Well said Bond.
You win 2 prizes: 1 for being correct and another for not agreeing with Buxton the Buffoon who continues to stand alone against the rest of the world with his opinion of the MHP.
" In the MHP the door that Monty did not open and that we did not initially select has a 2/3 chance of concealing a car." Take note of Bond’s wise words Richard, they speak the truth 
From Jonathan…
But your “chance probability” is not predictive, Richard. And probability is nly of any use if it predicts the result.
Probability predicts what MIGHT be the result -might be this - might be that - either can happen by proportion - probability does not forecast what’s going to happen - probability allows for either eventuality - it does not insist on one particular result.
This is the confusion that sends you into a fantasy world.
Acck!! Edit to comment 707, 2nd last paragraph.
Switching does not guarantee a win but increases your chances from 1/3 to 2/3, even when you know 1 of the 2/3 chances is a goat. You should know there must be a goat even before Monty shows you a goat.
I’m getting confused. I will bet with all those in favour of switching.
Well - this gives a lie to Mr Bond being the alter-ego of Buxton or Saltmarsh…
Mr Bond states…
In the MHP the door that Monty did not open and that we did not initially select has a 2/3 chance of concealing a car.
I don’t agree - a door can be considered to have a ⅔ chance of winning but it only represents a ⅔ chance.
He later corrects himself by referring to a SET of doors having a ⅔ chance - I agree absolutely - it’s the set that has the combined ⅔ chance - not an individual door.
Re 711 - correcting 707
even when you know 1 of the 2/3 chances is a goat.
Should read
even when you know 1 of the 1/3 chances is a goat
Confused indeed. Monty makes the offer (to switch) AFTER he reveals a goat. The offer is only a good one if a goat is revealed; without that it confers no advantage.
Well said indeed.
Correcting 713 correcting 711 correcting 707:
Switching does not guarantee a win but increases your chances from 1/3 to 2/3, even when you know there is still 1/3 chance of a goat.
Buxton
"Finally your case is weakened if you resort to personal criticism and the language of the gutter and the trailer-park social club"
Water off a ducks back isn’t it Richard? I’d have thought that such a bloated ego as yours would be impervious to a bit of mild, but accurate, criticism using some familiar industrial language. Your ‘faux outrage’ fools nobody, but I suppose it gives you another excuse to refuse to answer those tricky questions that expose your ludicrous probability ‘theory’ for the complete bollocks it is: such as “When Monty picks a red ball from the bag does it have a 1/3 chance of being a white ball?” or Jonathon’s "If the open door with a goat has a 1/3 chance of being an open door with a car (as you say) then how come anyone who picked that door would NEVER EVER win the car?
“I know it’s difficult for you but you can at least pretend to have some class"
says the man who wrote :
” I will critique any stupidity and wrongheadedness that crops up."
“then bow and grovel in abject humiliation”
“you have no imagination – alcohol has damaged you….”
“it’s language – the meaning of words that defeats you”
“This juvenile attempt at sophistry does not wash with me”
"…require him to confuse the easily confused. You for instance."
“And those people … are seriously misguided”
“Buxton has left – bored with the ramblings and petty challenges of closed minds”
So, a fckng hypocrite as well.
Say you showed the King of Spades and it was required to win the game. When you were dealt it, face down from a randomly-shuffled pack, it had a 51/52 chance of not being the King of Spades. What logic – force of nature – natural law takes the 51/52 chance the rest of the pack had of being the King of Spades…
Well - when I show the King of spades to the opposition players they can see that it’s the 
K - each of the other 51 cards might easily have been that card - but they wern’t - that’s the logic of the matter - possession is nine tenths of the law.
Interestingly in Duplicate Bridge - when a claim is made - all play stops - the claim is examined and agreed - if there’s a dispute the Director is called to settle the matter - the Director is interested only in what was said at the time of the claim - not by any subsequent statement. A person making a claim is well advised to state their line of play - but at the higher levels of the game this is usually not done - the claimer and the opposition both understanding all the potential lines of play and therefore needing no explanation to be given.
Switching is the important part.
Is the switch to a set of 2 doors (1 open, 1 closed) to or to a set 1 door (1 closed). When Monty opens a door we know there is a goat there. What reason is there to exclude the 1 open door from the set of 2 doors.
Alternatively, Monty is asking us to select closed doors. How can we include an open door in a set of closed doors.
I originally used SET to help to ‘non-switchers’ distinguish doors from chances, though there may be implications with using this word. I will check out some “set-theory”…
Anyways, I have enjoyed the chatting.
Thanks.
I am well-used to industrial language - my suggestion was for your benefit - an attempt to allow stronger criticism of me - all this, “That’s a load of Bollocks Richard.” and the like - is playground stuff - use a bit of class when you try to put me down - some gravitas if you’re able. I get so bored with the saloon-bar stuff.
I like the concept of switching to a set of doors - it makes sense - helps to lift the fog of confusion that blinds and confuses so many. Set is good.
Alternatively, Monty is asking us to select closed doors.
No he isn’t - the question is - Does it make sense to swap? Is there more chance of the car if we do swap?
No mention is made of doors open or closed - no mention is made of actually swapping - there is nothing to swap to - the doors are merely figments - we can only imagine the doors - the question is academic - if given the chance - does it make sense to swap?
It’s not real you know… never was…
This bullshit from Buxton:
“probability does not forecast what’s going to happen – probability allows for either eventuality – it does not insist on one particular result.”
