There are four balls, two black and two yellow, in a box. You pick out one at a time at random without replacement. Before picking each one out, you guess at the color, and if you're right, you receive in dollars the number of balls left in the container before you chose it. For example, if you guess the first ball correctly, you would receive $4 because there were 4 balls remaining in the box before you picked one out. Assuming optimal play, what is the expected payoff for this game?
