Optimal Stopping in the Red-Black Card Game

A deck contains $n$ red cards and $n$ black cards, shuffled uniformly at random. You draw cards one at a time without replacement. At any point you may stop, and your payoff is the number of red cards drawn minus the number of black cards drawn. 1. Compute the optimal stopping value $V(n)$ and describe the optimal strategy. 2. Now suppose an adversary gets to peek at the entire deck order in advance. Instead of you choosing when to stop, the adversary chooses the stopping time to minimize your payoff (but you still receive the payoff at that time). What is the minimax value of this game?