[jsp377]

My post has been replaced and edited due to not thinking on my part.

liquidsoap is absolutely right that just because the probability is low, that does not mean the game is rigged. If it DID mean the game were rigged, than any small number of hands in video poker that yielded an RSF would be considered to be rigged in favor of the player.

What makes this binomial distribution different from that is the Central Limit Theorem. By the time you've got a 235-sample binomial, that makes a pretty frickin' good approximation of the normal distribution. Therefore, we can judge the likelihood of getting only 84 wins with a normal distribution of mean mu =.5*235=117.5, and standard deviation sigma=sqrt(235*.5*.5)=7.665. Now, 84 wins is (117.5-84)/7.665 = 4.3706 standard deviations away from the mean. This has a probability of .0000062, even LOWER than that suggested by the original poster. In fact, despite using a binomial distribution, his analysis was basically spot on.


To liquidsoap and his statistics-hating...
The point is not the number of trials. The point is that the probability of getting as few wins (or fewer, for you doubters!) as he did was less than a one in one hundred thousand shot. Yes, the same proportions on a larger sample would be even more damning. But the fact that the sample size is small means little.

AS AN EXAMPLE, if I had a sample size of thirty and lost every single one, that would be pretty f'in' damning...that's a one in 1,000,000 shot, and enough for me to say that the coin flip weren't a fair game, despite the small sample size.

Similarly, although this sample size is small, it is equally damning, because the results he obtained were a one in 150,000 shot. If you don't think a 99.999% confidence interval is strict enough, you have no business arguing statistics.