When to quit a plus-one minus-one card game

A well-shuffled $52$-card deck is turned over one card at a time. Every red card earns you $1 and every black card costs you $1. You may stop the game after any card (or before the first one) and keep your running total. What stopping strategy should you use, and what is the game worth to you under that strategy?

About $2.62. Solve by backward induction on the numbers of reds and blacks left: the value is the larger of $0$ (stop) and the expected value of drawing once more. The optimal rule is to stop only once you are ahead by a threshold that shrinks as fewer reds remain (e.g. a lead of $1$ with one red left, around $5$–$6$ with 13–20 reds left), never while behind; since you can always play to the end and break even, the game is worth strictly more than zero.