A gambler will be playing three consecutive games with friends tonight. For each game, 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 games. For each game, the probability is 0.7 that he will win the game and thus win the amount bet, whereas the probability is 0.3 that he will lose the game and thus lose the amount bet. He will begin with $60, and his goal is to have $100 at the end. (Because these are friendly games, he does not want to end up with more than $100.) Therefore, he wants to find the optimal betting policy that maximizes the probability that he will have exactly $100 after the three games. Use dynamic programming to solve this problem. Clearly define stages, states, decision variables and recursive function