A gambler has $3 in hand and has to play a game 3 times. For each game, the change of winning is 0.4, chance of losing is 0.3, and chance of fair is 0.3. The gambler can only bet positive integers less than or equal to the amount of money the gambler currently has. If he wins, he can win a profit equal to the bets. His goal is to find a policy that maximizes the chance of ending up with at least $5. (1) Formulate this problem into a DP problem, and write down the Bellman Equation. (2) What is the optimal policy? A gambler has $3 in hand and has to play a game 3 times. For each game, the change of winning is 0.4, chance of losing is 0.3, and chance of fair is 0.3. The gambler can only bet positive integers less than or equal to the amount of money the gambler currently has. If he wins, he can win a profit equal to the bets. His goal is to find a policy that maximizes the chance of ending up with at least $5. (1) Formulate this problem into a DP problem, and write down the Bellman Equation. (2) What is the optimal policy