george wrote: > HERC777 wrote: > Inserting HERC777's original question.
>>> 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? >> >> there's about 1,000,000 combinations of a sequence of 20 coin flips >> 2^10 = 1024 >> 2^20 = a million >> >> so on average they should copy your sequence up to the 1st 20 flips.. >> >> Agree? > > No. Jesus. > First of all, you have to know what you are > averaging OVER. You are overaging over FLIPPERS, > or flip-sequences. You are averaging over a million > things. For each of these million strings (of H or T), > you want to know how long its prefix-matching-you is. > The number of flippers matching-you-so-far starts out > at a million after 0 flip-positions and falls by half > with every flip(in time) thereafter. Half the million > will flip opposite from you on the first flip and so > will have a prefix-matching-you of length 0. > 1/4 of them will match you on the first flip and > miss on the 2nd, and have a match-you length of 1. > 1/8 of them will match you on the first two but miss > on the 3rd, and have a match-you length of 2. > On the 20th flip, the EXPECTED number of flippers > continuing to match you all this way will be less than 1. > Furthermore, the AVERAGE, over all flippers, of the > initial-length-of-match-you-prefix, is ALSO > LESS THAN 1. > > NOT 20. > > This is HIGH SCHOOL algebra, herc.
He may have meant "on average, what will be the length of the longest matching prefix."