MathDB

In fencing, you win a round if you are the first to reach

15

points. Suppose that when

A

plays against

B

, at any point during the round,

A

scores the next point with probability

p

and

B

scores the next point with probability

q=1-p

. (However, they never can both score a point at the same time.)
Suppose that in this round,

A

already has

14-k

points, and

B

has

14-\ell

(where

0\le k,\ell\le 14

). By how much will the probability that

A

wins the round increase if

A

scores the next point?

Problem Statement