In the game show "Who Wants To Be A Millionaire?," a contestant is given a sequence of multiple choice questions with four alternative answers. The contestant can choose to keep the amount of money that he or she has currently earned and bow out of the game, or to gamble on answering the next question correctly. Each question answered correctly doubles the contestant's winnings; but with the first question that is answered incorrectly, the contestant loses the game and goes away with nothing. The game stops if the contestant reaches an amount in excess of \(\$ 1\) million. The questions become harder as the game proceeds; suppose that the chance of answering the \(i^{\text {th }}\) question correctly is \((3 / 2) /(i+1)\). If the contestant starts with \(\$ 1000\), when should he quit the game?