At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Yes, you should switch. It increases your chances of winning the car by 16 2/3 %.
Next.
Actually, it doubles your chances.
It makes no difference at all, unless you believe the host is trying to tell you something or mislead you. Your chance of success was 33.3%, and now it's 50%, but the position is exactly the same as if there had been only two doors to start with.
Mind you, living in car-unfriendly Islington, I'd be much better off in terms of the reaction of passers-by if I had a nice goat.
I have always had a problem with this because I have read more than once that if you change your chances of winning are greater. But not changing is also a choice on the new facts of 2 doors. I have never understood how that choice is any less valid than changing.
The possibilities are:
A. you originally picked the car (1/3) B. you didn't originally pick the car (2/3)
When the host opens the goat door he tells you that the other non-chosen door must have the car in the event of B. But the probability of B is still 2/3 while the probability of A is still 1/3. So you should switch.
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Yes, you should switch. It increases your chances of winning the car by 16 2/3 %.
Next.
Actually, it doubles your chances.
It makes no difference at all, unless you believe the host is trying to tell you something or mislead you. Your chance of success was 33.3%, and now it's 50%, but the position is exactly the same as if there had been only two doors to start with.
Mind you, living in car-unfriendly Islington, I'd be much better off in terms of the reaction of passers-by if I had a nice goat.
I have always had a problem with this because I have read more than once that if you change your chances of winning are greater. But not changing is also a choice on the new facts of 2 doors. I have never understood how that choice is any less valid than changing.
It's not a new fact of two doors: there are still three doors and the original odds still apply (unless the host was also guessing at random). That one door is open is beside the point of the original decision but *is* pertinent to the choice of whether to switch.
Mr. Rabbit, it's also counter-intuitive to bet on something you think won't happen, but do so because the odds are longer than they should be. Always seems a bit weird to me, but it does make sense.
At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Yes, you should switch. It increases your chances of winning the car by 16 2/3 %.
Next.
Actually, it doubles your chances.
It makes no difference at all, unless you believe the host is trying to tell you something or mislead you. Your chance of success was 33.3%, and now it's 50%, but the position is exactly the same as if there had been only two doors to start with.
Mind you, living in car-unfriendly Islington, I'd be much better off in terms of the reaction of passers-by if I had a nice goat.
I have always had a problem with this because I have read more than once that if you change your chances of winning are greater. But not changing is also a choice on the new facts of 2 doors. I have never understood how that choice is any less valid than changing.
If the host opens a random door with a goat, there is no new information and the remaining doors are 50/50. If the host knows where the car is and is helpfully eliminating the booby prize, you should swap.
The moral of this and the 10,000 coins problem is that probability would be easy if it weren't for all those nasty buried assumptions.
At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Yes, you should switch. It increases your chances of winning the car by 16 2/3 %.
Next.
Actually, it doubles your chances.
It makes no difference at all, unless you believe the host is trying to tell you something or mislead you. Your chance of success was 33.3%, and now it's 50%, but the position is exactly the same as if there had been only two doors to start with.
Mind you, living in car-unfriendly Islington, I'd be much better off in terms of the reaction of passers-by if I had a nice goat.
He has told you something, he opened a door with a goat. If he could open the door with the car, things would be different.
No -- as I said earlier, it depends whether the host *intended* to show you a goat or whether he opened a random door that just happened to have a goat behind it.
Yes, the questions should state this.
I hate the Monty Hall problem. I always get it wrong. The trick is to realise that the host cannot open a door with a car.
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
But if Hillary gets indicted and it looks like President Trump...you still buy US$???
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
But if Hillary gets indicted and it looks like President Trump...you still buy US$???
Mr. Rabbit, it's also counter-intuitive to bet on something you think won't happen, but do so because the odds are longer than they should be. Always seems a bit weird to me, but it does make sense.
Yes. You can get to grips with that one fairly quickly though, whereas a lot of eminent mathematics professors had a hard time with the Monty Hall problem.
If the host opens a random door with a goat, there is no new information and the remaining doors are 50/50. If the host knows where the car is and is helpfully eliminating the booby prize, you should swap.
No
If the host knows where the car is, rather than helpfully eliminating the booby prize they might also know you already picked the car so switching would be bad...
Again, if you know the host is going to show you goat, your chances are 50/50 either way.
I had a neighbour who had a contract with the council to keep the grass short on a plot of land.
He bought a goat.
Novartis, by some measures the world's largest pharma company, used when I worked there to hire goats to trim the headquarters grass, which was either charmingly green or ridiculous tokenism, according to your underlying view. As I liked goats and was happy in my job, I gave them the benefit of the doubt and thought it charming.
You don't know which door the host is going to reveal a goat to be behind.
If you know the host is going to reveal a goat, then you know the door the host is going to reveal a got behind. It's one of the 2 I didn't pick that has a goat behind it.
So I know one of the 3 doors is going to be eliminated, leaving only 2 that matter.
Just spent nearly half an hour watching a Labour Remainer leafleting on Poole High St. 3 people took a leaflet, 2 more made positive noises. 5 people took a leaflet then retuned it, some making 20 yard journeys back just to make their point. Over 50 people waved it off dismissively; I heard more than 10 of them say they were voting Leave.
