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