Jane Street–styleTraderTrading InternQuestion #565
Four 50-sided dice are rolled so that the numbers are all different, then assigned randomly to players A, B, C, and D. The players with the highest and lowest numbers pair up, as do the two with the middle numbers. The team with the higher total pays the team with the lower total the difference. You are one of the players. Someone offers you a way to fix the game so that you start with a given number from 1 to 50. Question 1: What is the best number to pick? Question 2: Assuming you choose X as the best number, and there is an auction to sell the hack that lets you start with X, how should you bid? (Is this just asking for the expected value of the hack, or is there more to consider about bidding strategies?)
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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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