Someone offers you the possibility to play a gambling game with the following rules. first, you decide how much money you’re willing to put at risk in this game: this amount — let’s call it a — is referred to as your stake (all the monetary quantities are in dollars in this problem). having chosen your stake, you’re allowed to bet any amount 0 ≤ b ≤ a (thus, as a decision problem, for any fixed value of a, your possible actions in this situation correspond to values of b). if you win the bet, which occurs with probability 0