God is in one of three boxes, if I show you one option is false, do you switch?

[Radagast]

I read through a rather extensive explanation... it still doesn't make sense to me.

Try the demo on the link I posted. A dozen or so trials are enough to illustrate the difference.

The key point is not the reduction in the number of doors, but the alteration in conditional probabilities based on new evidence.

Assuming the initial pick is A, the three equally likely options are:

1. Prize is in A, shown non-prize in B or C
2. Prize is in B, shown non-prize in C
3. Prize is in C, shown non-prize in B

In 2/3 of cases (cases 2 and 3), the prize can therefore be won by switching.

Yes, because when you pick option A, you have a 1/3 chance of being correct, but if you switch to B, that is one option between two, giving you a 1/2 chance of being right. It might seem counterintuitive, but it does actually increase your chances of picking right.

Actually, if you switch, you have a 2/3 chance of being right. Try the demo.

 

[Paradoxum]

I've heard the Monty Hall Problem before, but I don't get how this applies to God.

If I'm a Christian, and Scientology is shown to be incorrect, then I should become a Hindu? I'm sure many Christians wouldn't like that.

 

[Radagast]

I've heard the Monty Hall Problem before, but I don't get how this applies to God.

Neither do I, quite frankly.

If I'm a Christian, and Scientology is shown to be incorrect, then I should become a Hindu? I'm sure many Christians wouldn't like that.

Yes, that would be the flaw in Gottservant's argument. But Gottservant's posts are a little strange sometimes.

 

[Ana the Ist]

Try the demo on the link I posted. A dozen or so trials are enough to illustrate the difference.

The key point is not the reduction in the number of doors, but the alteration in conditional probabilities based on new evidence.

Assuming the initial pick is A, the three equally likely options are:

1. Prize is in A, shown non-prize in B or C
2. Prize is in B, shown non-prize in C
3. Prize is in C, shown non-prize in B

In 2/3 of cases (cases 2 and 3), the prize can therefore be won by switching.


Actually, if you switch, you have a 2/3 chance of being right. Try the demo.

The easiest way for me to think about it was like this.

At the onset, if you had a choice between picking any one door (1/3 chance being correct) or any two doors (2/3 chance of being correct) you would choose the two doors... they have a better chance. You still know that one of the two doors will be incorrect... even if one of them is the correct door. So when you choose one of the doors, and the host shows you one of the other two (always the incorrect one) the remaining door you didn't choose still has a 2/3 chance of being the correct door.

I don't feel as dumb about this knowing that PhDs still got it wrong.

 

[Radagast]

The easiest way for me to think about it was like this.

At the onset, if you had a choice between picking any one door (1/3 chance being correct) or any two doors (2/3 chance of being correct) you would choose the two doors... they have a better chance. You still know that one of the two doors will be incorrect... even if one of them is the correct door. So when you choose one of the doors, and the host shows you one of the other two (always the incorrect one) the remaining door you didn't choose still has a 2/3 chance of being the correct door.

Yes, that works.

 

[variant]

Neither do I, quite frankly.

Yes, that would be the flaw in Gottservant's argument. But Gottservant's posts are a little strange sometimes.

It doesn't, reality isn't a game show, and Gotts isn't our host.

Probability in game theory doesn't add to the discussion of whether God is true.

 

[Radagast]

Probability in game theory doesn't add to the discussion of whether God is true.

Well, Pascal thought it did.

Be that as it may, however, this thread is probably not a useful contribution to the topic.

 

[variant]

Yes, because when you pick option A, you have a 1/3 chance of being correct, but if you switch to B, that is one option between two, giving you a 1/2 chance of being right. It might seem counterintuitive, but it does actually increase your chances of picking right.

Swapping gives you a 66% chance of being right because it means you are betting on that you picked a goat the first time (66% chance).

It does if you know the behavior of the host anyway.

 

[variant]

Well, Pascal thought it did.

Pascal didn't seem to get the idea that attempting to force belief because of a small percentage chance of being rewarded for it is likely an overt insult to a supreme being.

