From A Practical Guide to Quant Interviews:
A casino offers yet another card game with the standard 52 cards (26 red, 26 black). The cards are thoroughly shuffled and the dealer draws cards one by one. (Drawn cards are not returned to the deck.) You can ask the dealer to stop at any time you like. For each red card drawn, you win \$1; for each black card drawn, you lose $1. What is the optimal stopping rule in terms of maximizing expected payoff and how much are you willing to pay for this game?
My approach: If I have n dollars currently and r red cards left and b black cards left, my expected payoff at this stage will be $(r/(r+b)) * (n+1) + (b/(r+b)) * (n-1)$ and this should be greater than $n$. I get after solving $b<0$, which is impossible. I don't understand why I am wrong.