I have been reading about this paradox for a few months now and I am not quite convinced.
Monty’s filtering is irrelevant. He is a trickster who does not share the player’s best interests. The player is faced with a set of two choices. The first is to choose between three doors and the second is to choose between two doors. If the player chooses the same door with their second choice it would be inaccurate and misleading to refer to this choice as “sticking” or “not switching”. The same statistical calculations can be applied to both choices.
Palmer dear chap… you said this… your stretch of the truth - your wild imagination…
…explain again how a door which Monty has shown us has a goat behind in actuality has a 33.3% of having a car behind it.
I have never said this - any door represents the same chance probability as do all the doors - 1/3 the car and 2/3 a goat - they represent this when they’re closed no matter what lies behind them - and - this is where it makes your brain hurt - they represent the same chance probability when they’re opened.
The door carries the chance probability which is fixed at the outset.
Two closed doors - each with a 1/3 chance probability of the car - will have behind them at least one goat - possibly two goats - but they still represent a combined 2/3 chance of the car - and yet … and yet YOU KNOW - yes YOU - you know that there’s a goat behind at least one of them - the door carries the 1/3 chance NOT what lies behind it. Chance probability is not retrospectively changed by one eventuality or another - to claim so makes a mockery of the original forecast - makes a mockery of common sense.
You have the problem of explaining what happens to the 1/3 chance the car that was attached to the goat-door going elsewhere - an impossibility.
You may carry on attempting to mock me - but it’s water off a duck’s back - like the late comic Bob Monkhouse famously said - They all laughed when I said I wanted to be a comedian - they’re not laughing now.
Try - try if you can to raise the game of your mockery - direct insults are juvenile - childish even - we adults should be more subtle - don’t you think?
"I have never said this – any door represents the same chance probability 1/3 the car and 2/3 a goat – they represent this when they’re closed … they represent the same chance probability when they’re opened.“
You just said it. An opened door with a goat behind it has " (the) chance probability 1/3 the car and 2/3 a goat”
"You have the problem of explaining what happens to the 1/3 chance the car that was attached to the goat-door going elsewhere – an impossibility"
Already explained. If you bothered to learn about probability (you know… as it’s taught in schools and universities and written about in maths text books) perhaps you’d understand how the probabilities in the MHP change after a door is opened. You’re too arrogant and too mired in your own ignorance to even try though, and prefer instead to invent your own absurd theories.
I mock you because you pretend to know what you’re talking about. You’re a buffoon and deserve all the ridicule you get.
I said that I was departing the field of play - but I read this from Mr Orrell in contribution 645…
…same game but with extra information (hence the first-choice door chance remaining 1/3)…
And would welcome an explanation -
What extra information? Between any two doors there will always be at least one goat - so what extra information is delivered when we’re shown what we know to be the case?
And this piece of great wisdom…
…hence the first-choice door chance remaining 1/3…
The probabilities of the originally chosen door remain unchanged because we see a goat somewhere else? - remarkable!
No - there’s so much rubbish on here i can’t stay away - I will critique any stupidity and wrongheadedness that crops up.
The bridge analogy was quite good - in Rubber Bridge the cards are newly dealt for each hand - but the most common form of Bridge - certainly competition Bridge is called Duplicate - each hand is dealt once and kept intact for others to play (duplicated) - the contest is to see who gets the better result with the same cards. And truly - with the fall of the cards new information is revealed - but not always - sometimes logic dictates that a certain card must be in a certain place - when that card falls there is no new information - just confirmation.
When Monty reveals a goat we learn nothing new - he just confirms what was already certain to be the case.
You boys will really need to sharpen up your thinking powers - lay off the alcohol for a while perhaps.
If you give up your selected door you can have these two doors together - one of which I’ve already opened to reveal a goat - each door representing - just like the door you selected - a 1/3 chance of the car and a 2/3 chance of a goat - remember - the chance probability of any door is a forecast and only a forecast - the chance probability allows for either eventuality - the chance probability (the forecast) is not changed because of one particular outcome or another.
" I will critique any stupidity and wrongheadedness that crops up."
Critique yourself then Richard, your posts are full of “stupidity and wrongheadedness” … or you can “leave the field of play” as you promised. You can’t even get that right.
“If you give up your selected door you can have these two doors together”. No you can’t. Where precisely does it say that Richard, where? Show me. In the MHP you win either a goat or a car, in your made-up game you win either 2 goats or a goat and a car. Different prizes different games, even someone as ignorant as you must see that.