 

[Radagast]

Pascal didn't seem to get the idea that attempting to force belief because of a small percentage chance of being rewarded for it is likely an overt insult to a supreme being.

Well, I'm not sure you quite get Pascal's point, but it's probably off-topic for this thread.

 

[variant]

Well, I'm not sure you quite get Pascal's point, but it's probably off-topic for this thread.

I don't think it's off topic at all, this is a thread about probability theology.

Pascal supposes I can or should endeavor to change what I believe so I get better odds at being rewarded for it.

I think that treating belief like a game (with the prospect of being rewarded as the goal) is likely to be insulting to any Gods I may encounter which Pascal does not consider.

 

[Radagast]

I don't think it's off topic at all, this is a thread about probability theology.

Pascal supposes I can or should endeavor to change what I believe so I get better odds at being rewarded for it.

I think that treating belief like a game (with the prospect of being rewarded as the goal) is likely to be insulting to any Gods I may encounter which Pascal does not consider.

Ok then, let me say that you're totally misrepresenting what Pascal actually said (you can read him here). He says explicitly that the argument is intended to "incite to the search after God." The wager itself is addressed to those who are uncertain about the existence of God. Nor does he "treat belief as a game," except in the technical mathematical sense.

 

[variant]

Ok then, let me say that you're totally misrepresenting what Pascal actually said (you can read him here). He says explicitly that the argument is intended to "incite to the search after God." The wager itself is addressed to those who are uncertain about the existence of God. Nor does he "treat belief as a game," except in the technical mathematical sense.

I've read Pascal.

The "wager" aspect automatically treats belief as a game (He says so explicitly) with a goal of being rewarded, it can not in any way shape or form work if this idea is removed.

 

[Paradoxum]

Neither do I, quite frankly.

Yes, that would be the flaw in Gottservant's argument. But Gottservant's posts are a little strange sometimes.

 

[True Scotsman]

Hi there,

So this is a little philo-theo thought experiment for those of you that like neuroscience. See there is this very well established science that if you are given a choice of three options, and you pick, but then you are shown one of the other options is false, it is statistically more likely that you have chosen the wrong door, based on the fact that you now have only two options to choose from - your odds increase, if you gamble in more and more limited contexts.

The thing is, what if the thing behind one of those doors is God? If you knew that it was more likely that He would be behind the other door, would you switch or does the permissiveness of God - the indifference - put you off increasing your odds all of a sudden? What if I told you that as a habit of thought, putting God off in this way, would make you unlucky in general? Still not interested? What if I told you that where God is, there is always something Christ has created, so in essence, there was no way you could lose, just by committing to increase your odds? Still really not interested?

It's just a thought. I am truly very curious to see what your initial responses will be.

No. There's a 50/50 chance either way.

 

[Ana the Ist]

No. There's a 50/50 chance either way.

Lol something tells me that you didn't read the rest of the thread before posting True...

 

[PsychoSarah]

Swapping gives you a 66% chance of being right because it means you are betting on that you picked a goat the first time (66% chance).

It does if you know the behavior of the host anyway.

Oh gosh darn it, did my maths wrong, how embarrassing. Guess it proves I didn't cheat off of someone else though, and I was right still about it increasing one's chances.

 

[Gottservant]

Yes, because when you pick option A, you have a 1/3 chance of being correct, but if you switch to B, that is one option between two, giving you a 1/2 chance of being right. It might seem counterintuitive, but it does actually increase your chances of picking right.

So even though you know you will discover something you don't believe in, you would rather win? Or are you just intent on being lucky in general?

 

[Gottservant]

I've heard the Monty Hall Problem before, but I don't get how this applies to God.

If I'm a Christian, and Scientology is shown to be incorrect, then I should become a Hindu? I'm sure many Christians wouldn't like that.

Touche.

But I would still believe in something related to a deity, correct?

In certain circumstances a believer will accept even that, for a time.

 

[Gottservant]

Pascal didn't seem to get the idea that attempting to force belief because of a small percentage chance of being rewarded for it is likely an overt insult to a supreme being.

While an intelligent invocation of God to refute an argument for belief in that God, I find your tone depressing.