The Monty Hall Problem | Undrstanding Games

The Monty Hall Paradox

The Monty Hall problem is a counter-intuitive probability puzzle based on the American television game show Let's Make a Deal.

The Setup:

You pick one of three doors. Behind one is a Car, behind the others are Goats.
Monty Hall (who knows what's behind the doors) opens another door, always revealing a goat.
He then asks: "Do you want to stick with your original choice, or switch to the remaining door?"

Should you switch?

Yes. Always. Most people think it's a 50/50 chance once one door is removed, but the math says otherwise.

When you first pick, you have a 1/3 chance of being right. The other doors collectively have a 2/3 chance. By opening a door he knows is empty, Monty "concentrates" that 2/3 probability into the one door you didn't pick.

Keep playing the simulation to see your "Switch Efficiency" climb toward the theoretical limit of 66.7%.

Pick a Door

Choose one door to find the hidden car.

Selection

Rotate Your Device

The Monty Hall Paradox

The Setup:

Choose one door to find the hidden car.