# Calculating minumum representative sample

Let's say I played 500 hands in poker and earned 345 units ( dollars not, important for calculation). So on long term I'm earning 345/500 = 0.69 * 100 = 69 every 100 hand session. But 500 hands is just to small sample. I could easly loose 200 dollars in next 500 hands( -40 dollars every 100 hand session). So in 1000 hands I've played my neto won would be 345-200 = 145 / 1000 = 0.145 * 100 = +14.5. What minumum sample of hands would be necessary to find out how much I'am wining/loosing every 100 hand session with error of lets say of +-5%. I know if I play 100,000 hands and my wining rate is 9 dollars every 100 hand sesion I will have approximately same result if I played 200,000 hands. How to calculate those stuff?

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It rather depends on how often you win or lose large amounts and how large these amounts are. If they change over time (perhaps as the game progresses) then it gets very hard to calculate – Henry May 2 '12 at 23:34
You also need to specify how sure you want to be that your estimate is within $5\%$ of the truth. Even if we assume that the daily winnings are and will forever remain independent identically distributed random variables, absolute certainty of estimating the mean within $5\%$ is not achievable. – André Nicolas May 2 '12 at 23:56
Yes, I tought so that this isn't exact science. I would have to split my 10000 hands in lets say 100 parts and create distribution. – Shark4Ever May 3 '12 at 0:11
why isn't 500 enough, (Law of large numbers), as stated before, you have to make a choice if each hand is independent of the previous one, and then you can model it as stochastic process. – yiyi May 3 '12 at 1:44
if the hands are all iid, then I don't believe E(x) will change. – yiyi May 3 '12 at 1:45