This is not 100 % pertinent to the issue here, but I'll mention it as a curiosity. When there are exactly two possible outcomes for a random experiment (e.g. dealing a random hand from a constrained set of possibilities, where a certain line either makes the contract or goes down one--the two possibilites), and you seek to estimate the probability of it making, making the a priori assumption that it may equally well be any number in the range 0 to 1, then the probability after simulations that resulted in m successes and n failures [corrected now; thanks barmar] is (m + 1) / (m + n + 2); e.g. if in 26 simulations (randomly dealt hands, of course), there were 26 successes, the p of success in the actual hand is 26/27 = 96.3 %. This assumes, of course, that the sampling is perfect, i.e. the hand generator depicts the actual situation perfectly.
