I just found such a quant interview question but could not find a similar post in StackExchange. The question is pasted below.
Jane offers to play the following game with you. Starting with a standard deck of 52 cards, you take turns drawing two cards. Jane goes first. If the two cards are black, Jane keeps them. If the cards are red, you keep them. If there is one red and one black card, the cards are discarded. When you have gone through the deck, you and Jane combine your cards, shuffle them, and resume, playing until one of the colors is eliminated. If there are red cards remaining, you win $100. What is a fair price to pay to play this game?
Best Answer
That's a trick question.
The cards are always discarded by pair (red, black) so the number of discarded red cards and discarded black cards is always equal.
Thus the red and black colours are going to be eliminated only when the whole deck is eliminated. And there will be no red cards remaining.
You are never going to win your $100.