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The Magic Cafe Forum Index » » Betchas » » The Monty Hall Paradox<< (0 Likes) Printer Friendly Version

wulfiesmith
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Beverley, UK
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Yet another gem from Scamschool ...
http://revision3.com/scamschool/scamschool-108

your opinion on this one guys?
griffindance
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I'd heard of this awhile ago (ie years). Its arguement amongst academics is mainly a question of defining the human elements. Do you start the maths at the beginning or the end of the equation.
wulfiesmith
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Check the link griffindance ...
it's a gambling bet
griffindance
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Im not saying its not cool. This is a great gem to work into a three card monte or a shells routine.
What I was replying to was the theory behind "Why it works" Mathmaticians (those PhD students who were referred to) argue about what the statistical benefits of flipping your choice actually is.
But thanks Smith. I didn't know about ScamSchool before.
Bryan Smith
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It's a really interesting one, but it makes complete sense once you understand it. One thing that he didn't stress enough in that video is that the host knows what's behind the doors and the door he opens MUST be a goat.

Also, why does he keep calling it the Monte Hall Paradox? It's counter-intuitive but is in no way paradoxical...
"I'm half drunk most the time
and I'm all drunk the rest"
--Tom Waits
RiffRaff
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It's not Monte Hall; it's Monty Hall. Monty Hall was the host of a game show called "Let's Make a Deal". This game show typically included a segment in which the contestant was asked to select one of three doors.
kmpx18
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Who likes math? statistics and probability the hardest class I took.

Pr[E1|E2] = Pr[E1 \ E2]
Pr[E2] .
slyhand
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Hmm, for some reason he shows that there are only three possible outcomes. There is actually four. Which makes it 2 for the car and 2 for the donkey.
I am getting so tired of slitting the throats of people who say that I am a violent psychopath.

Alec
MeetMagicMike
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No. There is one car and two donkeys. (Should that be "There are one car and two donkeys??
Magic Mike

MeetMagicMike.com



I took the Pledge
Gordon the discombobulator
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Documentary on the Monty Hall effect here:-

http://www.bbc.co.uk/programmes/p00wj3bd
silverking
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It's not called the Monty Hall Paradox, it's called The Monty Hall Problem.
silverking
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....of course common sense tells you that you can call it whatever you want, but in general terms, it doesn't fit the definition of a paradox (as noted above), because there's no chance at all that the intuitive (but wrong) solution may be right.

(BTW, Martin Gardner published this problem and solution under another name long before it was ever referred to as the Monty Hall Problem.)

Although the Scamschool chap referred to it by an incorrect name, his demonstration with playing cards was somewhat accurate in illustrating the "problem" such that it can be understood by laymen.

The gist of the entire process is that the "player" should re-evaluate game odds with each and every new piece of information acquired during the play of the game.
Although the game itself may not change, the players knowledge acquired during the game can (and will) have a direct effect on changing the odds as the game proceeds.
In this case, the "dealer" has apparently done something (betrayed a piece of information) having no impact on the game itself, but the astute player has understood that everything that happens during the "game" itself proceeds to contribute to the ever changing numbers used to describe the players actual chance of winning.
Scott Cram
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There's some great thoughts on this over in Magical Equations: http://www.themagiccafe.com/forums/viewt......forum=99
DelMagic
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My original thoughts on the Monty Hall Problem were the same as Slyhand's. If you pick the right door initially, there are two options for the initial reveal. When you pick incorrectly initially (two ways), the host must reveal only one door in each case. Thus, 4 scenarios are possible - two in which you win and two in which you lose when switching. Though I can't give a reason that is mathematically irrefutable, I became convinced the two acenarios which may occure when you guess right initially should only be counted as one scenario.

I became persuaded that switching was the best course when considering a very large set of doors, rather than just 3. Assuming a trillion doors, after you make your initial guess, the host opens (one trillion - two) doors. Do you want to switch with the one that is left? This drives home the thought that the inital odds in picking the correct door should drive your thinking. Since it is very likely that you didn't pick the correct door out of the initial one trillion available, then switching makes perfect sense. With that in mind, even with just 3 doors available, switching is your best choice since picking the correct door originally is less likely than picking the wrong door.
Ultrahaggis
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DelMagic - yes, 99 or a trillion that's the best way to visualise it
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