# Aces for Dinner

## Aces Pay or Aces Free?

You and a friend order a pizza and your friend says they will put 6 playing cards on the table, two of which will be aces. You can pick two of the cards and if you get one or both of the aces, then s/he will pay for the pizza and you can pay for the tip. When you hesitate your friend says. If you don't think I am giving you better odds, then you put 6 cards, two of which are aces and I will pick two of the cards and if I get one or two aces, then you can pay for the pizza and I will pay the tip.

Would it be better to pick two cards
or
to deal the cards and let your friend pick two?

Hint: Generate all the different possible combinations of cards that could be drawn. Try the aces in different positions.

Cards Card paired with others
Ace other other other other
Card 1, Ace Ace, Ace Ace, other Ace, other Ace, other Ace, other
Card 2, Ace
Card 3, other
Card 4, other
Card 5, other
Card 6, other

Cards Card paired with others
Card 2 Card 3 Card 4 Card 5 Card 6
Card 1 Card 1, Card 2 Card 1, Card 3 Card 1, Card 4 Card 1, Card 5 Card 1, Card 6
Card 2
Card 3
Card 4
Card 5
Card 6

Discussion: