Credit for this problem goes to Jason McCarthy. Thanks!

Red Black Cards


We are going to play a card game. I will shuffle a standard deck of 52 cards and then flip over two cards at a time.

Once I am through the entire deck, you count your pile and I will count mine. If you have more cards in your pile than I have in mine, I will pay you $100.

What is the most that you would pay to play this game?