MathNet 1997 — Part 01 Question 73

Question 73

Three friends each have three tokens.
After each game the winner receives a token from each of the other two friends.
What is the probability that the game will not have to stop within five games because one of the players runs out of chips?

$\frac{2}{9}$
$\frac{1}{6}$
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{2}{3}$