Date: Apr 13, 2005 12:22 AM
Author: Glenn C. Rhoads
Subject: Re: say I flip a coin 100 times...
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."