The role of probability in solving the Monty Hall problem

[IATIA]

I would keep the initial door I picked. Though my chances of being correct have changed from 1 in 3 to 50/50, it will not change what is behind the door that I chose. By opening door #3 and showing me a goat, it affirms the possibility that I chose the right door, but gives me no reason to assume that I chose incorrectly (or correctly).

Game-wise however, I would assume that I had picked the right door as they would rather I chose the goat and will try to get me to change my mind.

[robvalue]

I will tell you what you're doing wrong pool. You won't believe me, but I'll tell you.

You are over-simplifying probability. You're assuming that if there are two choices, they are equally weighted, regardless of what we know about them. That's just plain wrong.

I'm not convinced you guys even understand the game, so I'm going to have go give up. All I can say is go learn about probability. It's a useful skill.

[Mr.wizard]

I would keep the initial door I picked.  Though my chances of being correct have changed from 1 in 3 to 50/50, it will not change what is behind the door that I chose.  By opening door #3 and showing me a goat, it affirms the possibility that I chose the right door, but gives me no reason to assume that I chose incorrectly (or correctly).

Game-wise however, I would assume that I had picked the right door as they would rather I chose the goat and will try to get me to change my mind.

The probability does not become 50/50 right after one goat is open, its's still 33%. Think of 100 doors, you pick 1 and the host opens 98 doors revealing goats, the probability you choose correctly initially does not become 50/50, it is still based on 1/100, because the host knows where the car is and he is going to open only goats.

[IATIA]

The key word being "initial". After door #3 is opened, if I am asked if I want to change my mind, I have only two doors left to choose from.

[Fidel_Castronaut]

But your odds of selecting the right door if you swap have also gone up above what it would be if you stayed.

[Fidel_Castronaut]

I give up. I've explained it every way I can think of.

It's really very, very simple. Giving up is probably the right option considering something that should take one post to explain has taken umpteen pages.

[robvalue]

Here's the important point, I'll say it again once more:

We know he will open one of the other two doors. We know it will be a goat. Whether we picked right or not, he will do the same thing. It gives us no more information about whether we picked right, because he can't pick our door and he can't pick the car.

This is the crucial part. If you miss the significance of this, then you misunderstand the whole thing. He knows where the car is, and he can't pick my door. These are not meaningless details.

I tell you, I could make a lot of money out of this. I'll bet £4 against £5 that I will find the prize. I'll clean you guys out. Promise me. You have to promise... Never go to a casino!

[Fidel_Castronaut]

This puts the problem into the most parsimonious terms possible. People who still don't get it need to read it again and again until they understand before asking any questions:

http://betterexplained.com/articles/unde...l-problem/

[Mr.wizard]

The key word being "initial".  After door #3 is opened, if I am asked if I want to change my mind, I have only two doors left to choose from.

Not to short change you on a response but I just can't go through it again, the math does work.

[robvalue]

Panda: Hey that's really good, I like that. He's giving you the best choice out of the other 2 doors for you. So it's not a fair choice anymore. He never improves your own chance.

I knew he was a cunt.