Let's say a Martian lands here and starts to play BJ (or SP21) in a casino. He does not know whether the game is 50/50 or if there is an edge for house or for players. He uses perfect basic strategy, flat bets, keeps perfect records of number of hands played and outcomes. Unlike me he has excellent knowledge of the mathematics of hypothesis testing. Given the standard deviation of BJ (or the slightly higher SD for SP21), how many hands would the Martian need to play to test the hypothesis that the game is 50/50?

What motivates this question is observing such abysmal SP21 play. Just when I think I've seen everything, a guy surrenders soft 13 against a 5 (true) or whatever. Between poor play and the huge popularity of the Match bet (HE 3%), the ploppies must be playing at minus 2 - 3% anyway. Yet they keep playing. I'm wondering if, to be charitable, the inherent volatility of the game is such that even an intelligent, "scientific" player would have to lose over a very long run before realizing that it is hopeless.