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Originally Posted by 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.
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Actually my analysis was spot on, it was not basically spot on.
The binomial distribution is the distribution of n trials of a 2-valued event with probability p.
The result you have used is the normal
approximation to the binomial distribution. The only reason to use the normal distribution for this is if it is inconvenient to use the binomial distribution (which it is not if Excel calculates it for you). The binomial distribution is exact.
As you say, it does not make much difference, but the binomial distribution is the better one to use here.