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

1. ## 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.

2. 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