Suppose I have four cards: two black, two red. I draw them one by one. Every time I draw a red card, I win a dollar, and every time I draw a black card, I lose a dollar. I can choose to stop at any time I want. What is the optimal strategy for choosing when to stop, and what is its expected value?
I did this by brute force to get $2/3$, but I don't know if there is a more clever way out there.