HMMT 2002 T11

In this problem assume $s_{1}=3$ and $s_{2}=2$. Determine, with proof, the nonnegative integer $k$ with the following property:

• 1. For every board configuration with strictly fewer than $k$ blank squares, the first player wins with probability strictly greater than $\frac{1}{2}$; but
• 2. there exists a board configuration with exactly $k$ blank squares for which the second player wins with probability strictly greater than $\frac{1}{2}$.