Jane Street–styleQuant ResearcherQuantitative ResearcherQuestion #388
There are 100 coins, each flipped and the results are hidden. You can ask one yes/no question, after which you must guess the outcome of each coin flip. For each correct guess, you earn 1 dollar; for each incorrect guess, you lose 1 dollar. What is the optimal strategy for maximizing your expected return, and what is the maximum expected value?
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More Jane Street–Style Quant Researcher Questions
In a Rock-Paper-Scissors game where your opponent is not allowed to play rock, you win $1 for each win, lose $1 for each loss, and draw $0 for a tie. What should you play to maximize your expected profit?You are rolling a die. Each time you roll, you can either stop the game and receive payment equal to the face-up value, or choose to roll again. You may roll up to three times in total. What is the expected gain from playing this game optimally?Suppose you are playing Russian roulette. What is the probability that the person who fires first wins?Given the probabilities with which your opponent will play Rock, Paper, and Scissors, how should you respond to maximize your expected winnings?You have 3,000 apples in Edinburgh and want to transfer as many as possible to London. You have a truck with a maximum capacity of 1,000 apples. London is 1,000 miles away from Edinburgh. For every mile the truck drives while carrying apples, it consumes (or drops) one apple. What is the maximum number of apples you can deliver to London?
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