I have a 750K hand DB (hero excluded). I would like to take a look at the population's turn and river frequencies. For example how often the SB takes a B, B, XF line versus BB in SRP.

How many hands do I need to analyze these turn and river frequencies?

perhaps this should go in the probability forum.

I have posted several versions of the following, which uses binomial distribution confidence interval theory to develop a required sample size. It has not been challenged as far as I know, yet I haven’t seen any great acceptance either. Use or ignore as you see fit.
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For a binomial measure such as VPIP or 3-bet percentage, to be C% confident that the sample mean deviates + - d percentage points from the true mean when the true mean is believed to be P, the required sample size is

N = (Zc^2)*P*(1-P) / d^2,

where Zc is the standardized normal deviate corresponding to a C% confidence interval. For 80%, Z = 1.28; 90%, Z=1.645; 95%, Z = 1.96.

You have to make a guess on P, perhaps using a limited sample; N is maximized with P = 0.50.

Example: Suppose limited data on a villain indicates a frequency of a certain action is 20%. How large a sample is required so you can be 95% confident that the sample frequency is within + - 3% from the true value.

N = (1.96^2)*0.2*0.8 / 0.03^2 = 683

For 90% confidence for a 5% deviation, N reduces to 173.

Fantastic response. A question (coming from someone that is not very good at math):

Why would P change things? For example if we estimate Villains frequency of taking a certain action at 20% and want to be 95% confident that we are within 3% of the true frequency, we need 683 hands in that spot. But if we estimate a totally different frequency at 40%, we need 1024 hands. Just intuitively I don't understand why this changes things.

You can think of it as follows.

The "spread" in the distribution of the number of successes in 100 trials is the largest if the underlying probability of success on each trial is 50%. As the underlying probability of success moves away from 50% in either direction (towards 0% or towards 100%), the spread in the distribution of the number of successes gets smaller.

So it takes many more samples to construct a 95% confidence interval of a given width under an assumption that the underlying success probability is 50% than if you are testing a success probability of 10% or 20%.

Intuitively, 50/50 coin flips have the highest variance.

Hope this makes sense.

yea that does makes sense. Thanks!