# Thread: The Monty Hall Problem

1. ## The Monty Hall Problem

This is a famous puzzle. Most people find the answer surprising. Many people simply cannot be convinced of the correct answer, even after having it explained to them. It goes like this...

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

-Rusty

2. I figured out how to make this problem into a great bar bet you can play with quarters. It is also a great way to convince non-believers that the correct answer is indeed correct. When their money is on the line, it starts to get real pretty quickly.

-Rusty

p.s. That Dog in the Night-Time book sounds interesting.

3. wilhouse

4. If I understand your answer, your numbers are incorrect. You are saying if you switch doors, you will have a 50% chance of getting it correct.

5. well, that's what I was saying.

your first choice gave you a 1 out of 3 chance of getting it right. choosing that door will always give you a 1 out of three chance.

abandoning that choice for the other door gives you a 1 out of 2 chance, improving your odds from 1/3 or 33% to 1/2 or 50%.

wilhouse

6. You are close, but you underestimate the improved odd of switching. If you switch, your probability of winning will increase to 2/3.

-Rusty

7. we're going to have to agree to disagree.

cause I disagree.

as a matter of fact, one could argue that since the winning door was determined while there were three choices, no matter what happens the odds of picking the right door will ALWAYS be 1/3. Even after you've picked both wrong doors.

wilhouse

8. This is one of those great problems where the answer seems paradoxical. But it is not. It is a bit counter-intuitive.

You are correct that the chance of picking the correct door at the start is 1/3. This means you probably picked the wrong door with a probability of 2/3.

Given that you probably picked the wrong door, and Monty shows you another wrong door, don't you think you should switch doors?

The only randomness involved in this problem is the first choice.

-Rusty