Weighing The Odds In HE Question: Monty Hall

[HoneyBadger]

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I wish i could remember the exact mathematical forumla that proved it..if anybody has it please post it...

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I did... about 5 posts earlier. I proved both cases.

[BigF]

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If the golf ball scenario is similar, then the guy eliminating golf balls is actually demonstrating that the 9,998 balls he eliminates are losers. I'd say that's pretty conclusive evidence that he does, in fact, know which ball is the winner.

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So you are saying if he doesn't know which ball is the winner, there's no way he could show you 9,998 losers?

[Felipe]

3 doors, one has a car, two have goats.

You have 1/3 chance of getting the car, 2/3 chance of selecting a goat.

You pick a door. It will *MOST LIKELY* have a goat behind it ( 66%) so when he shows you the other door with a goat, switching is +EV because you have 2/3 chance of selecting the car (now with one goat exposed) (because you have MOST LIKELY already selected a goat as your first door)

That's why switching is the *best* decision.

1. you can choose a door with a goat, he shows you a goat, and you switch win
2. you can choose a door with a goat, he shows you a goat (diffrent order), you switch, and you win
3. You select a car, he shows you a goat, you switch, and you lose

Switching is +EV.

[321Mike]

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A more interesting case of the Monty Hall problem is when you are not sure if Monty is trying to help you or trying to screw you, and you are not sure if Monty knows the math, and if he does, if he thinks you know the math. Then it gets much more interesting as you have to try to figure out how smart he is, how devious he is and how smart he thinks you are. Hey, that sounds like poker to me!

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I like this idea. Forget the math. It's all about the metagame. Monty knows where the car is and he is out to screw us over. We've got to out think him.

zeroth level thinking: "I've got door #2 and I've seen a lot of people win cars by picking door #2 so I'm sticking with it."

first level thinking: "Monty revealing the goat behind door #1 makes it more likely that the car is behind door #3 so I'll switch."

second level thinking: "Monty probably knows that I have a math degree because I put that down on the questionnaire they make us fill out. So he believes that I would know that I should switch if he reveals a goat. He wants me to switch. Therefore, I'm sticking with door #2."

third level thinking: "Monty knows that I know that he knows that I have a math degree and probably know the math behind switching. He would expect me to be suspicious of him revealing a goat. He knows that I would expect him to be attempting to trap me into a bad play. So he is only pretending to try to get me to switch when he really wants me to stick. Therefore, I will switch to door #3.

2+2 level thinking: "I wonder how much that goat is worth on Ebay."

[Matt Ruff]

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If the golf ball scenario is similar, then the guy eliminating golf balls is actually demonstrating that the 9,998 balls he eliminates are losers. I'd say that's pretty conclusive evidence that he does, in fact, know which ball is the winner.

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So you are saying if he doesn't know which ball is the winner, there's no way he could show you 9,998 losers?

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It's not literally impossible, but he'd have to be an amazing guesser.

[HoneyBadger]

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It's not literally impossible, but he'd have to be an amazing guesser.

[/ QUOTE ] Guess what, he'd have to be about as an amazing guesser as you choosing the right ball from the start [img]/images/graemlins/wink.gif[/img]

The problem here is that we are dealing with a specific outcome of a chance experiment. thats why it feels so counter intuitive.

[Matt Ruff]

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Guess what, he'd have to be about as an amazing guesser as you choosing the right ball from the start [img]/images/graemlins/wink.gif[/img]

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Which is why I don't think he's guessing at all.

Same deal with Monty: I could buy him picking a goat door at random on *one* show, but if he's picking doors every day, and never gets the one with the car behind it, pretty soon it becomes obvious that he must know where the car is.

[HoneyBadger]

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Guess what, he'd have to be about as an amazing guesser as you choosing the right ball from the start [img]/images/graemlins/wink.gif[/img]

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Which is why I don't think he's guessing at all.

Same deal with Monty: I could buy him picking a goat door at random on *one* show, but if he's picking doors every day, and never gets the one with the car behind it, pretty soon it becomes obvious that he must know where the car is.

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Yes, so that's why you should _always_ switch. If you don't know if he is guessing or not, given the outcome, the chance he is guessing is slim. Either way, you never loose expectation if you switch, but you might (very probably) gain it when you do. Switching is a win-win situation.

[Matt Ruff]

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Yes, so that's why you should _always_ switch. If you don't know if he is guessing or not, given the outcome, the chance he is guessing is slim. Either way, you never loose expectation if you switch, but you might (very probably) gain it when you do. Switching is a win-win situation.

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Yes, I know. We are in violent agreement.

[HoneyBadger]

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Yes, I know. We are in violent agreement.

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Haha, yes, isn't it fun for a change? [img]/images/graemlins/smile.gif[/img]