I've got a decent script now for performing game runs until a given
confidence level and interval are obtained.  The bad news is that it
took about 380 games to determine with 95% certainty a confidence
interval of less than 10% around the estimated win ratio.  And even then
the estimated win ratio was 47.92%, when the actual value is probably
50%.  There were 182 wins and 198 losses for player 1.  Both were using
the random-shooter AI.