Jane Street–styleInternInternshipQuestion #587
You have 100 white balls and your opponent has 100 black balls. Each of you may put any number of your balls into a common pot. A third party randomly draws one ball from the pot. Whoever's ball is drawn wins an amount of money equal to the number of balls they have left over. If you know your opponent will put in 99 balls, how many balls should you put in to maximize your expected winnings?
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 Intern Questions
Design a real-time system to process millions of trades per second. How would you ensure low latency, fault tolerance, and exactly-once processing?If I roll two dice, what is the expected value of the product of the two faces?Suppose we play a game with a die where we roll and sum our rolls. We can stop at any time, and the sum is our score. However, if our sum is ever a multiple of 10, our score becomes zero and our game is over. What strategy will yield the greatest expected score? What about if the target multiple is a value other than 10?Implement the game Tetris in 30 minutes.What is the optimal strategy for winning in rock-paper-scissors if your opponent can only choose between rock and paper?
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