Most of the times that I’ve been asked to look at randomization software that “couldn’t be right,” the software was fine. But the probability of seeing five heads in a row any time during a series of flips is much higher. The chances that the first five flips are heads would indeed be 1/32. You might argue, for example, that the chances of flipping five heads in a row would be (1/2) 5 = 1/32, but that underestimates the probability because a run could start at any time. Long sequences of the same assignment are more likely than you think. My first thought was that the software was working as designed, and that the users were just seeing a long run. I got a call one time to take a look at randomization software that wasn’t randomizing.
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