In the casino game of blackjack the dealer is dealt two cards, one face up and one face down, and each player is dealt two cards, both face down. If the dealer is showing an ace the player can look at his down cards and then make a bet called an insurance bet. (Expert players will recognize why it is called insurance.) If you make this bet you will win the bet if the dealer’s second card is a ten card: namely, a ten, jack, queen, or king. If you win, you are paid twice your insurance bet; otherwise you lose this bet. Show that, if the only cards you can see are the dealer’s ace and your two cards and if your cards are not ten cards, then the insurance bet is an unfavourable bet. Show, however, that if you are playing two hands simultaneously, and you have no ten cards, then it is a favourable bet. (Thorp13 has shown that the game of blackjack is favourable to the player if he or she can keep good enough tracks of the cards that have been played.)