Use dynamic programming.

For <code>0 < i < n - 1</code>, <code>-n < j < n</code>, and <code>k</code> in <code>{’F’, ‘W’, ‘E’}</code>, let <code>dp[i][j][k]</code> be the number of sequences consisting of the first <code>i</code> moves such that the difference between bob’s points and alice’s point is equal to <code>j</code> and the <code>i^th</code> move that Bob played is <code>k</code>.

The answer is the sum of <code>dp[n - 1][j][k]</code>over all <code>j > 0</code> and over all <code>k</code>.