# Distribution of percentage of occurences of each streak length in an infinite sequenc

• Apr 24th 2008, 06:32 AM
ThodorisK
Distribution of percentage of occurences of each streak length in an infinite sequenc
For fair coin tosses, in an INFINITE sequence-number of tosses the average length of consecutive wins (or losses) is 1/(1-p)=2, right?

Now imagine the distribution that: At the axis of x we see all possible streak lengths (which we meet in an infinite number of tosses), and at the axis of y we see the number of occurences of a particular streak length (in an infinite number of tosses) divided by the total number of occurences of all streak lengths (in an infinite number of tosses). So the axis of y counts percentages. If the infinite number of tosses confuses you, think of 1 trillion tosses.

So since the average streak length is 2, I guess the highest percentage, is that of the "streak length 2", and all other streak lengths have a lower percentage? That is, in a future infinite sequence of tosses, we will meet the "streak length 2", more times than any other streak length?

The question is, where can I find the formula that gives the values for this distribution? Please, no mathematical symbols without explaining what they mean.
• Apr 24th 2008, 06:43 AM
CaptainBlack
Quote:

Originally Posted by ThodorisK
For fair coin tosses, in an INFINITE sequence of tosses the average length of consecutive wins (or losses) is 1/(1-p)=2, right?

Now imagine the distribution that: At the axis of x we see all possible streak lengths (which we meet in an infinite sequence of tosses), and at the axis of y we see the number of occurences of a particular streak length divided by the total number of occurences of all streak lengths (in an infinite sequence of tosses). So the axis of y counts percentages.

So since the average streak length is 2, I guess the highest percentage, is that of the "streak length 2", and all other streak lengths have a lower percentage. That is, in a future infinite sequence of tosses, we will meet the "streak length 2", more times than any other streak length.

The question is, where can I find the formula that gives the values for this distribution?

I think the most likely streak length is 1.

RonL