Where precisely does it say that Richard, where? Show me. In the MHP you win either a goat or a car, in your made-up game you win either 2 goats or a goat and a car.
What do you mean - where precisely does it say that? Of course (it) Monty doesn’t say that - if he did say it then it would give the game away to all the naive simple-minded people who’re unable to work out what’s actually going on - but that effectively is what’s going on based on the most simple analysis.
As for winning a goat - don’t be silly - the goats are a symbol to indicate not a car - they need not be real - there would be goat shit all over the studio - and the smell - and they would eat any flowers or sandwiches - I can not imagine real goats on the set of the MHP - just token goats…
Adults are sometimes economical with the actualité - especially when playing tricks on children - in the entertainment world I think they call it theatrical license -Monty is an entertainer - he is not a notary public - he means you well but the conditions placed on him require him to confuse the easily confused. You for instance.
And my game is not a made-up-game - it’s the same game as yours - it’s my superior analysis that’s different.
Should I regret my return here? It’s tiresome - I had forgot how tiresome…
You might think you comments are witty Richard … problem is no one else does. They’re crass and tiresome.
Come on Richard give us a proper laugh… explain again how a door which Monty has shown us has a goat behind in actuality has a 33.3% of having a car behind it. That had us all in stitches last time! What do you call this part goat part car mechanical animal anyway?
Go away Richard, wilful ignorance such as yours is a most unappealing trait.
Richard, the logic is that if you pick door one and turn your back on the doors and the host opens door 2 to reveal a goat, you cannot name the closed door to which you want to switch. So knowing which door conceals the goat is vital as the host will not allow you to choose both door.
More particularly, the question posed by Ms vos Savant does not refer to switching to 2 doors, it refers to switching to one door only:
From Parade magazine in 1990 (vos Savant 1990a):
“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?”
The choice is from one door to another, not from one door to two others, even though switching to two doors effectively is what is happening. That does not mean that is what is actually happening.
Fine words dear friends but you confuse Chance Probability with Result.
The first is a prediction of what might happen in the future and the second a statement of what actually happened. There is no connection between them.
What actually happens does not cancel the prediction of what might happen - if this were so then it would be pointless to have, calculate or even consider a chance probability - probability would be made conditional on result - tantamount to saying ⅔ chance of a goat but only if there is a goat -completely illogical.
You must train your mind(s) to accept either eventuality - ⅔ a goat and ⅓ the car means that either can be the case - the goat more likely - the car less so. There is no guarantee of one result over another - probability just makes a comparison of one against another.
We see a goat? Well that was the most likely outcome but the door had (and still represents) a less likely chance of the car.
A result can not alter a chance probability - a probability allows for either eventuality in proportion…
You may think that a single door represents a ⅔ chance of the car - but as far as a car is concerned to have a ⅔ chance of it you need two doors - both closed or both open or one of each. Even both with a goat - still a ⅔ chance of the car because a chance probability is irrespective of and not conditioned by content.
Probability talks of the future - result talks of the present - they’re not connected.
And there’s really no point in discussing multiple iterations of the MHP to obtain a proof - we do not need to get a proof - it’s beyond doubt that the greater chance is to swap.
@Seph By eliminating the other door you’re essentially being offered the opposite of what you initially picked. So if there is 2/3 chance of getting a bad option then you will get a 2/3 chance of a good option if you always swap.
You can get rid of the words ‘By eliminating the other door you’re essentially’
and say
You’re being offered the opposite of what you initially picked. So if there is 2/3 chance of getting a bad option then you will get a 2/3 chance of a good option if you always swap.
Get rid of a few more words!
Eliminating the other door don’t mean shit. He doesn’t have to open anything - he’s just saying Hey , bet that is in these two rather than the one you chose first’
(Hello Jonathan, Gingold Buxton here, I’m from Venus)
“Hey , bet that is in these two rather than the one you chose first.”
That’s just your (and other’s, including Buxton’s, at least at some stage) take on what Monty is saying.
Monty is actually saying:
“Would you like to switch from your initial choice to the other remaining door?”
As for the elimination of one door not meaning “shit”, the elimination is an essential step that makes the choice between two doors possible and gives rise to the entire problem.
If, like Buxton, you prefer to imagine that Monty is offering you two doors when only one other door remains, that is a matter for you. However, that imagining does not reflect the reality of the situation.
