my experience in the estimation of sample size is little, in other fields of statistics i got sufficient knowledge. I am unsure which routine i should use to answer my question. Since the topic might be unfamiliar to a lot of you, let me give an example.

There are 1326 possible holdings (2 cards drawn from a deck of 52 cards) in texas hold'em poker, from AA to 72. Let's say, from early position, one should raise according to the game-theoretical optimum, outcome from nash solver, 15,5% of all hands, or 205 combinations, and fold the rest.

Now i just record how often 1 opponent did raise from early position every time he had the opportunity to do so. Since i will not play forever against this player, my sample size will be finite. The question is, how big the sample size has to be, to get a significant (whatever effect size and according confidence value, and power i will choose for my hypothesis test) value for this player. This can and will of course vary, in let's say 10 hands, one player could be lucky and had 5 times good cards and raises 50%, another player can just play too many non optimal holdings, like K7, and also raises 50%. But the larger the sample size gets, the more exact i see how the players openraising strategy is from first position.

1. How do i determine the minimum sample size needed to get a significant value for the players openraising percentage? From the population the mean will be around the optimal value, but the standard deviation is unknown.

2. If the mean would be unknown too, how to proceed?

I just want to get an idea which test routine i should use, i can look into the mathematics by myself ofc. I dont want to run Monte Carlo sims, since i think this is a simple to solve problem, and just my lack of experience on sample size estimation holds me from seeing the obvious approach.

Best