Jane Street·Data Scientist·Technical Phone Screen
- You roll a fair six-sided die repeatedly, accumulating a running sum. You can stop anytime and collect the current sum, but if the sum ever hits a perfect square (1, 4, 9, 16, ...) you lose everything and get zero. There's no roll limit. What's the optimal stopping strategy, and what's the expected payoff under that strategy starting from zero?
“This one wrecked me for the first few minutes.”