Jane Street–styleTraderAssistant TraderQuestion #216
You play a game where you roll a 100-sided die labeled with the numbers 1 to 100. After each roll, you may either accept the payout equal to the number rolled in dollars or pay $1 to roll again. You can continue to pay $1 to reroll as many times as you like until you choose to accept your current roll. What is the optimal strategy for this game, and what are your expected winnings using this strategy?
Build Your Approach
State the assumptions, try a simple case, then work toward a general solution. Check the result and explain how it changes if an assumption changes.
Try the free diagnostic with worked solutions →Get Free Interview Prep Resources
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?
Practice the Reasoning Behind the Answer
Bring your target roles and interview timeline to a free quant consult. Discuss your preparation priorities and how Quant Blueprint’s lessons, practice and mock interviews can help.
Book a Free Quant ConsultYour goals · your preparation · your next steps