?

http://www.raosoft.com/samplesize.html

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05-07-2015 , 07:26 PM

Cranberry Tea

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Yeah. Basically, there's a tradeoff where the more certainty you want, you need an exponentially-increasing number of hands. I think that online calculator will probably do the heavy lifting you need.

It's not easy to say what confidence interval you need. Most of the time in poker, we make judgement calls with far less than 95% confidence.

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05-08-2015 , 05:20 PM

statmanhal

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That calculator is useful only for a binomial distribution – where there are only two possible outcomes, good-bad, heads-tails, win-lose, etc. OP was asking about more general metrics, I believe.

In general, you need a measure of variability such as the standard deviation to determine the sample size needed for a given confidence level. Also. you need to know the underlying distribution; for many cases, a normal distribution is satisfactory,

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05-10-2015 , 05:12 AM

jukofyork

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Quote:

Originally Posted by onlinepokerwiz

Curious about how big of a sample do i need on a specific stat like 3bet vs HERO%, or call vs BB 3bet after raising from the BTN, etc., for it to be actually usefull in practice and/or can be used as baseline to support/justify certain decission...Cheers.

See: http://en.wikipedia.org/wiki/Binomia...ation_interval

* Important to notice how poker stats based off very frequent and/or very infrequent actions will require a much larger sample size to get the same level of confidence...

You can also define a "prior" distribution of player stats and then update using Bayes Theorem after each observed opponent action (search google for "beta conjugate prior for binomial likelihood" and/or read some of the "Poker Sleuth HUD" thread/site for better explanation of how to do this).

Juk

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05-10-2015 , 12:17 PM

statmanhal

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Originally Posted by jukofyork

Maybe I’m misinterpreting this statement, but for a binomial distribution the required sample size for a given confidence level is maximized when the occurrence probability is 50%. Clearly if an event always (or never) occurs, you only need a sample of one to find that out.

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