Jane Street–styleTraderAssistant TraderQuestion #173
Given a fair 6-sided die, you roll once and observe the outcome n (where n is the number rolled). What is your expected value (EV) of the roll? If you are allowed one optional reroll (meaning you can choose to accept the first roll or reroll), what is your EV now? If you are allowed to reroll one additional time (meaning you can roll up to two times, always choosing whether to accept the current roll or reroll), what is your EV?
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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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