Question about expectation and sample size.

[razyn_kayn]

How much of a sample size is needed to expect a given result(e.g., 1BB/100) with 98% confidence? I have tried to find this using the search feature, but I'm not too saavy with that just yet. So, sorry if this is a tired topic. If anyone has a link to an explanation of an applicable formula, that would be great. Thanks.

[CityFan]

You cannot achieve a precise result with a certain level of confidence - you're mixing incompatible concepts.

If you calculate that your a gain over a series of hands is 1BB/100, you can give a RANGE (e.g. 0.9-1.1BB/100) within your EV lies with a given level of confidence.

However, you can never say that your EV is precisely 1BB/100 with any positive probability at all.

[razyn_kayn]

"If you calculate that your a gain over a series of hands is 1BB/100, you can give a RANGE (e.g. 0.9-1.1BB/100) within your EV lies with a given level of confidence."

So, if pokertracker tells me that I am winning at a rate of 1.00 BB/100, what sample size would I need to consider this my EV for a game. Hopefully this clarifies my question. Thanks.

[CityFan]

Hmmm... that depends on the variance, which I don't know. Someone will be able to tell you a "usual" figure, but it's not me.

In fact, Pokertracker should be giving you a confidence range or standard error, unless it's a complete heap of [censored].

[AaronBrown]

To be 98% confident, you have to go 2.33 standard deviations in either direction. There are some assumptions you need to make for that to be true, but they should be reasonable here.

If your standard deviation is 20BB/100 hands, then 100 hands tells you your expected win rate only within 2.33*20 = 46.6BB in either direction with 98% confidence. If you won 1 BB over 100 hands, knowing your true win rate is between -45.6 and +47.6 is not very helpful (and there's 2% chance you're wrong and it's outside this range).

The standard deviation, and hence the range, goes down with the square root of the number of 100 hand series played. After 10,000 hands (100 100 hand sessions) it's 1/10 (10 is the square root of 100) or 4.66 BB in either direction. After 1 million hands (10,000 100 hand sessions) it's 1/100th (100 is the square root of 10,000) or 0.466 BB.

[ViolentGandhi]

I think the exact number that pokertracker is giving you is the exact BB/100 for the sample. They don't do any confidence intervals for the population.