Jane Street–styleTraderTraderQuestion #47
You and a friend are betting on individual games of the World Series. For each game, if your team wins, you win a certain positive amount of money, and if your team loses, you lose that same amount. You and your friend want to construct a betting scheme so that you will win $1000 if your team wins the series and lose $1000 if your team loses the series, regardless of the final game score (e.g., 4-3, 2-4, etc.). How much should you bet on the first game?
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More Jane Street–Style Trader Questions
A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the center cube?You flip 4 fair coins and receive $1 for each coin that lands heads. What is the expected value of your total winnings?If you roll two dice, and you have the option to roll again and get paid the highest roll, when is it optimal to reroll?What is 2,000,000 minus 2,022?How many digits does 99 raised to the 99th power have?
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