Probability predicts the likelihood of one particular event, such as the winning of the car if a particular door is selected.
A ascribing, as you do, a probability of 1/3 to the open goat door means that the producer of the Monty Hall Show could expect to give away 33 cars every 100 episodes if every contestant chose the open goat door.
Same for the closed door. Except they would give away around 67 cars if everyone switched to the only other closed door.
And 33 cars if no one switched.
So how can you say the goat door and the closed door each have an equal 1/3 probability of providing a prize is one, the goat, door yields no cars no matter how many times it is selected and the other will, over time, yield 67 cars per 100 times it is selected?
A theory be it 1/3 or 2/3
This bullshit from Buxton:
“probability does not forecast what’s going to happen – probability allows for either eventuality – it does not insist on one particular result.”
Probability predicts the likelihood of one particular event, such as the winning of the car if a particular door is selected.
A ascribing, as you do, a probability of 1/3 to the open goat door means that the producer of the Monty Hall Show could expect to give away 33 cars every 100 episodes if every contestant chose the open goat door.
Same for the closed door. Except they would give away around 67 cars if everyone switched to the only other closed door.
And 33 cars if no one switched.
So how can you say the goat door and the closed door each have an equal 1/3 probability of providing a prize if one, the goat, door yields no cars no matter how many times it is selected and the other will, over time, yield 67 cars per 100 times it is selected?
A theory be it 1/3 or 2/3
K – each of the other 51 cards might easily have been that card – but they wern’t – that’s the logic of the matter – ’Richard, are you saying that the card in question, having been shown, no longer possesses a 51/52 chance of not being the King of Spades, or indeed no longer possesses any chance at all of not being the king of Spades? Is that the logic of the matter?
Johnathan… You wrote…
Probability predicts the likelihood of one particular event, such as the winning of the car if a particular door is selected.
Probability concerns itself - in this case - with what might lie behind a door - this or that - probability knows nothing of goat or car just the likelihood of one or the other - probability is not bothered one way or another - probability does not understand the concept of winning.
Probability is to do with what might happen in the future - it can enable us to select the most favourable path to a preferred outcome.
We do not readjust probability because one of particular outcome - because we don’t get what we wanted - that’s the stuff of spoiled children.
One-third the car?
Oh! It’s a goat - can’t have been one-third the car then.
It’s not like that - it’s more like…
One-third the car?
Oh! It’s a goat - well we should have expected a goat - there’s more of them - but it was still a one-third chance of the car.
Probability is exclusively of the future - not the present.
"We do not readjust probability because one of particular outcome"
Apart from you, EVERYBODY else does precisely that. And that’s because your knowledge of probability is limited to saying “Probability predicts the likelihood of one particular event” over and over and over again, whilst the rest of us (having studied, read or researched the subject) know considerably more than that.
Since you’re particularly fond of analogies, it’s like comparing a 17 year old with slow reflexes taking their 1st driving lesson (that’d be you) with Lewis Hamilton, Mark Webber or Jenson Button. You don’t have to remain so ignorant Richard, you’re not too old to learn - perhaps you could take an adult education course in mathematics
“but it WAS still a one-third chance of the car.” The operative word being WAS. It WAS a 1/3 chance of the car when it was hidden, NOW it’s a zero chance of the car because it’s a goat. You’ve said it yourself without even realising it.
Freddie - you raise an interesting discussion point about the Spade King - that’s how Bridge players talk - King of Spades is for outsiders and beginners - experienced people talk of the Spade King - they will write SK or - as you’ve seen - K.
But you asked this…
Richard, are you saying that the card in question, having been shown, no longer possesses a 51/52 chance of not being the King of Spades, or indeed no longer possesses any chance at all of not being the king of Spades? Is that the logic of the matter?
Well it certainly IS the King of Spades - not in dispute but - strange as it may seem to you - it possesses the attribute that it might have been that card before it came into view. And even more difficult for you - it will always possess the attribute of possibly having been the K even after it was played and shown to be some other card.
I think I can see where you’re trying to go with this…
If something stands the chance of being one particular thing - and it transpires that it’s not that particular thing - then was the chance of it actually being the thing in question erroneous?
Well not in the MHP scenario - Two-thirds a goat and we get a goat - to be expected. One-third the car and we get a goat - also to be expected.
What’s to be done with that oh-so-naughty one-third chance the car when a goat turns up?
In my world - nothing at all - leave it where it is…
In your world - shift it to where you can make better use of it.
Of course - this works for you - it makes the solution what you would wish it to be - I am unable to accept that a single door can possibly have a ⅔ chance of the car - that takes a SET of two doors as Mr Bond graciously points out.
Please drop the balls in bags and the pack of cards analogies - I don’t find them useful.
One more thing - with K questions - better to say 1/52 chance OF being the K rather that 51/52 chance of Not being the K - for clarity - too many negatives can confuse matters. Like in the MHP - people do not say a ⅔ chance of not hiding the car or a ⅓ chance of it not being a goat. I’m sure you understand…
You saw the trap eventually didn’t you Richard - if you agreed that, once you’ve seen the card, it’s 100% the King of Spades and not 1/52 chance of it, the only thing left is to substitute the word ‘goat’ for ‘King of Spades’ and ‘not 2/3’ for ‘not 1/52’ and we establish that Monty’s revealed goat door has 0/3 chance of a car.
Do you think you managed to obfuscate your way out of the trap? I don’t - you fell for it in 717.