# Minimum number of hands required to establish a conclusion about win-rate?

What is minimum number of hands required to establish a conclusion about win-rate at particular level (10NLHE, 30NLHE, etc)?

e.g. You can play 1000 hands and have a win-rate of 53bb/100 but that is of course a very small sample.

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You can´t be certain just from bb/hand value, if you are winning because of skill or long upswing. There surely isn´t any magic number of hands, which makes you certain about your actual winrate, the only thing we can measure is, how propable is your winrate in certain range.

This calculation depends HEAVILY on the game you play, and also on your playstyle. Some rock with <10% vpip doesnt have to face variance as 60%/50% VPIP/PFR LAG. This tool should help you get some insight: http://www.evplusplus.com/poker_tools/variance_simulator/

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That depends on what sort of confidence level you would like to have. You can never be 100% sure. What you can calculate is the probability that your true win rate is within a given range, based on your measured win rate, sample size, and standard deviation.

To do this, you would take several 100 hand samples, measure average win rate, and standard deviation. From there, it is basic statistics to calculate confidence intervals, etc. The tough part will be collecting the required data.

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thx for answer, but approximately what would be standard error on say 10,000 hands 20,000 and 30,000 hands. If someone knows approximately (don't need to calculate) – Shark4Ever May 2 '12 at 18:12
Do you mean standard deviation? If so, that depends on your playing style. Generally, a looser playing style will tend to have a higher standard deviation, but it is unique to each player. However, to actually know your standard deviation, you will need to take take several 100 hand samples, calculate your win rate for each, and then calculate the standard deviation as follows: en.wikipedia.org/wiki/Standard_deviation#Basic_examples – Chris Marasti-Georg May 2 '12 at 18:26
I meant like if I played 10,000 hand and have 10bb/100 win rate error could be +-2 (that mean my real win rate is 8 or 12) but on 20,000 hands sample error would be like +-1 or my real win rate be 9 or 11 – Shark4Ever May 2 '12 at 19:34
I know what you meant, but it's just not that simple. Sample size and average are not the only things that determine probability/confidence You need to know standard deviation. – Chris Marasti-Georg May 3 '12 at 12:34