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: