11. In the following game of batter-versus- pitcher in baseball, the batter’s batting averages are given in the game matrix. The batter tries to maximize his batting average, while the pitcher tries to minimize the batter’s batting average; this is a zero-sum game. The pitcher decides between throwing a fastball or a knuckleball. When the batter is in the batter’s box, he guesses which pitch is coming (either a fastball or a knuckleball). If he guesses correctly, then his batting average goes up. For example, it is easier for him to hit a fastball when he correctly guesses that one is coming. However, if he guesses incorrectly, then his batting average goes down. If the pitcher and the batter follow their mixed-equilibrium strategies, what will the batter’s batting average be?