Your interpretation of what Monty is saying is based on a figment of your imagination, no matter how much the effect of what you imagine is happening might correspond to what is in fact happening.
“Hey , bet that is in these two rather than the one you chose first.”
That’s just your (and other’s, including Buxton’s, at least at some stage) take on what Monty is saying.
Monty is actually saying:
“Would you like to switch from your initial choice to the other remaining door?”
As for the elimination of one door not meaning “shit”, the elimination is an essential step that makes the choice between two doors possible and gives rise to the entire problem.
If, like Buxton, you prefer to imagine that Monty is offering you two doors when only one other door remains, that is a matter for you. However, that imagining does not reflect the reality of the situation.
Your interpretation of what Monty is saying is based on a figment of your imagination, no matter how much the effect of what you imagine is happening might correspond to what is in fact happening.
"Buxton has left the field of play " So you keep saying…but you’re still here.
“bored with the ramblings and petty challenges of closed minds” More like bored with everybody else pointing out your inconsistent arguments, invalid logic, and nonsensical mathematics.
“bored too by constantly having to repeat himself”. You were wrong the first tiime, repeating the same crap over and over and over and over again doesn’t make you right.
“You can think the swap offer is to exchange one door for another single door” It is , that what the problem says.
"or …you can think it’s a swap from one door to two doors " It isn’t.
“If you adopt my approach then there’s no confusion”. If we adopt your approach probability theory needs to be rewritten.
"the insurmountable problem of having to explain how a door’s chances of hiding a car begin at 1/3 and miraculously change to 2/3 " It’s been explained many times… you’re just too stupid to understand. Alternatively YOU can believe a goat has a 33.3% chance of actually being a car instead - even though you see the goat standing there in front of you. Preposterous!!
“It’s the stuff of fantasy” It’s the stuff of mathematics, fantasy to an ignoramus like you no doubt.
“this is absolutely and positively my last contribution here.” I wish I could believe that. Please Richard … just go away.
‘BTW, Seph, that’s the business. Shortest line I’ve seen to get it explained right.’
… unless you look at post 1 from 9/4/04 above (yes, the very first comment on this thread) in which ‘uwe’ says precisely the same thing as Seph in only four more words. Five years and over six hundred posts later we have come full-circle.
statistics theory dictates that a 1 0f 2 choice is better odds than a one of three, agreed. however a 50/50 (one of two choice) is always going to be 50/50, the theory derived by nfactors indicating elimination somehow increases your chance of success is flawed, 50/50 chance - keep rolling the dice staticisions…
‘… the theory derived by nfactors indicating elimination somehow increases your chance of success is flawed …’
Load up a six-shooter and aim at your screen. Now pause, remove two of the bullets, spin the chamber and aim again. Has the chance of blasting a hole in your screen not decreased?
Take a pack of cards, pick one out but don’t look at it. Give the remaining 51 cards to a friend and ask him/her to remove 50 cards that are NOT the Ace of Clubs. There are now 2 cards left, you have one and your friend has one. What makes you think your card has a 50% chance of being the Ace of Clubs?
Perhaps you should change your moniker to “nomathjohn”
'Clue #5. Saltmarsh has disappeared.'
Clue #6. Buxton and Saltmarsh have reappeared just 4 hours 33 minutes apart (627-9 and 632).
‘… the insurmountable problem of having to explain how a door’s chances of hiding a car begin at 1/3 and miraculously change to 2/3 … Do not attempt to answer any of these questions – they’re unanswerable.’
I’m going to try anyway, Richard. You’re on the show; Monty has locked all three doors and gives you a key that can unlock only one of them (the one with the car). You pick a door, and Monty takes the key to one of the other doors and tries it in the lock. It does not work. He gives you the key back. Now what are the chances you can unlock the same door Monty just chose with that key? Is there still a 1 in 3 chance it will unlock it? If you try it three times might it unlock on the third attempt? Just to be clear, I’m suggesting the chance you have of unlocking it with that key has changed from 1 in 3 to 0 in 3. Miraculous.
While Buxton may not be Saltmarsh (although I maintain my suspicions), he sure as hell sounds like Lord Monckton:
As for nonamejohn, he appears to have been tutored by Buxton-Saltmarsh so tortured and flawed is his reasoning, including this circular gem “… a 50/50 … is always going to be 50/50…”
Can’t argue with that. Except it has little to do with the MHP other than the chances of picking the winning door in the final stage of MHP by flipping a coin or some other equally random method.