Here's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this)
We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result.
I do the same. You do not know whether I've re-drawn and I do not know whether you've re-drawn. Decisions are made independently. We compare our numbers and the highest one wins $1.
What strategy do you use?
EDIT: The answer is not 0.5, it is not 0.7 either.
We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result.
I do the same. You do not know whether I've re-drawn and I do not know whether you've re-drawn. Decisions are made independently. We compare our numbers and the highest one wins $1.
What strategy do you use?
EDIT: The answer is not 0.5, it is not 0.7 either.