Pricing a card game won only if reds survive

Starting from a standard $52$-card deck, Jane and you alternately draw two cards (Jane first). Two blacks go to Jane, two reds go to you, and a mixed pair is thrown away. After the deck runs out, your piles are merged, shuffled and the process repeats until one colour has disappeared. You receive $100 if any red cards are left at the end. What should you pay to play?

$0. Cards are only ever removed as a red and a black together, so the numbers of red and black cards remaining stay equal ($26$ each initially). One colour can vanish only when both do, so no red cards ever remain and the payoff is zero.