09 Mar '06 22:051 edit

Suppose I play chess. I win my first game and lose my second. Thereafter, the probability that I win is equal to the proportion of previous games I have won. What is the probability that I win k of my first n games, for each possible value of k?

Now consider the same game, except that or my first a+b games, I win a and lose b. What is the probability of winning k of my first n games?

For an extra-credit rec, give a coherent mathematical account of how the title of this relates to the problem.

For an extra-credit PFCF rec, give a coherent account of any kind of how the title relates to RHP matters at large.

Now consider the same game, except that or my first a+b games, I win a and lose b. What is the probability of winning k of my first n games?

For an extra-credit rec, give a coherent mathematical account of how the title of this relates to the problem.

For an extra-credit PFCF rec, give a coherent account of any kind of how the title relates to RHP matters at large.