Monty Hall and choosing your religion

pH

I'm not sure if everyone is familiar with the Monty Hall problem.

Monty Hall Problem wrote:

Monty Hall is a quiz show host, and a contestant is playing for the the big prize at the end of the show. There are 3 doors, behind one is the star prize (a car), and behind the other 2 are goats.

First the contestant makes a choice of a door. At this stage Monty (who knows where the car is) opens one of the 2 not-chosen doors to reveal a goat (he always reveals a goat and will never open the door with the car).

Now the contestant is given a choice of either sticking with his original door or switching to the other closed door. When this choice (sticking or switching) is made, Monty then opens the door and the contestant wins the prize behind it.

What is the probability of winning for either option (sticking or switching) and which should the contestant do?

There are plenty of discussions of the Monty hall problem on the net (including some very clever people making fools of themselves).

I'm not including the correct answer just for the moment in case anyone wants to figure it out for themselves.

The problem can be extended from 3 doors to N doors.

Imagine that you are a theist and believe God/Gods exists. You have never consciously chosen your religion - it is in fact a random choice based on geography/culture/parents etc. You however are strongly convinced that God exists and have revealed himself on earth - ie one religion is correct.

Is this now a direct analogy for the Monty Hall problem? Is your best option to eliminate (somehow! yes I know that part might be problematic*) the ones that can't be right and switch to one of the remaining ones? Does this give you a better chance of being in the right religion than by birth/parents/chance?

*Yes I know the "eliminate the ones that can't be right" step is a problem, however we've seen posters here who are certain that some religions are not correct and can be discounted

Scofflaw

The correct answer is clearly to be an Ethiopian farmer.

cordially,
Scofflaw

Rev Hellfire

Scofflaw wrote: »

The correct answer is clearly to be an Ethiopian farmer.

Now that you say it, its just so obvious. Bravo.

Dades

I'm just not getting the connection required for this to be an analogy.

Though I'd say the Monty Hall probability is 50/50, as he always eliminates one wrong door, without giving any clue as to which of the remaining doors are right.

pH

Dades wrote: »

I'm just not getting the connection required for this to be an analogy.

Though I'd say the Monty Hall probability is 50/50, as he always eliminates one wrong door, without giving any clue as to which of the remaining doors are right.

Hence why it is such a famous puzzle that has driven so many people mad - suffice to say the probability is not 50/50.

And the analogy ...
Given your initial choice of religion is random(ish)
You eliminate all but one other religion (through some means)
What is the probability that your staring religion is the right one?
What is the probability that your possible 'switch' religion is the right one?

(but none of this makes sense until you see the probability is not 50/50)

Dades

Dades wrote: »

I'm just not getting the connection required for this to be an analogy.

Though I'd say the Monty Hall probability is 50/50, as he always eliminates one wrong door, without giving any clue as to which of the remaining doors are right.

If the host didn't know which was behind which door, then yeah. It seems to be partly a psychological problem instead of pure maths and chance, I think.
That said, I never got it til just now, I was always a 50/50 person. So maybe I'm totally wrong.

http://en.wikipedia.org/wiki/Monty_Hall_problem

If either the assumption that the host knows which door the car is behind or the assumption that the host always offers the choice to switch is omitted, then choosing to switch doors may not increase the probability of success. If the host doesn't know, switching and staying have the same probability. If the host does not have to make the offer to switch, switching yields an unknown probability of success.

I think the increasing the number of doors idea explained in the link helps a lot...

Scofflaw

Dades wrote: »

I'm just not getting the connection required for this to be an analogy.

Though I'd say the Monty Hall probability is 50/50, as he always eliminates one wrong door, without giving any clue as to which of the remaining doors are right.

Your chance of picking the right door in the first place is 1/3. That remains unchanged when the host opens one of the other doors. However, the chance of the car being behind one of the doors is 1. When the host eliminates one of the goats, the chance of the car being behind one of the two doors remains 1, and the chance of your having picked the right door in the first place remains 1/3 - therefore the chance of the car being behind the other door is 1-1/3 = 2/3.

Choose between Catholicism, Judaism, and Islam. One of them offers a chance of eternal life, the others don't. We'll assume you're Catholic by birth.

Your chance of picking the right one is 1/3. If the Monty Hall scenario is a good analogy, then if you manage to find Islam false, you should convert to Judaism, because it is twice as likely to be right.

However, for the analogy to work, God should tell you that Islam is incorrect - but not tell you which religion is?

not convinced,
Scofflaw

pH

Scofflaw wrote: »

However, for the analogy to work, God should tell you that Islam is incorrect - but not tell you which religion is?

Well some folks (PDN for instance) can tell that some religions are frauds (Mormonism for example) ... for him - once he eliminates the fake ones ... is he better sticking or switching (And I appreciate that PDN specifically may not be currently in a religion randomly assigned to him at birth/by parents - I'm only using his certainty that some religions are fakes as an example).

Scofflaw

pH wrote: »

Well some folks (PDN for instance) can tell that some religions are frauds (Mormonism for example) ... for him - once he eliminates the fake ones ... is he better sticking or switching (And I appreciate that PDN specifically may not be currently in a religion randomly assigned to him at birth/by parents - I'm only using his certainty that some religions are fakes as an example).

Sure - the problem, though, is that PDN is certain of which doors the goats are behind, and of which door the car's behind. The nearest analogy to that in Monty Hall is to put PDN as the knowing host, not the 'guest'.

cordially,
Scofflaw

Dades

Scofflaw wrote: »

Your chance of picking the right door in the first place is 1/3. That remains unchanged when the host opens one of the other doors. However, the chance of the car being behind one of the doors is 1. When the host eliminates one of the goats, the chance of the car being behind one of the two doors remains 1, and the chance of your having picked the right door in the first place remains 1/3 - therefore the chance of the car being behind the other door is 1-1/3 = 2/3.

Hmm, but isn't the question what is the probability of winning? If Monty always knows what doors are what you will always be choosing between 2 options.

As for how this applies to religion??
I think I'll just get a glass of wine from the fridge and let you lot beat it to death!

stereoroid

Dades wrote: »

As for how this applies to religion??
I think I'll just get a glass of wine from the fridge and let you lot beat it to death!

Personally, I find it easier not to play the game at all. I don't want a goat or a car - no space in my life for either.

stevejazzx

pH wrote: »

Is this now a direct analogy for the Monty Hall problem? Is your best option to eliminate (somehow! yes I know that part might be problematic*) the ones that can't be right and switch to one of the remaining ones? Does this give you a better chance of being in the right religion than by birth/parents/chance?

I think the problem with this anaology is that people don't really chose their religon as such. For this anaology to work the people in question would have to wake up at a young age behind one of the doors, dazed and confused, not sure what the prize was. It then takes them around 20 years for them to figure out what they've got by which time they can't tell the difference between the goat and the car;)