You are about to appear on a TV game show. To start the competition, the show...

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You are about to appear on a TV game show. To start the competition, the show gives you a "pot" of $1,000. You will then be asked a sequence of three questions: Question Payoff 1 2 3 Chance you think you will answer Correctly $ 1,000 0.5 $ 2,000 0.4 $ 3,000 0.3 Before being asked each of the three questions, you can choose between quitting the game and trying to answer the question. If you quit, you keep the money in your pot and the game is over. If you choose to try to answer, there are two possibilities. If you answer correctly, the payoff from the question is added to your pot and you may continue to the next round of the game. If you do not answer correctly, you forfeit half the money in your pot and exit the game with the other half. If you answer all three questions correctly, you get to keep all the money in your pot (which would be $7,000 at that point). What strategy should you pursue? You are about to appear on a TV game show. To start the competition, the show gives you a "pot" of $1,000. You will then be asked a sequence of three questions: Question Payoff 1 2 3 Chance you think you will answer Correctly $ 1,000 0.5 $ 2,000 0.4 $ 3,000 0.3 Before being asked each of the three questions, you can choose between quitting the game and trying to answer the question. If you quit, you keep the money in your pot and the game is over. If you choose to try to answer, there are two possibilities. If you answer correctly, the payoff from the question is added to your pot and you may continue to the next round of the game. If you do not answer correctly, you forfeit half the money in your pot and exit the game with the other half. If you answer all three questions correctly, you get to keep all the money in your pot (which would be $7,000 at that point). What strategy should you pursue?

Answer rating: 100% (QA)

To determine the optimal strategy in this game we can calculate the expected value for each decision ... View the full answer