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

Ana the Ist said:

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

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PsychoSarah said:

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.

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Paradoxum said:

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

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Paradoxum said:

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.

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Radagast said:

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.

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Ana the Ist said:

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.

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Radagast said:

Neither do I, quite frankly.

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

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variant said:

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

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PsychoSarah said:

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.

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Radagast said:

Well, Pascal thought it did.

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variant said:

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.

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Radagast said:

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

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variant said:

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.

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Radagast said:

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.

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Radagast said:

Neither do I, quite frankly.

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

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Gottservant said:

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.

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True Scotsman said:

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

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variant said:

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.

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