Listen to Mr Saltmarsh and mark his words well.
To Richard Buxton (and everyone else):
Richard, you have cracked it many times in this thread. It’s to do with the language.
I have had problems with it until it became obvious that showing a goat is irrelevant. Then that bit of indirection goes away and it all makes (linguistic) sense.
Isn’t it all lovely? Magicians do this.
Yes - part of the preamble at the very top says…
The fatal flaw in the Monty Hall paradox is not taking Monty’s filtering into account, thinking the chances are the same before and after. But the goal isn’t to understand this puzzle — it’s to realize how subsequent actions & information challenge previous decisions.
To which I take great exception -
The goal IS to understand the puzzle - unquestionably it’s to understand it.
Subsequent actions and information (what information?) do not challenge anything.
What filtering? How can the act of opening a door be considered filtering?
Clearly the person who wrote the opening paragraphs has little appreciation of this superb puzzle.
@Chris Saltmarsh
It’s nice to see that Richard has a sockpuppet. Just in case you are a separate individual, please explain the proposed game in comment 570. It has baffled Richard so far (So much for him cracking it! Of course he can’t extend his flawed logic to a very similar game)
@Richard
Please, please re-read the fist line of comment 581.
Indeed Monty does no filtering. Chances in each box do not change.
What Monty does is change the contract.
‘Bet on your first pick being right’
‘Bet on any one of the other 99’ (or 2, or 76…) being right’
Showing goats changes zilch, it is the new proposition which is more attractive (unless, of course, you want a goat)
HAHAHAHA what fun!
Mr Ross, name calling does not help. I shall read what you refer to.
However, the immediate little nasty doesn’t give me a lot of respect for you.
@Chris Saltmarsh
Ok. If what you say is true and showing a goat changes nothing let’s remove that silly distraction. It doesn’t filter anything, makes no difference, right?
So, now you have a choice: Keep your original door or switch to one of the two other closed doors. Uh-oh. What now? As I’ve pointed out several times, you only get to open one door. Please re-read the proposed thought exercise in comment 570 and tell me what the odds are. I want hard numbers, not hand waving.
- There are not two closed doors. The contract has changed. ‘Anything in the other doors’. In the 3-door one Monty gives you a clue - he opens a goat door.
- Hard numbers are easy. Just try it.
- End of. You call me a sockpuppet for no goddam reason, you ain’t worth talking to. Bug off.
If Saltmarsh-Buxton wants to view the MHP as choosing between his first guess and all of remaining doors, I say let him.
But as yet another explanation shows,
in reality, it is a choice between two closed door, no matter how many doors are presented in the first place.
For instance, Saltmarsh-Buxton, if a stranger to round 1 of the MHP entered the room when only two doors remained and was asked to pick the car door, they would have a 50/50 chance of picking correctly.
However, if they were told which door the contestant chose first, they would then know that one door had a 1/n chance (where n = total number of doors) and the only other door would have a n-1/n chance.
So if the choice for someone who comes in after the first phase of the MHP is between two doors, why is not also a choice between two doors for the contestant standing next to them?
Well, it is, of course.
Salmarsh-Buxton likes to see it as something different, a choice between one door and n-1 doors, and that is fine if that is what he needs to do to understand the problem and the probabilities, but it is an unnecessary pretense for anyone who can deal with the reality of the MHP and what really happens.
Now, through his alter-ego, he starts talking about “contracts” having changed and of being offered “anything in the other doors” when the actual offer is to stick with the first choice or switch to the only other closed door, the offer being made after the location of the goat(s) has been revealed.
This is perfectly true… what Ross says…
As I’ve pointed out several times, you only get to open one door.
Because…
Monty has craftily and prematurely opened the other door - your own door - one of the doors you’re swapping to - the door with your own goat behind it - he shows you your own goat - the goat you knew was there all along - the goat that comes as no surprise and changes nothing… then he offers you the chance to swap - after he’s shown you your own goat - he sets out to fool you and he succeeds.
One door has a 1/3 chance of the car so the other two doors together have a 2/3 chance and you know at least one of those doors hides a goat – Monty shows a goat and then he makes the offer to swap. The effective offer is to swap one door for two doors – one closed and the other showing a goat. You know there’s a goat so seeing it is no help.
