# Question: A backgammon player will be playing three consecutive matches with

A backgammon player will be playing three consecutive matches with friends tonight. For each match, he will have the opportunity to place an even bet that he will win; the amount bet can be any quantity of his choice between zero and the amount of money he still has left after the bets on the preceding matches. For each match, the probability is ½ that he will win the match and thus win the amount bet, whereas the probability is ½ that he will lose the match and thus lose the amount bet. He will begin with $75, and his goal is to have $100 at the end. (Because these are friendly matches, he does not want to end up with more than $100.) Therefore, he wants to find the optimal betting policy (including all ties) that maximizes the probability that he will have exactly $100 after the three matches.

Use dynamic programming to solve this problem.

Use dynamic programming to solve this problem.

## Relevant Questions

Imagine that you have $5,000 to invest and that you will have an opportunity to invest that amount in either of two investments (A or B) at the beginning of each of the next 3 years. Both investments have uncertain returns. ...Consider the following statements about solving dynamic programming problems. Label each statement as true or false, and then justify your answer by referring to specific statements in the chapter. Suppose that a mathematical model fits linear programming except for the restrictions that 1. At least one of the following two inequalities holds: 2. At least two of the following three inequalities holds: Show how to ...Consider the following special type of shortest-path problem (see Sec. 10.3) where the nodes are in columns and the only paths considered always move forward one column at a time. The numbers along the links represent ...Follow the instructions of Prob. 12.5-2 for the following BIP problem: Maximize Z = 2x1 + 5x2, Subject to and x1, x2 are binary.Post your question