Apparently this is a lot more complicated than I thought:

Hi, <Aggathon's Real Name>:

This problem is known as the "runs" problem and has tabulated values often

in an appendix of a textbook.

I haven't thought about how the runs table was constructed, perhaps one of

the ideas posed in your email.

What I do know is that there is a statistical solution. f there are, say,

20 random numbers, there is a 95% probability that the number of runs is

between 6 and 13. This doesn't give the probability that any run is exactly

five in length.

I have a runs table somewhere in my books. Let's take a look at it.

Dr. <professor's name>

PS: This exact problem was posed during a probability course I took so long

ago.

I recall that it was also included in a Homework Set 3 early in the courses

I taught.

Also, and probably most important, I used this concept to solve a

consulting problem for <company name edited>, using an expanded version of the

idea and a short (20 line or so) computer program. I may be able to find

those results.

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