Luck of the Draw
Your good friend Skinny Dakota stops by one afternoon for a friendly
game of cards. Of course, you know Skinny well enough to suspect that
any time there's a game being played, he'll be ready to make a quick buck
at your expense.
But this time, he assures you it'll be different, "This game is
complete chance, here I'll show you. Gotta deck of cards?"
You find a set of cards and hand them to him. Skinny proceeds to find
nine cards: 2H, 3C, 4S, 5C, 6S, 7H, 8S, 9H, 10C. He hands the nine cards
"Group them by suit," he says.
You do as he instructs- you now have three groups of three cards.
"Now flip them face down and shuffle the cards within each pile,
but don't mix the piles together."
When you've done this, he proposes the game:
"Okay, here's how this game is played. You pick a random card from
any pile, but don't show me. Then I'll point to one of the other piles,
and then you pick a random card from that pile. If your card is higher,
I owe you a dollar. If my card is higher, you owe me a dollar. Can't be
much fairer than that, can it?"
Knowing Skinny, it probably could be. But it does sound fair-
so what's the catch?