Even accounting for the usual 'I'm not wanting to talk about politics' factor which I've experienced myself around here, and the geneal demographic of 11am shoppers in Poole, this gee'd me up to plump for the 40-45 and under 40 % remain bands on BF. DYOR!
Wish I could recall the article - may be in The Times re Labour MPs not canvassing for Remain, even in their own seats. They know it's a nightmare and don't want to be tarred with it.
If you find it, might be worth HYUFD having a read. He is convinced that this referendum won't hurt Labour at all....
I never said it would not harm Labour at all, just that it would harm the Tories more, especially if a close Remain, so on a net basis that would help Labour
At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Yes, you should switch. It increases your chances of winning the car by 16 2/3 %.
Next.
Actually, it doubles your chances.
It makes no difference at all, unless you believe the host is trying to tell you something or mislead you. Your chance of success was 33.3%, and now it's 50%, but the position is exactly the same as if there had been only two doors to start with.
Mind you, living in car-unfriendly Islington, I'd be much better off in terms of the reaction of passers-by if I had a nice goat.
He has told you something, he opened a door with a goat. If he could open the door with the car, things would be different.
No -- as I said earlier, it depends whether the host *intended* to show you a goat or whether he opened a random door that just happened to have a goat behind it.
Yes, the questions should state this.
I hate the Monty Hall problem. I always get it wrong. The trick is to realise that the host cannot open a door with a car.
The problem using probabilities with a single event is much simpler. It is impossible to prove a probability is right or wrong unless it is 1 or 0. All other predictions of probability are unprovable therefore useless.
Probability should only be applied where there are multiple events. It works in betting on single events, as the event itself is not what is being measured, it is the bets. Each bet placed is an event, therefore there are multiple events.
I see people are making a right mess of understanding and explaining the Monty Hall problem...I wish I had a £1 for every time I had to explain this to undergraduates during my time in academia, I would be lounging on a beach on a tropical island as a very rich man.
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
But if Hillary gets indicted and it looks like President Trump...you still buy US$???
If Hillary gets indicted could be President Sanders!!
Novartis, by some measures the world's largest pharma company, used when I worked there to hire goats to trim the headquarters grass, which was either charmingly green or ridiculous tokenism, according to your underlying view. As I liked goats and was happy in my job, I gave them the benefit of the doubt and thought it charming.
EDS, at one time the largest pure play IT services company on the World, used cattle to trim the grass at the GodPod. There were cowboys on staff to look after them (It is in Texas)
"Rural depopulation has taken place though, with former low value cottages now occupied by weekenders "
Lincolnshire is different to the twee places in the South. Boston has seen a massive population rise. Lincolnshire is an industrial county, but the industry is agriculture.
Ditto Norfolk - and that's very eurosceptic too. When I worked there a decade ago - there were 30 000 Portuguese plucking chickens et al, and almost as many assorted Eastern Europeans.
Small things matter on a regional or county level. A lot of people in Norfolk were angered by the factories a few years ago that were advertising jobs for Polish speakers only. Even those well disposed to the EU thought it was indefensible.
The best way to get the Monty Hall problem through to people is to up the number of doors.
Or, more succinctly, say that you win £1000 if you can pick the Ace Of Spades at random from a pack. You pick a card, keeping it face down, then your questioner flicks through the rest of the pack and discards 50 cards face up saying "well, it wasn't these".
Daniel Hannan @DanHannanMEP "We asked for very little, failed to get even that, but voted to stay in anyway. Now can we please have some reform?" Yeah, right.
I see people are making a right mess of understanding and explaining the Monty Hall problem...I wish I had a £1 for every time I had to explain this to undergraduates during my time in academia, I would be lounging on a beach on a tropical island as a very rich man.
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
But if Hillary gets indicted and it looks like President Trump...you still buy US$???
If Hillary gets indicted could be President Sanders!!
I'm already making the bumper stickers: "No Reds in the White House!"
If the host opens a random door with a goat, there is no new information and the remaining doors are 50/50. If the host knows where the car is and is helpfully eliminating the booby prize, you should swap.
No
If the host knows where the car is, rather than helpfully eliminating the booby prize they might also know you already picked the car so switching would be bad...
Again, if you know the host is going to show you goat, your chances are 50/50 either way.
No ! Your chances are 50-50 if the host explicitly stands by a door and informs you they will be opening that door and they tell you there is a goat behind it !
Your chance is 1/3 because you may well pick the door that the host was originally going to open.
Go out and about and ask some Labour voters... It's Hobson's choice - will you support Cameron and Osborne by voting to Remain? * Euuuugggghhhhh.... * Or support IDS, Gove and Boris by voting to Leave *Looks at shoes, mumbles, throws up a little bit of sick...*
Yes indeed.
So why would any 'shy Labour' factor be one-sided?
I'm not trying to make a partisan point, I'm just trying to understand whether there's likelky to be any systematic distortion of the polling. A priori, it looks neutral to me.
I see people are making a right mess of understanding and explaining the Monty Hall problem...I wish I had a £1 for every time I had to explain this to undergraduates during my time in academia, I would be lounging on a beach on a tropical island as a very rich man.
Which is the whole point Francis!
:-) ...unfortunately my pay at the time wasn't "performance" related to people understanding this and other problems. Which is a shame for my bank balance.
The best way to get the Monty Hall problem through to people is to up the number of doors.
