In article <email@example.com>, HERC777 <firstname.lastname@example.org> wrote: >and 1,000,000 other people all flip 100 coins themselves. >on average, will someone flip the same 100 long sequence I did? >how long a sequence will they match up to on average?
As clarified later in this thread, what you're asking for is, given a fixed sequence of coin flips, suppose I generate 1,000,000 other sequences of coin flips, and take the sequence that best matches my given sequence, in the sense of having the longest matching prefix. What is the expected value of the length of this prefix?
For all practical purposes, your "100" can be treated as infinity here, and I will do so.
The probability that the length of the matching prefix is at most n is 1 - (1/2)^(n+1). With 10^6 series of flips, the probability that the *longest* matching prefix is at most n is thus (1 - (1/2)^(n+1))^(10^6). The desired expected value is
sum_(n>=0) n * ( (1-(1/2)^(n+1))^(10^6) - (1-(1/2)^n)^(10^6) )
which works out to be about 20.26. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences