Pick any card from the deck above.
When the cards are dealt, the Ace is placed randomly under one of 52 cards. You point to one. Your odds of having picked the Ace: 1 in 52. That means there's a 51 in 52 chance it's somewhere in the other 51 cards.
Now the dealer — who knows where the Ace is — flips over 50 of those 51 cards, and he's forbidden from flipping the Ace. This is the key: he can't act randomly. If the Ace is among those 51 cards (which it is 51 out of 52 times), he must leave it face-down. He has no choice. His knowledge forces his hand.
So ask yourself: why did that last card survive?
Your card survived because you froze it — a blind guess, protected by the rules of the game, not by any information. The other card survived because the dealer was forced to protect it while eliminating everything else. One card was preserved by ignorance. The other was preserved by knowledge.
They look the same — two face-down cards — but they have completely different origins. That's why they have completely different odds. You're not choosing between two equal unknowns. You're choosing between the output of a blind guess and the output of an informed elimination process.
With 3 cards (the classic Monty Hall problem), this same logic applies — switching wins 2 out of 3 times. But 33% vs 67% is close enough to 50/50 that your brain rebels. With 52 cards, the asymmetry is so extreme that nobody would hesitate. The math is identical. Only the feeling changes.
For any number of cards n: keeping your card wins 1/n of the time. Switching wins (n−1)/n of the time. With 3 cards, that's 33% vs 67%. With 52 cards, it's 1.9% vs 98.1%. The classic Monty Hall problem with 3 doors is just this game with n = 3.