Or, more succinctly, say that you win £1000 if you can pick the Ace Of Spades at random from a pack. You pick a card, keeping it face down, then your questioner flicks through the rest of the pack and discards 50 cards face up saying "well, it wasn't these".
The best way to get the Monty Hall problem through to people is to up the number of doors.
Or, more succinctly, say that you win £1000 if you can pick the Ace Of Spades at random from a pack. You pick a card, keeping it face down, then your questioner flicks through the rest of the pack and discards 50 cards face up saying "well, it wasn't these".
Do you swap?
One way I used to explain / demo it was a tree diagram that showed the various paths, whereby you then see how many times you win vs lose depending on each option...then you can count up your win / losses vs total plays.
But I quite like your "hand wavey" thought exercise.
So, let me get this straight: there are 3 doors. Two are marked "Brexit". You select one of these. David Cameron opens the other Brexit door to reveal the burning fires of hell and a contraction of around 0.7% of GDP.
No ! Your chances are 50-50 if the host explicitly stands by a door and informs you they will be opening that door and they tell you there is a goat behind it !
Your chance is 1/3 because you may well pick the door that the host was originally going to open.
No
The host will open either door with a goat. If I pick one he opens the other. If I pick the other he opens the first. If I pick the car he opens either. It doesn't matter, as long as I know he will show me a goat.
It might help you if we label the doors.
They are
1. The one I pick 2. The one I can switch to 3. The one with a goat the host shows me, which I didn't pick, which I can't switch to, that has no part in the event if I know in advance he will show me it
So, only 2 doors matter. Each of which has a 50% chance of goat/car
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
Seeking euros for July holiday in Italy. All a bit of a gamble but all the holiday already paid at approx 1.28 so only pocket money really
So, let me get this straight: there are 3 doors. Two are marked "Brexit". You select one of these. David Cameron opens the other Brexit door to reveal the burning fires of hell and a contraction of around 0.7% of GDP.
Go out and about and ask some Labour voters... It's Hobson's choice - will you support Cameron and Osborne by voting to Remain? * Euuuugggghhhhh.... * Or support IDS, Gove and Boris by voting to Leave *Looks at shoes, mumbles, throws up a little bit of sick...*
Yes indeed.
So why would any 'shy Labour' factor be one-sided?
I'm not trying to make a partisan point, I'm just trying to understand whether there's likelky to be any systematic distortion of the polling. A priori, it looks neutral to me.
The point is they'll abstain. We keep being told Labour are pro Remain, only if they vote.
I've been banging this drum for weeks, amazed its taken so long for people to catch on.
Go out and about and ask some Labour voters... It's Hobson's choice - will you support Cameron and Osborne by voting to Remain? * Euuuugggghhhhh.... * Or support IDS, Gove and Boris by voting to Leave *Looks at shoes, mumbles, throws up a little bit of sick...*
Yes indeed.
So why would any 'shy Labour' factor be one-sided?
I'm not trying to make a partisan point, I'm just trying to understand whether there's likelky to be any systematic distortion of the polling. A priori, it looks neutral to me.
The point is they'll abstain. We keep being told Labour are pro Remain, only if they vote.
I've been banging this drum for weeks, amazed its taken so long for people to catch on.
The polls now all include certainty to vote figures
You don't know which door the host is going to reveal a goat to be behind.
If you know the host is going to reveal a goat, then you know the door the host is going to reveal a got behind. It's one of the 2 I didn't pick that has a goat behind it.
So I know one of the 3 doors is going to be eliminated, leaving only 2 that matter.
The one I pick
The one I don't pick
Each if which has a 50% chance of car, or goat.
How do you know which door the host is going to open?
On leave vote the pound is expected to fall by 10-15% against the dollar but I would expect a similar fall in the euro but as I am not an expert does anyone have a view on this
I have got no idea which way EURvsGBP will go - could go up, down or sideways - but I am certain that both will suffer in respect to a third currency (USD) or commodity (gold). So if you are looking to insure yourself against currency movements, buy USD or gold.
But if Hillary gets indicted and it looks like President Trump...you still buy US$???
If Hillary gets indicted could be President Sanders!!
I'm already making the bumper stickers: "No Reds in the White House!"
At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Yes, you should switch. It increases your chances of winning the car by 16 2/3 %.
Next.
Actually, it doubles your chances.
It makes no difference at all, unless you believe the host is trying to tell you something or mislead you. Your chance of success was 33.3%, and now it's 50%, but the position is exactly the same as if there had been only two doors to start with.
Mind you, living in car-unfriendly Islington, I'd be much better off in terms of the reaction of passers-by if I had a nice goat.
Incorrect Mr P I am afraid.
this is a really famous question, surprised you don't know it.
You should ALWAYS switch your choice, you have a 2/3 chance of winning then. This is because the only way you lose by always switching is if you picked the winning door to start with - which is a 1/3 chance. hence switching is a 2/3 chance.
(And yes, since it was 1/3 before switching, it doubles your chances.)
Yougov today has it Remain 50% Leave 50% UK wide but Leave ahead in every UK region outside London and Scotland
I think we're discovering now precisely why Labour never wanted to offer an EU in/out referendum. They didn't want this particular genie let out of its bottle.
Whatever happens, and to his credit, I will always commend Cameron for having the bollocks to offer one.