Hang fire, it ain’t Saltmarsh-Buxton, I never hit this thread and i don’t know Buxton (although I can get his argument, it makes sense)
I’m trying to explain my take on how to get your head around the classic problem.
In the classic problem, all the goat doors are opened - except (perhaps) one
My way of describing that is that showing the goats adds nothing. The proposition changes. Bet on the (n-1) having the good stuff, or your original one.
Now, for hard numbers, do the math or try it. Just run the thing through a bit of code (that’s what I do for a living. Code stuff)
The answer, in the 3-box case, is ‘change’. Can’t argue with that. So try to explain.
And my LINGUISTIC call is that the CONTRACT changes, not the numbers.
Wow! ‘Sockpuppet’? ‘Alter-ego’. Where are you guys?
Bye.
Chris Saltmarsh … you are Richard Buxton and I claim my 10 pounds!
Richard (Chris) you said: “This will be my last here…”. You promised, and you… lied! 
OK, last one. There’s some weird people around.
Get your rocks off on it.
This is a wee problem. Not a bloody religion, and no reason to trash someone.
Go suck, losers.
Since “showing the goats adds nothing” - in your opinion does it make any difference if Monty accidently opens a goat door as opposed to intentionally opening a goat door (or even if a ‘gust of wind’ blows a door opens to reveal a goat)?
Apologies, that last comment was addressed to you Chris
Buxton says:
“The effective offer is to swap one door for two doors – one closed and the other showing a goat.”
That’s right, Richard. That is the effect, and it is what is effectively happening that helps people understand the more favourable odds of switching, eg swapping from one door to n-1 doors.
No argument that is EFFECTIVELY, ie for all intents and purposes, what is happening.
However, in reality, what is ACTUALLY happening is that AFTER the location of one of the goats has been revealed, the “host” is giving the “contestant” the choice of sticking with their first pick or switching to just ONE other door, being the only other closed door. After all but one of the goat doors have been opened, the other door now carries probability of n-1/n instead of 1/n.
BEFORE the goat(s) was/were revealed, one would need to be offered the opportunity to swap to all of the other doors to achieve a chance of winning of n-1/n.
But in reality, that does not actually happen. The offer to switch is made when the only choice is between the first pick and the only other closed door.
When MHP is played in its purest form and explained for the first time, the “contestant” is not told and is unaware that the offer to switch will be made until it is actually made. So how can any contestant be said to have “mentally” switched to the remaining doors when they do not even know that an offer will be made?
Furthermore, if sometimes the host in the MHP offers a switch and sometimes he does not, the contestant cannot possibly know to pick the other doors in advance.
And why would the explanation for what is happening after the goat door is opened vary depending on whether the contestant thought the switch would be offered or not?
To be consistent, we have to assume that the contestant does not know the switch will be offered until the offer is made. This is how the MHP is played and this is how we present it to enquiring minds. We don’t tell them about the switch option until after the goat has been revealed, so in reality no one can do any mental gymnastics and choose to switch beforehand. Even if they did, it would make no difference to the explanation that the only other closed door now carries the odds all of the doors that were opened and its own original odds of 1/n, ie n-1/n.
Buxton-Saltmarsh are inhabiting an imaginary world, population between 1 and 2, in which they that see an open door as a closed door because, against the rules of the game and the offer being made, they were going to choose it even before they knew the offer would be made!
Bizarre and unhelpful.
Furthermore,
Buxton says:
“The effective offer is to swap one door for two doors – one closed and the other showing a goat.”
That’s right, Richard. That is the effect, and it is what is effectively happening that helps people understand the more favourable odds of switching, eg swapping from one door to n-1 doors.
No argument that is EFFECTIVELY, ie for all intents and purposes, what is happening.
However, in reality, what is ACTUALLY happening is that AFTER the location of one of the goats has been revealed, the “host” is giving the “contestant” the choice of sticking with their first pick or switching to just ONE other door, being the only other closed door. After all but one of the goat doors have been opened, the other door now carries probability of n-1/n instead of 1/n.
BEFORE the goat(s) was/were revealed, one would need to be offered the opportunity to swap to all of the other doors to achieve a chance of winning of n-1/n.
But in reality, that does not actually happen. The offer to switch is made when the only choice is between the first pick and the only other closed door.
