During the Australian Open, the sisters Venus and Serena Williams face off against each other in a singles’ tennis match. At one point, Venus serves and Serena returns. Venus has to decide whether to aim her serve to the right or to the left and Serena decides whether to lunge left or right (defined from the perspective of the server) to hit the ball. The speed of the ball is so high that Serena has to react by intuition, thus making both player’s decisions simultaneous in practice. If Venus serves to the left and Serena lunges to the right, Venus wins the point 89% of the time. If Venus serves to the right and Serena lunges to the left, Venus wins the point 70% of the time. If Serena correctly anticipates the side, the odds of winning are evenly split between both players.

i. What are the best strategies for both players?

Now consider that Serena has a third strategy, which is to stay in the middle, while Venus still only serves to left and right. If Serena uses this new strategy, she wins the point 31% of the time if Venus serves to the left or 36% if Venus serves to the right.

ii. Would you recommend Serena to stay in the middle?

Answer rating: 100% (QA)

i Considering the payoff matrix If Venus serves to the left and Serena lunges to the right Venus win... View the full answer