This thread is taking me back a few years and putting a smile on my face. It is like watching a class of cocky 18 year olds, all with their 5 A's at A-Level :-)
BTW, when is comp sci 101 class scheduled to end and back to the politics?
The best way to get the Monty Hall problem through to people is to up the number of doors.
Or, more succinctly, say that you win £1000 if you can pick the Ace Of Spades at random from a pack. You pick a card, keeping it face down, then your questioner flicks through the rest of the pack and discards 50 cards face up saying "well, it wasn't these".
Do you swap?
One way I used to explain / demo it was a tree diagram that showed the various paths, whereby you then see how many times you win vs lose depending on each option...then you can count up your win / losses vs total plays.
But I quite like your "hand wavey" thought exercise.
I came across, some time ago, a strategy for picking a bar or eating place in a strange town. You find one you like, then of course your partner is doubtful. You walk a little further and find another which at least one of you likes. You go ion there, because no matter how much further you walk you won’t find anything better.
Yougov today has it Remain 50% Leave 50% UK wide but Leave ahead in every UK region outside London and Scotland
I think we're discovering now precisely why Labour never wanted to offer an EU in/out referendum. They didn't want this particular genie let out of its bottle.
Whatever happens, and to his credit, I will always commend Cameron for having the bollocks to offer one.
Only because Cameron's bollocks were already on the line prior to his offering it.
You don't know which door the host is going to reveal a goat to be behind.
If you know the host is going to reveal a goat, then you know the door the host is going to reveal a got behind. It's one of the 2 I didn't pick that has a goat behind it.
So I know one of the 3 doors is going to be eliminated, leaving only 2 that matter.
The one I pick
The one I don't pick
Each if which has a 50% chance of car, or goat.
Sorry Scott, putting all politics aside you are wrong on this. This is a known mathematical problem and the answer is very clear even if counter intuitive.
You don't know which door the host is going to reveal a goat to be behind.
If you know the host is going to reveal a goat, then you know the door the host is going to reveal a got behind. It's one of the 2 I didn't pick that has a goat behind it.
So I know one of the 3 doors is going to be eliminated, leaving only 2 that matter.
The one I pick
The one I don't pick
Each if which has a 50% chance of car, or goat.
No
The host knows where the car is and picks a door he knows is a goat
i will attempt a table based on doors numbered 1, 2 & 3 and assuming you switch. o is win, X is lose
The car is (read across) > 1 2 3 Your pick (read down) 1 X o o 2 o X o 3 o o X
If you pick right first time the host can open either door, both are goats. you switch, you lose. If you pick a goat, the host has only one goat door to open, so if you switch, you win, since you must be switching to the car.
So if you always switch, you only lose if you pick eh car first time. which is 1/3. So you switch, your win odds are 2/3.
Have a look at Tissue Price's post at 12.57pm and try applying your logic to his problem with the 52 playing cards.
But the condition is still the key. If I know in advance the host will show me the losers I didn't pick , and I am left with the 1 I picked and the 1 I didn't, then the odds don't change
After you've made your choice, the gameshow host is always going to be able to show you a goat. But does he have a choice? He only has a choice if you have chosen the door with the car. So it is twice as likely as not that he has no choice and you should switch to the door that neither you nor the gameshow host has chosen.
You get a similar problem playing bridge when trying to work out where cards are. If two cards of identical rank are outstanding and one of your opponents plays one of them, you should ordinarily assume in later play that he had no choice in the matter and that he doesn't have the other. It's called the principle of restricted choice.
Sorry Scott, putting all politics aside you are wrong on this. This is a known mathematical problem and the answer is very clear even if counter intuitive.
Depending on the actions of the host
If I know the host is going to eliminate a loser, the answer is 50/50
I have always had a problem with this because I have read more than once that if you change your chances of winning are greater. But not changing is also a choice on the new facts of 2 doors. I have never understood how that choice is any less valid than changing.
It depends entirely on the actions and motives of the host.
Without knowing what the host will do, the classic interpretation is that your first pick has 33% chance of being a car
But if you know in advance the host is going to show you a goat, your first pick has 50% chance of being a car, so no value in changing
Have a look at Tissue Price's post at 12.57pm and try applying your logic to his problem with the 52 playing cards.
But the condition is still the key. If I know in advance the host will show me the losers I didn't pick , and I am left with the 1 I picked and the 1 I didn't, then the odds don't change
Quite so - the odds of you being right don't change. They were 1/3 (or 1/52) and remain so. Unless of course you swap.
Sorry Scott, putting all politics aside you are wrong on this. This is a known mathematical problem and the answer is very clear even if counter intuitive.
Depending on the actions of the host
If I know the host is going to eliminate a loser, the answer is 50/50
I know this is hard Scott (and that is not being patronising, it was hard for me as well the first time it was explained to me) but I am afraid you are wrong. Go look at the explanations.
Mathematically (and in practice because it is a problem that has been analysed and experimented hundreds of times in reality) you should always switch.
After you've made your choice, the gameshow host is always going to be able to show you a goat. But does he have a choice? He only has a choice if you have chosen the door with the car. So it is twice as likely as not that he has no choice and you should switch to the door that neither you nor the gameshow host has chosen.
No
It is you who is being led astray.
