Stopping rule for a red-black card payoff game

A shuffled deck has $26$ red and $26$ black cards. You turn cards over one at a time without replacement; each red card earns you $1 and each black card costs you $1. You may quit at any point and keep your net winnings. What is the optimal strategy, and how much is the game worth?

About $2.62. Let $f(r,b)$ be the value with $r$ red and $b$ black left; then $f(r,b)=\max\big(0,\tfrac{r}{r+b}(1+f(r-1,b))+\tfrac{b}{r+b}(-1+f(r,b-1))\big)$, measured relative to current winnings. Keep drawing while the continuation value is positive and stop as soon as it falls to zero; the recursion gives $f(26,26)\approx2.624$.