
A casino offers a card game. There are 52 cards in a deck. Each time the cards are thoroughly shuffled (so each card has equal probability of being selected). You pick up a card from the deck and the dealer picks another one without replacement. If you have a larger number, you win; if the numbers are equal or yours is smaller, the house wins — as in all other casinos, the house always has better odds of winning.
What is your probability of winning?