Consider the three-players variant of Example 13.6. Calculate the optimal strategy for the first player A, assuming that the other two players B and C play optimally. What is the probability distribution function of the final score of player A under his optimal strategy? What are the win probabilities of the players A, B, and C? Example 13.6 Two players A and B in turn draw one or two random numbers between 0 and 1. For each player, the decision whether to go for a second draw depends on the result of the first draw. The object of the game is to have the highest total score, from one or two draws, without going over 1. Player A takes the first draw of one or two random numbers and then waits for the opponent’s score. The opponent has the advantage of knowing the score of player A. What strategy maximizes the probability of player A winning? What is the value of this probability?