Reconsider Example 7. Suppose that the bet is changed as follows: "Starting with two chips, she will not have at least five chips after five plays of the game." By referring to the previous computational results, make additional calculations to determine the new optimal policy for the enterprising young statistician.
Example 7
Winning in Las Vegas
An enterprising young statistician believes that she has developed a system for winning a popular Las Vegas game. Her colleagues do not believe that her system works, so they have made a large bet with her that if she starts with three chips, she will not have at least five chips after three plays of the game. Each play of the game involves betting any de sired number of available chips and then either winning or losing this number of chips. The statistician believes that her system will give her a probability of 
of winning a given play of the game.