The condition as stated in ever post above is that the host is going to show me a goat. He is going to eliminate one of the losing propositions.
That leaves only 2 choices, each of which has a 50% chance.
If the host picks another door at random, the numbers change, but that was not what I said.
If I know the host is going to show me a goat, eliminate one of the losing options from the game, in advance, the odds are 50%
At present it is said that the probability of remain is around 0.70.
No it isn't. It's said that that's the view of the betting markets, or to be more exact, the view of the money that's been placed with general-purpose mass-market bookmakers.
Probability is not a physical reality that can be measured, whether accurately or otherwise. There is no "real" probability of Remain or Leave.
If people think I'm talking crap, they should try the following problem.
You're on a game show, and you're given a choice of three doors. Behind one is a car; behind the others, goats. You pick door no.1. The host, who knows what's behind all three doors, then opens another one, no. 2, to reveal a goat. He then asks whether you want to change your choice to no.3. Should you switch or not?
Good post, few understand probability, even fewer value.
A simpler question is if you flip a coin 1000 times and every time it comes up heads, what price is tails next time? Watch the furrowed brows.
The answer is:-
If you know the coin to be unbiased:- 1/2 If you don't know it is unbiased, but you know one of the sides is a tail:- 1/1002 If you know nothing about the coin:- ~0
Re Monty Hall. The easiest way to think of it is you are being offered the choice to swap opening just one door, with the opportunity to open two [one of which is opened by the host]
Re Monty Hall. The easiest way to think of it is you are being offered the choice to swap opening just one door, with the opportunity to open two [one of which is opened by the host]
Who wouldn't swap, giving twice the chance?
Because it depends on the actions of the host.
You are being offered the chance to choose between 2 doors. A 3rd guaranteed losing door is opened by the host.
Have a look at Tissue Price's post at 12.57pm and try applying your logic to his problem with the 52 playing cards.
But the condition is still the key. If I know in advance the host will show me the losers I didn't pick , and I am left with the 1 I picked and the 1 I didn't, then the odds don't change
Quite so - the odds of you being right don't change. They were 1/3 (or 1/52) and remain so. Unless of course you swap.
Though then you can swap back if you so choose in a second swap. Your original door yet improved odds.
Have a look at Tissue Price's post at 12.57pm and try applying your logic to his problem with the 52 playing cards.
But the condition is still the key. If I know in advance the host will show me the losers I didn't pick , and I am left with the 1 I picked and the 1 I didn't, then the odds don't change
Quite so - the odds of you being right don't change. They were 1/3 (or 1/52) and remain so. Unless of course you swap.
Though then you can swap back if you so choose in a second swap. Your original door yet improved odds.
No it has not. The original door has its original odds. The door that Monty hasn't opened has all remaining odds.
Re Monty Hall. The easiest way to think of it is you are being offered the choice to swap opening just one door, with the opportunity to open two [one of which is opened by the host]
Who wouldn't swap, giving twice the chance?
Because it depends on the actions of the host.
You are being offered the chance to choose between 2 doors. A 3rd guaranteed losing door is opened by the host.
Switching doesn't help
But before the host does his door-opening thing, it's more likely that you've chosen a goat. Therefore it's more likely to advantageous to reject your first choice.
So why would any 'shy Labour' factor be one-sided?
Trying to put myself in the shoes of a life-long Labour supporter, brought up to believe that his instincts towards his fellow man are better than those of "the bloody Tories". Someone who hated Thatcher. But has also come to feel embarrassed hey voted for Blair. And (s)he is now faced with a Labour leader who they didn't vote for and was until very recently anti-EU, but who now seems to have a very lukewarm acceptance that we should Remain.
They are getting no effective guidance from the Labour Party.
Nigel Farage sets their teeth on edge. Bloody pub bore.
So if (s)he wants to vote in the Referendum, which set of Tories are they going to end up grudgingly siding with? They've always hated the Bullingdon Boys of Cameron and Osborne - they're as far from their own personal understanding of the Working Man as you could get. He doesn't warm to Gove either - has some unformed memory that he was trying to do something bad to schools. He's not sure about Boris, but his antagonism isn't provoked by him. And London seemed to do alright when he took over from Livingstone.
He doesn't have strong views on the EU itself. He holidays in Spain, maybe even has a dream of retiring there in a few years. But he has worries that the EU is run by people just as elitist and distant as the Tories. And bleeds money away to places that don't ever get round to including his home town.
And even though it goes against the grain of their upbringing - he has doubts about immigration. Doubts about the changes he is seeing in his working-class neighbourhood. Worries about pressures on housing, on schools, on the NHS. He feels bad about it, but by doing nothing to change it, is he failing his own kids? The TUC says that the EU protects workers rights. And as a lifelong Union member, they carry some sway. But - niggling doubt - isn't it just as likely that those EU protections are helping a Pole or a Romanian get a job one of his kids could have been doing?
So this person is deeply conflicted, doesn't want to think they may be reacting to base human instincts. God forbid anybody might think them a racist. But on a cool, clinical assessment, they are maybe looking after their own and their family's interests by having the UK look after the UK.
