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
So a few questions in probabilities arise. Find the probabilities as
reduced fractions of:
- One hand being dealt a blackjack from a freshly shuffled deck.
- Two hands being BOTH dealt blackjacks from a fresh deck.
- Neither of two hands being dealt a blackjack
A Blackjack is the combination of an Ace and one of [Ten, Jack, Queen,
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?
Source: Reader Rich Polster.
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