20 Jan '10 03:10

I was looking through my stats on another online chess site this morning. I've played 136 games in total, of which I have won 81.

I was suprised by another stat on the page - my longest winning streak. 14 consequtive wins. This struck me as being well outside the norm, considering my overall win ratio is just ~60%.

Obviously, I'm human, and my wins are not distributed chronologically randomly. I have weeks in which I play great chess, and others in which I'm decidedly off. The length of my streaks - both winning and losing - is likely to longer than those that might be expected of a purely random distribution.

However, I think it raises an interesting problem.

Let's say Bob Jones plays x games of chess. Of these x games, he wins w games.

Assuming that his victories are distributed randomly throughout the chronological sequence of games, what is the most likely length of his longest winning streak?

I was suprised by another stat on the page - my longest winning streak. 14 consequtive wins. This struck me as being well outside the norm, considering my overall win ratio is just ~60%.

Obviously, I'm human, and my wins are not distributed chronologically randomly. I have weeks in which I play great chess, and others in which I'm decidedly off. The length of my streaks - both winning and losing - is likely to longer than those that might be expected of a purely random distribution.

However, I think it raises an interesting problem.

Let's say Bob Jones plays x games of chess. Of these x games, he wins w games.

Assuming that his victories are distributed randomly throughout the chronological sequence of games, what is the most likely length of his longest winning streak?