Now, I would suggest there are a significant number of Labour voters for whom at least some of these points would resonate. They still aren't quite sure how they will vote, but if it is to be Leave, it won't be something they will admit to. Certainly not something to admit to a polling organisation. Nor colleagues. Maybe not even to the family. They'll vote Leave, feel a little bit dirty about it, but convince themselves in their quiet moments that it's the right thing to do, on a purely selfish level. And that seems a bit, Tory - and they feel a bit dirtier about the whole bloody process.
After you've made your choice, the gameshow host is always going to be able to show you a goat. But does he have a choice? He only has a choice if you have chosen the door with the car. So it is twice as likely as not that he has no choice and you should switch to the door that neither you nor the gameshow host has chosen.
No
It is you who is being led astray.
The condition as stated in ever post above is that the host is going to show me a goat. He is going to eliminate one of the losing propositions.
That leaves only 2 choices, each of which has a 50% chance.
If the host picks another door at random, the numbers change, but that was not what I said.
If I know the host is going to show me a goat, eliminate one of the losing options from the game, in advance, the odds are 50%
Your logic is faulty. The host is not eliminating a losing option "in advance". To do that, he would have to start the game as a two door option, with one goat and one car.
Him opening a door does not alter the choice you have already made, or its chance of being the car, which remains at 1/3. Therefore switching to the remaining unopened door must double the chance to 2/3.
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Your logic is faulty. The host is not eliminating a losing option "in advance". To do that, he would have to start the game as a two door option, with one goat and one car.
Him opening a door does not alter the choice you have already made, or its chance of being the car, which remains at 1/3. Therefore switching to the remaining unopened door must double the chance to 2/3.
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Look at the explanation tweet posted upthread.
It shows 3 games, with the car in 1 of 3 places, and it claims you win twice and lose once.
Except there are 4 game outcomes. You lose twice, if Monty opens door 2 or door 3
You win 2 out of 4, or 50%
I will gladly play this game with you for money with three cards (2 black and 1 red) !
The UK has a massive balance of trade deficit because its exports are not sufficiently competitive and imports are cheap.
The traditional way to correct the position is to devalue the currency, making exports cheaper and imports more expensive.
The only downside would normally be the increase in inflation due to highjer inport costs. However, when inflation is 0.3% and target inflation is 2%, any fall in sterling just helps to raise inflation to target.
So a fall in the sterling exchange rate should surely be welcomed by economists and the government?
The "thing" that correlates best with trade deficit (or surplus) is savings rate. So,
Germany, China, Switzerland: very high savings rates, balance of payment surpluses UK, US, and lately Spain: very low savings rates, balance of payments deficit
If you chart all the countries in the world, the correlation is remarkably strong. In other words, it's not that we do not export enough, but that we consume too much. And the easiest way of changing that is to move our savings rate from 4-6% (where it is today, and which is among the worst in the world), to 10-12% where we would be running a balance of payments surplus.
It's worth noting that a low savings rate means the cost of capital is elevated for business who want to invest. (The bank can lend to you or a business, your desire to borrow to spend crowds out the business who needs the loan to invest in productive capacity.)
Your logic is faulty. The host is not eliminating a losing option "in advance". To do that, he would have to start the game as a two door option, with one goat and one car.
Him opening a door does not alter the choice you have already made, or its chance of being the car, which remains at 1/3. Therefore switching to the remaining unopened door must double the chance to 2/3.
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Look at the explanation tweet posted upthread.
It shows 3 games, with the car in 1 of 3 places, and it claims you win twice and lose once.
Except there are 4 game outcomes. You lose twice, if Monty opens door 2 or door 3
You win 2 out of 4, or 50%
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Which of us is the host?
Wrong. The two winning game options have odds of 1/3 each. So winning is 2/3.
The two losing game options have odds of 1/6 each. So losing is 1/3.
The odds of picking the right door originally was 1/3. From there the two losing options are possible with a 50% chance each from that original 1/3.
Good post Mr Mark. Although our friend might welll not vote at all. Or be capable of being influenced by the last pewrson he sees, the last piece of info he receives.
Good post Mr Mark. Although our friend might welll not vote at all. Or be capable of being influenced by the last pewrson he sees, the last piece of info he receives.
I think a 2015 Labour voter not voting at all counts as a win for Leave. But you're right, in that their soul-searching likely goes down to the wire. The TV Q&A sessions could prove really decisive on this. Gove coming across as surprisingly human or Cameron really struggling and looking shifty on the "tens of thousands pledge " versus "330,000 reality" could be what wins this for Leave.
Your logic is faulty. The host is not eliminating a losing option "in advance". To do that, he would have to start the game as a two door option, with one goat and one car.
Him opening a door does not alter the choice you have already made, or its chance of being the car, which remains at 1/3. Therefore switching to the remaining unopened door must double the chance to 2/3.
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Look at the explanation tweet posted upthread.
It shows 3 games, with the car in 1 of 3 places, and it claims you win twice and lose once.
Except there are 4 game outcomes. You lose twice, if Monty opens door 2 or door 3
You win 2 out of 4, or 50%
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Which of us is the host?
You are! I'll pay you a quid if I end up with a black card, you pay me a quid if I end up with a red.
The easiest way to imagine Monty hall is to consider picking a card from the pack. If it is the Ace of Spades you win. After you pick your card at Random, Monty removes 50 other cards (knowing what they are and that none of them are the Ace of Spades).
You are left with two cards. Is it REALLY 50-50?
