The final answer is that the probability of the banker getting 52 or more wins is. Then you'll have to make a half point correction for a binomial distribution and look up the Z statistic in a standard normal table (this step is left to the reader). The standard deviation is thus 4.329727904. The probability of a banker win, given that there wasn't a tie, is 0.506788499 and the probability of a player win is 0.493211501. The standard deviation is the square root of the product of 75, the probability of a banker win, and the probability of a player win.
The expected number of banker wins out of 75 bets resolved is 38.00913745. It would be very unlikely to go 75 hands without a tie. In other words, you mean 75 bets resolved. First, I'm going to assume that you are not counting ties.
