Quote:
Originally Posted by NewOldGuy
This is a pretty standard confidence interval problem using standard deviation. Post it in the Probability Forum and you'll get a number of people willing to show you the math. I don't have time right now or would take a stab at it.
I wouldn't use standard deviation here because it's a binomial distribution, so an exact probability is easy to calculate.
The probability of hitting (denominators rounded):
<= 351/1000 bets: 1/30
<= 378/1000 bets: 1/6683
<= 405/1000 bets: 1/27814008
However, these probabilities don't accurately test the hypothesis that an edge exists or you'd see casinos banning anybody who hits 378/1000 of these bets. The OP mentioned Bayes' in his title, so I'm assuming he wants to incorporate that some way, but I'm not sure how, other than to note that casinos have an interest in protecting their games, and it's extremely unlikely that a defect that would have potentially been exposed to millions of people over the course of time would be significant. Surely other people can see these "particles," and potentially take advantage of them, tipping the casino off that something is wrong?
A potential flaw that takes expertise to spot, or was introduced very recently is far more likely to be statistically meaningful as a smaller pool of people are capable of finding it.