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?