## Two Blackjacks

Before dealing from a fresh deck of cards, the dealer offers you two bets: You can bet any amount that you will be dealt a blackjack, and you can bet any amount that the dealer will be dealt a blackjack. If either hand is dealt a blackjack, you will be paid 17-to-1 for the respective bet. If BOTH hands get a blackjack, both bets will be paid 20-to-1 (as long as you originally placed both bets; placing a single bet will only be paid 17-to-1). So a few questions in probabilities arise. Find the probabilities as reduced fractions of:
1. One hand being dealt a blackjack from a freshly shuffled deck.
2. Two hands being BOTH dealt blackjacks from a fresh deck.
3. Neither of two hands being dealt a blackjack
• If you bet one dollar on both your own AND the dealer's hand for each fresh deck, what would be your expected rate of loss (the odds are ALWAYS in the house's favor.)
• If you only bet on your hand for each fresh deck, what would be your expected rate of loss?
• What odds would provide even gain/loss expectations?
A Blackjack is the combination of an Ace and one of [Ten, Jack, Queen, or King].