Some time ago, Farmer Joe made the mistake of gambling against one of his regular customers.
The game was Greenjack, a popular betting game in Serendipity. It is played with a deck of only 16 cards, divided into four 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.
Farmer Joe, who is not the dealer, is dealt a card face up which both players can see. The dealer deals themselves a card, which they look at and then place face down. The dealer then makes three true statements which are capable of identifying which card is higher. If Farmer Joe correctly identifies which card is higher from the statements, he wins; otherwise he loses.
On this occasion, Farmer Joe was dealt the Blue King.
The dealer said:
1) My card would beat a Green King.
2) Knowing this, if my card is more likely to be a Jack than a Queen, then my card is a King. Otherwise, it isn't.
3) Given all of the information that you now know, if my card is more likely to beat yours than not, then my card is Red. Otherwise it isn't.
Farmer Joe got it wrong and lost the bet. Can you do better? Who holds the higher card?
The game was Greenjack, a popular betting game in Serendipity. It is played with a deck of only 16 cards, divided into four 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.
Farmer Joe, who is not the dealer, is dealt a card face up which both players can see. The dealer deals themselves a card, which they look at and then place face down. The dealer then makes three true statements which are capable of identifying which card is higher. If Farmer Joe correctly identifies which card is higher from the statements, he wins; otherwise he loses.
On this occasion, Farmer Joe was dealt the Blue King.
The dealer said:
1) My card would beat a Green King.
2) Knowing this, if my card is more likely to be a Jack than a Queen, then my card is a King. Otherwise, it isn't.
3) Given all of the information that you now know, if my card is more likely to beat yours than not, then my card is Red. Otherwise it isn't.
Farmer Joe got it wrong and lost the bet. Can you do better? Who holds the higher card?
