I deal a standard deck of 52 cards to you face up, one card at a time. Before any deal of any card you can shout out "NOW". If you shout out "NOW" and the next card I deal is a queen, then the game finishes and I give you $100. If the next card isn't a queen, then the game finishes and I give you nothing. What is a fair price for you to pay me in order to play this game with me?
What I think of is to use the optional sampling theorem and show it is a martingale. But I am a bit lost on the setup.