Not convinced? Suppose you have a mole of atoms, one of which is radioactive - you pick one at random - Monty Removes 6.0223 X 10^23 -1 atoms knowing they aren't radioactive - you are left with 2 atoms - one is radioactive, one isn't. - Still 50-50?
Good post Mr Mark. Although our friend might welll not vote at all. Or be capable of being influenced by the last pewrson he sees, the last piece of info he receives.
I think a 2015 Labour voter not voting at all counts as a win for Leave. But you're right, in that their soul-searching likely goes down to the wire. The TV Q&A sessions could prove really decisive on this. Gove coming across as surprisingly human or Cameron really struggling and looking shifty on the "tens of thousands pledge " versus "330,000 reality" could be what wins this for Leave.
Agree on all counts. However, I suspect that both sides could do with an “honest face” late in the process; Gove was torn apart on Breakfast when he was talking about energy prices being reduced, and Cameron is looking more desparate and less sincere by the minute.
I have to pick 1 of 1,000,000 doors. After I choose the host opens 999,998 other doors showing goats behind them. The host then offers me the choice to stick or switch to the other unopened door.
Comments
A. you originally picked the car (1/3)
B. you didn't originally pick the car (2/3)
When the host opens the goat door he tells you that the other non-chosen door must have the car in the event of B. But the probability of B is still 2/3 while the probability of A is still 1/3. So you should switch.
The moral of this and the 10,000 coins problem is that probability would be easy if it weren't for all those nasty buried assumptions.
If you know the host is going to show you a goat, then there are only 2 doors that matter
A. The door you picked 50/50
B. The door you didn't pick 50/50
Switching doesn't help
https://twitter.com/MichaelLCrick/status/737951230325096449
If the host knows where the car is, rather than helpfully eliminating the booby prize they might also know you already picked the car so switching would be bad...
Again, if you know the host is going to show you goat, your chances are 50/50 either way.
So I know one of the 3 doors is going to be eliminated, leaving only 2 that matter.
The one I pick
The one I don't pick
Each if which has a 50% chance of car, or goat.
Probability should only be applied where there are multiple events. It works in betting on single events, as the event itself is not what is being measured, it is the bets. Each bet placed is an event, therefore there are multiple events.
Or, more succinctly, say that you win £1000 if you can pick the Ace Of Spades at random from a pack. You pick a card, keeping it face down, then your questioner flicks through the rest of the pack and discards 50 cards face up saying "well, it wasn't these".
Do you swap?
"We asked for very little, failed to get even that, but voted to stay in anyway. Now can we please have some reform?" Yeah, right.
Your chance is 1/3 because you may well pick the door that the host was originally going to open.
So why would any 'shy Labour' factor be one-sided?
I'm not trying to make a partisan point, I'm just trying to understand whether there's likelky to be any systematic distortion of the polling. A priori, it looks neutral to me.
But I quite like your "hand wavey" thought exercise.
Do you swap?
The host will open either door with a goat. If I pick one he opens the other. If I pick the other he opens the first. If I pick the car he opens either. It doesn't matter, as long as I know he will show me a goat.
It might help you if we label the doors.
They are
1. The one I pick
2. The one I can switch to
3. The one with a goat the host shows me, which I didn't pick, which I can't switch to, that has no part in the event if I know in advance he will show me it
So, only 2 doors matter. Each of which has a 50% chance of goat/car
I've been banging this drum for weeks, amazed its taken so long for people to catch on.
this is a really famous question, surprised you don't know it.
You should ALWAYS switch your choice, you have a 2/3 chance of winning then. This is because the only way you lose by always switching is if you picked the winning door to start with - which is a 1/3 chance. hence switching is a 2/3 chance.
(And yes, since it was 1/3 before switching, it doubles your chances.)
Whatever happens, and to his credit, I will always commend Cameron for having the bollocks to offer one.
Let me try it another way, for the hard of thinking
There are 3 doors. 1 is a winner, 2 are losers.
I know in advance the host is going to show me a loser.
So the door I pick is either a winner or a loser. The other loser doesn't matter, as the host will eliminate it, whatever I have picked.
So the door I picked is either a winner or a loser.
50% either way
NEW THREAD NEW THREAD
BTW, when is comp sci 101 class scheduled to end and back to the politics?
You go ion there, because no matter how much further you walk you won’t find anything better.
(Or, of course, you go to TripAdvisor.)
Have a look at Tissue Price's post at 12.57pm and try applying your logic to his problem with the 52 playing cards.
The host knows where the car is and picks a door he knows is a goat
i will attempt a table based on doors numbered 1, 2 & 3 and assuming you switch. o is win, X is lose
The car is (read across) > 1 2 3
Your pick
(read down)
1 X o o
2 o X o
3 o o X
If you pick right first time the host can open either door, both are goats. you switch, you lose. If you pick a goat, the host has only one goat door to open, so if you switch, you win, since you must be switching to the car.
So if you always switch, you only lose if you pick eh car first time. which is 1/3. So you switch, your win odds are 2/3.
(EDIT - OK the table didn;t work...)
https://twitter.com/numberphile/status/634113819019771904
To help @Scott_P, who is being led astray:
After you've made your choice, the gameshow host is always going to be able to show you a goat. But does he have a choice? He only has a choice if you have chosen the door with the car. So it is twice as likely as not that he has no choice and you should switch to the door that neither you nor the gameshow host has chosen.
