I have a well-shuffled deck of n red cards and n black cards, all facing down. I let you draw one card at a time. If you draw a black card, I pay you $1. If you draw a red card, you pay me $1. You can stop the game at any time. (As long as you want to play, I’ll accommodate.)
1. What’s the expected payoff of this game to you?
2. What’s your optimal stopping rule?
[A real interview question I was asked at a Goldman Sachs on-site interview]