Dynamic Card Game

The Problem

A deck has 26 red and 26 black cards. Cards are drawn one at a time without replacement. After each draw you may stop. If you stop, your payoff is \1 \times (\text{reds drawn} - \text{blacks drawn})$ \u2014 a dollar for every red drawn so far, minus a dollar for every black drawn so far.

Questions

1. Write the Bellman recurrence for $V(r,b)$, the expected payoff-to-go given $r$ reds and $b$ blacks remain in the deck.
2. What is the value of the game, $V(26,26)$?