In a normal deck of cards, you can either reveal the top card or guess whether that card is black. If you reveal the top card, you get to see what the card is and the game continues with one less card in the deck. If you were to make a guess, the game ends, and you get paid out $\$100$ if the card is black and $\$0$ if it's red.
What is the optimal strategy of this game and its expected value?
The lower bound has to be $0.5\times \$100 = \$50$ since you can just guess on the first card.