You get a similar problem playing bridge when trying to work out where cards are. If two cards of identical rank are outstanding and one of your opponents plays one of them, you should ordinarily assume in later play that he had no choice in the matter and that he doesn't have the other. It's called the principle of restricted choice.
Depending on the actions of the host
If I know the host is going to eliminate a loser, the answer is 50/50
Mathematically (and in practice because it is a problem that has been analysed and experimented hundreds of times in reality) you should always switch.
It is you who is being led astray.
The condition as stated in ever post above is that the host is going to show me a goat. He is going to eliminate one of the losing propositions.
That leaves only 2 choices, each of which has a 50% chance.
If the host picks another door at random, the numbers change, but that was not what I said.
If I know the host is going to show me a goat, eliminate one of the losing options from the game, in advance, the odds are 50%
If you know the coin to be unbiased:- 1/2
If you don't know it is unbiased, but you know one of the sides is a tail:- 1/1002
If you know nothing about the coin:- ~0
Re Monty Hall. The easiest way to think of it is you are being offered the choice to swap opening just one door, with the opportunity to open two [one of which is opened by the host]
Who wouldn't swap, giving twice the chance?
You are being offered the chance to choose between 2 doors. A 3rd guaranteed losing door is opened by the host.
Switching doesn't help
https://en.wikipedia.org/wiki/Rule_of_succession
They are getting no effective guidance from the Labour Party.
Nigel Farage sets their teeth on edge. Bloody pub bore.
So if (s)he wants to vote in the Referendum, which set of Tories are they going to end up grudgingly siding with? They've always hated the Bullingdon Boys of Cameron and Osborne - they're as far from their own personal understanding of the Working Man as you could get. He doesn't warm to Gove either - has some unformed memory that he was trying to do something bad to schools. He's not sure about Boris, but his antagonism isn't provoked by him. And London seemed to do alright when he took over from Livingstone.
He doesn't have strong views on the EU itself. He holidays in Spain, maybe even has a dream of retiring there in a few years. But he has worries that the EU is run by people just as elitist and distant as the Tories. And bleeds money away to places that don't ever get round to including his home town.
And even though it goes against the grain of their upbringing - he has doubts about immigration. Doubts about the changes he is seeing in his working-class neighbourhood. Worries about pressures on housing, on schools, on the NHS. He feels bad about it, but by doing nothing to change it, is he failing his own kids? The TUC says that the EU protects workers rights. And as a lifelong Union member, they carry some sway. But - niggling doubt - isn't it just as likely that those EU protections are helping a Pole or a Romanian get a job one of his kids could have been doing?
So this person is deeply conflicted, doesn't want to think they may be reacting to base human instincts. God forbid anybody might think them a racist. But on a cool, clinical assessment, they are maybe looking after their own and their family's interests by having the UK look after the UK.
Now, I would suggest there are a significant number of Labour voters for whom at least some of these points would resonate. They still aren't quite sure how they will vote, but if it is to be Leave, it won't be something they will admit to. Certainly not something to admit to a polling organisation. Nor colleagues. Maybe not even to the family. They'll vote Leave, feel a little bit dirty about it, but convince themselves in their quiet moments that it's the right thing to do, on a purely selfish level. And that seems a bit, Tory - and they feel a bit dirtier about the whole bloody process.
Him opening a door does not alter the choice you have already made, or its chance of being the car, which remains at 1/3. Therefore switching to the remaining unopened door must double the chance to 2/3.
I will gladly play this game with you for money with three cards (2 black and 1 red) !
It shows 3 games, with the car in 1 of 3 places, and it claims you win twice and lose once.
Except there are 4 game outcomes. You lose twice, if Monty opens door 2 or door 3
You win 2 out of 4, or 50%
I will gladly play this game with you for money with three cards (2 black and 1 red) !
Which of us is the host?
Germany, China, Switzerland: very high savings rates, balance of payment surpluses
UK, US, and lately Spain: very low savings rates, balance of payments deficit
If you chart all the countries in the world, the correlation is remarkably strong. In other words, it's not that we do not export enough, but that we consume too much. And the easiest way of changing that is to move our savings rate from 4-6% (where it is today, and which is among the worst in the world), to 10-12% where we would be running a balance of payments surplus.
It's worth noting that a low savings rate means the cost of capital is elevated for business who want to invest. (The bank can lend to you or a business, your desire to borrow to spend crowds out the business who needs the loan to invest in productive capacity.)
The two losing game options have odds of 1/6 each. So losing is 1/3.
The odds of picking the right door originally was 1/3. From there the two losing options are possible with a 50% chance each from that original 1/3.
Or play with yourself (^_-)
http://www.mathwarehouse.com/monty-hall-simulation-online/
You are left with two cards. Is it REALLY 50-50?
Not convinced? Suppose you have a mole of atoms, one of which is radioactive - you pick one at random - Monty Removes 6.0223 X 10^23 -1 atoms knowing they aren't radioactive - you are left with 2 atoms - one is radioactive, one isn't. - Still 50-50?
http://www.spiegel.de/international/europe/european-union-preparing-for-a-possible-brexit-a-1094603.html
Do you really think it is a 50/50 chance?