Jane Street–styleTraderAssistant TraderQuestion #189
You have two dice and two players. Each player picks a number. The winner is the player who picks the number closest to, or equal to, the sum of the rolls of the dice. What is the optimal strategy to maximize your chances of winning? Is it always better to pick the number that has the highest probability of being rolled? Discuss whether this strategy also applies if the two dice numbers are multiplied instead of summed.
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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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