Jane Street–styleTraderAssistant TraderQuestion #203
You are given a die with 100 sides, numbered from 1 to 100. When you roll the die, you can choose to either (a) take the number of dollars equal to the number of dots that show up, or (b) pay $1 to reroll. You can continue to reroll as many times as you like, but you can only keep the result of your final roll. What is the optimal strategy, and what is the expected value of playing optimally?
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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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