I had been working on this problem, and ran into trouble because I couldn't easily use the "find the opposite probability and subtract from one" trick. So for example I think I can find the probability of getting at least two in a row rolling a die 5 times, by finding the probability of getting no duplicates at all and then subtracting from one to find the opposite: ( 1 - (5/6)^4 )
But how to find the probability of a sequence of at least three? The extension of the problem is to write a formula generalizable to the number of trials, number of possible outcomes per trial, and the length of the repeated sequence.
I like working on this on my own so if you can just give a little hint or guidance I'd appreciate it very much!