MathDB

Suppose a biased coin gives head with probability

\dfrac{2}{3}

. The coin is tossed repeatedly, if it shows heads then player

A

rolls a fair die, otherwise player

B

rolls the same die. The process ends when one of the players get a

6

, and that player is declared the winner.
If the probability that

A

will win is given by

\dfrac{m}{n}

where

m,n

are coprime, then what is the value of

m^2n

Problem Statement