Guessing ball colours for shrinking prizes

A box has $2$ black and $2$ yellow balls. You draw them one by one without replacement, and before each draw you guess its colour. A correct guess pays as many dollars as there are balls in the box just before that draw ($4$, then $3$, then $2$, then $1$). Playing optimally, what is your expected total payout?

$19/3$ dollars. Always guess the colour with more balls left. The first guess is right with probability $\tfrac12$ (worth $2$), the second with $\tfrac23$ (worth $2$), the third with $\tfrac13\cdot1+\tfrac23\cdot\tfrac12=\tfrac23$ (worth $\tfrac43$), and the last is certain (worth $1$), totalling $\tfrac{19}{3}$.