When MHP is played in its purest form and explained for the first time, the “contestant” is not told and is unaware that the offer to switch will be made until it is actually made. So how can any contestant be said to have “mentally” switched to the remaining doors when they do not even know that an offer will be made?
Furthermore, if sometimes the host in the MHP offers a switch and sometimes he does not, the contestant cannot possibly know to pick the other doors in advance.
And why would the explanation for what is happening after the goat door is opened vary depending on whether the contestant thought the switch would be offered or not?
To be consistent, we have to assume that the contestant does not know the switch will be offered until the offer is made. This is how the MHP is played and this is how we present it to enquiring minds. We don’t tell them about the switch option until after the goat has been revealed, so in reality no one can do any mental gymnastics and choose to switch beforehand. Even if they did, it would make no difference to the explanation that the only other closed door now carries the odds all of the doors that were opened and its own original odds of 1/n, ie n-1/n.
Buxton-Saltmarsh are inhabiting an imaginary world, population between 1 and 2, in which they that see an open door as a closed door because, against the rules of the game and the offer being made, they were going to choose it even before they knew the offer would be made!
Bizarre and unhelpful reasoning.
Furthermore,
For Mr Eldritch - your 601… You ask…
Since “showing the goats adds nothing” – in your opinion does it make any difference if Monty accidently opens a goat door as opposed to intentionally opening a goat door (or even if a ‘gust of wind’ blows a door opens to reveal a goat)?
My reply…
Given that there’s only one door with a car behind it perforce there are two goat-doors. Hold that thought…
Between any two doors there will always be at least one goat - you know this.
The arrangement of two doors will be one of three possible conditions like this
Goat Goat
Goat Car
Car Goat
Notice that in each of the three possible combinations that there’s always at least one goat. Try to remember that…
Think about it for a moment or two - the significance of there always being a goat - it’s impossible not to have a goat - dead cert there’s a goat in there somewhere.
And for whatever reason - forgetful host - passing vandal - act of God - we get to see the goat we already knew about - so what has changed?
Well - nothing really - a previously closed door is now open - we see a goat - the most likely thing to be hiding behind any door in the ratio two to one (2:1).
The initial probabilities remain as they were before the door was opened - each door 2:1 a goat - probabilities do not change as new information arrives - how can they change? The numbers don’t know that a door has been opened or the method of its opening - the numbers involved are unaffected - casual observers feel a wave of emotion and assume an event of great significance - they feel an urge to recalculate the original probabilities but they forget this…
The probabilities are determined by there being three doors - Two Goats and a Car - and when the wind blows the door open or a stage-hand crashes into it and a goat comes into view - Guess What? There are still three doors two goats and a car.
The result - the appearance of the one of the goats - does not retrospectively cause the probabilities to change - for some simple-minded people the numbers do change - but the numbers don’t know a door has opened and the numbers don’t bother themselves about the car or the goats - the numbers are ambivalent about the content of a door - in short - they don’t give a toss.
It makes no difference one way or another way or even not at all.
The Host shows a known quantity - a wise contestant knows of the goat in advance and because of that wisdom does not need to see it - and if the wise contestant does actually see a goat he or she is smart enough not to be influenced by it or by the manner of its exposure - the wise contestant is blind to the revealed goat - it’s a don’t-care goat.
Others throw themselves into a mild trance and imagine a blinding and significant event of great importance - whatever floats their goat I suppose - but they’d just be allowing the host to spook and confuse them.
No it makes no difference - we see what we knew in advance to be the case.
If a door as a 2:1 chance of hiding a goat - and we see a goat - how and why are the natural laws of the universe and our numbering system affected?
To change that 2:1 probability is to fly in the face of the original calculation - to fly in the face of logic and reason - and it’s not exactly rocket science - don’t you think?
Could you not have reached this conclusion on your own?
Do you genuinely have trouble thinking this through?
Or are you teasing me?
Richard,
Can’t you keep your comments a bit shorter? Your prose is tedious to read at the best of times, 50+ lines of misinformed nonsense is almost too much, particularly when, as usual, you arrive at the wrong answer.
“No it makes no difference – we see what we knew in advance to be the case.” is demonstrably wrong. Prove it yourself, get 3 playing cards and randomly turn over one of the 2 not initially picked. Only consider those games where the prize card is not revealed, and see how many games you win by staying and by switching