Mathematicians' Casino
Puzzle 3: Greenjack
You find yourself at the Greenjack tables, with three dollars to spend. Greenjack is similar to Blackjack, except that it is completely different. It is played with a deck of only 16 cards, divided into 4 suits: Red, Blue, Orange and Green. There are four cards in each suit: Ace, King, Queen and Jack. Ace outranks King, which outranks Queen, which outranks Jack - except for the Green Jack, which outranks every other card. If two cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green, again except for the Green Jack, which outranks everything. Here's how the game is played: you are dealt one card, face up, and the dealer is dealt one card, face down. The dealer will make some true statements, and you will place a bet as to who has the higher card, you or the dealer. If you are right, you win. It's just that simple! TEN-DOLLAR TABLE You put a dollar on the table, and you are dealt a Green Ace. The dealer says: - My card would beat any Queen.
- Given only the information you know now, if my card is more likely to beat yours than not, then I have a Blue card. Otherwise, I don't.
- Given only the information you know NOW, if your card is more likely to beat mine than not, then I have a King. Otherwise, I don't.
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