## Problem of the Day #331: AlbertFebruary 13, 2012

Posted by Sreenath in : potd , trackback

Albert and Billy are playing a game:

At the starting of each round, both players write down a number. They then play rock-paper-scissors $8$ times.

If a player wins at least as many times as the number he wrote, his score increases by the cube of the number written. Else, the score is cut in half.

Albert is exceptionally good at rock-paper-scissors, and wins $\frac{3}{4}$ of the time.

Assuming both players play optimally, compute the probability that Albert has the higher score after $5$ such rounds.