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Annual Monty Hall Game Show Thread 2015
Posted on 1/13/15 at 10:10 am
Posted on 1/13/15 at 10:10 am
quote:
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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
I have to disagree with the "always switch" conclusion. The correct answer about the probability is that it is 50/50.
The problem is not in the math--it is that the setup and explanation of the problem always given is a cheat. The problem is changed in the middle, but the original probabilities are not. That is why it is so counterintuitive.
Those who discuss the probability in terms of 33% and 66% after the first door is eliminated are carrying forward into the new problem (where only two doors exist) information from the original problem, and thus not establishing anything more earth shattering than the fact that we originally had 66% goats and 33% cars to choose from.
In fact, the reason people commonly say the answer is 50/50 is that most people intuitively accept the initial premise that a door is simply removed from the problem--leaving two doors, known to hide a goat and a car. This is clearly a 50/50 choice.
You can appreciate this truth if you consider the person who comes into the game at the point where the contestant is told that there is goat behind one of the doors he didn't pick. That door is effectively removed from the game, as if it never existed. The new person faces simply two doors, with no knowledge about what has gone on before, and the certainty that there is one goat and one car. It does not matter which of the two doors he picks (or whether he "picks" one then "switches", or doesn't switch.) In the end, he chooses one door--and has a 50/50 shot at getting it right. Thus, for him, it doesn't matter if he switches or not--his probability is always 50/50.
Again, the problem with this riddle is that the mathematical explanations always start with the premise that you must carry forward the old 33/66 probabilities from the first problem into the second. That is the cheat--you don't. The Monty Hall problem really is a 33/66 probability problem changed into a 50/50 problem, but discussed mathematically (incorrectly)after the basic premise has been changed as if it is still a 33/66 problem.
This post was edited on 1/13/15 at 11:17 am
Posted on 1/13/15 at 10:11 am to link
I agree with you and am prepared to take my beating.
Posted on 1/13/15 at 10:11 am to link
quote:
have to disagree with the "always switch" conclusion. The correct answer about the probability is that it is 50/50.
you dumb
Posted on 1/13/15 at 10:12 am to link
God dammit, dude. Do a fricking experiment at your house with two red cards and a black card and keep track of how many times you win switching vs not.
Posted on 1/13/15 at 10:15 am to link
quote:
Those who discuss the probability in terms of 33% and 66% after the first door is eliminated are carrying forward into the new problem (where only two doors exist) information from the original problem, and thus not establishing anything more earth shattering than the fact that we originally had 66% goats and 33% cars to choose from.
This is because the door selected by Monte is NOT random. He will ALWAYS pick a door without a winner.
Have fun in the thread.
Posted on 1/13/15 at 10:17 am to link
quote:Yes.
Is it to your advantage to switch your choice?
Posted on 1/13/15 at 10:19 am to link
quote:
The correct answer about the probability is that it is 50/50.
You mean that if you have to choose between 2 things the odds are 50/50 you'll be right???? Damn, math and shite
Posted on 1/13/15 at 10:19 am to link
Let Marylyn explain it to you.
Note how she uses even MORE doors to explain it to you. When you see the "more doors" explanation, if you don't get it then, I can't help you.
Note how she uses even MORE doors to explain it to you. When you see the "more doors" explanation, if you don't get it then, I can't help you.
Posted on 1/13/15 at 10:20 am to link
quote:
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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
That bolded part is the key and is what separates this from "Deal Or No Deal" or other shows where choices are removed at random.
So, always switch. Always.
Posted on 1/13/15 at 10:21 am to link
We should have saved this thread for tomorrow..
Posted on 1/13/15 at 10:22 am to genro
quote:
Solid troll. 8/10
This too.
(The plane will take off, morons.)
Posted on 1/13/15 at 10:23 am to ShortyRob
To make it simple, assume there are 5 doors. You pick one.
Of course, Monty is going to open 3 other doors with nothing behind them because, well, that's what he does. He isn't going to open the door with the prize.
What about if he did it with 50 doors? You pick one, then he opens 48.
If you are STILL saying you aren't switching after he picks 48, you're a damned idiot.
You see, sure, you're trying to argue as if Monte isn't PART of why you switch. But of course, he is. His choices to open aren't random. If they were, occasionally, HE would open the winning door. But, he doesn't. As such, he most certainly is part of the odds decision.
Of course, Monty is going to open 3 other doors with nothing behind them because, well, that's what he does. He isn't going to open the door with the prize.
What about if he did it with 50 doors? You pick one, then he opens 48.
If you are STILL saying you aren't switching after he picks 48, you're a damned idiot.
You see, sure, you're trying to argue as if Monte isn't PART of why you switch. But of course, he is. His choices to open aren't random. If they were, occasionally, HE would open the winning door. But, he doesn't. As such, he most certainly is part of the odds decision.
Posted on 1/13/15 at 10:25 am to ShortyRob
Him knowing what's behind each door doesn't mean jack shite. I know there's a car behind 1 of the 2 doors. If he uses the same schtick each time this happens, you would switch out of a winner just as often as you would switch into a winner
Posted on 1/13/15 at 10:26 am to ShortyRob
quote:It's easier to understand if you use bigger numbers.. If you are given 100 doors, you pick #1 and Monty opens 98 of them leaving, your #1 and #63 you're obviously better off if you switch.
If you are STILL saying you aren't switching after he picks 48, you're a damned idiot.
Posted on 1/13/15 at 10:29 am to ShortyRob
Thanks ShortyRob for proving my point.
In your explanation, you are absolutely correct--but only because you consider it all one game.
However, the problem is always described by asking what the odds are of choosing the car once one door is eliminated (and is always a goat). That IS a new game, and the probabilities are 50/50. If mathematicians don't like the fact that people perceive it correctly to be a new game, that is fine, they can continue to run it all together as one multi-stage probability exercise. But that is mere slight of hand, not math.
In your explanation, you are absolutely correct--but only because you consider it all one game.
However, the problem is always described by asking what the odds are of choosing the car once one door is eliminated (and is always a goat). That IS a new game, and the probabilities are 50/50. If mathematicians don't like the fact that people perceive it correctly to be a new game, that is fine, they can continue to run it all together as one multi-stage probability exercise. But that is mere slight of hand, not math.
Posted on 1/13/15 at 10:29 am to Thib-a-doe Tiger
quote:Nope.
Him knowing what's behind each door doesn't mean jack shite. I know there's a car behind 1 of the 2 doors. If he uses the same schtick each time this happens, you would switch out of a winner just as often as you would switch into a winner
But, you keep on going. Don't let well proven math stop you.
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