MathDB

Sarah stands at

(0,0)

and Rachel stands at

(6,8)

in the Euclidena plane. Sarah can only move

1

unit in the positive

x

y

direction, and Rachel can only move

1

unit in the negative

x

y

direction. Each second, Sarah and Rachel see each other, independently pick a direction to move, and move to their new position. Sarah catches Rachel if Sarah and Rachel are every at the same point. Rachel wins if she is able to get

(0,0)

without being caught; otherwise, Sarah wins. Given that both of them play optimally to maximize their probability of winning, what is the probability that Rachel wins?

Problem Statement