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Tags Newcomb's Paradox

View Poll Results: Should you choose just one box or both boxes
Just one box 12 54.55%
Both boxes 2 9.09%
Other 2 9.09%
Don't know 0 0%
On planet X we only answer sensible questions 6 27.27%
Voters: 22. You may not vote on this poll

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Old 27th April 2017, 08:09 PM   #1
Robin
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Newcombe's Box asked a certain way

Undoubtedly this has come up before, but I want to pose this puzzle in a particular way.

You have two closed boxes and there is money in one of them. You have a choice of opening one box or both boxes and you get to keep any money you find. You are informed that the machine which loaded the money was able to predict your choice and has put $1,000,000 in box A if it predicted you chose just box A and $1,000 in box B if it predicted you chose both boxes.

You check and find that this machine has always made perfect predictions in the past, including in situations just like this. You have done your homework sufficiently to be sure there has been no trickery.

The question is, do you open just one box, or do you open both?

One answer says that your choice cannot change what is in the boxes and so you will get as much money as it is possible to get by opening both.

Now I say that there is a flaw in that. It assumes that you have a choice in the matter - that it is possible for you to open just one box, or to open both boxes.

But, by the premises of the puzzle, something has consistently made perfect predictions of people's choices and so it is highly likely that you have no choice in the matter, the fact of which you will do is already inevitable, you just don't know which yet.

If you have no choice in the matter and the machine makes perfect prediction then the amount of money in the box is correlated to your choice.

So your reasoning should be "The choice I make is already inevitable and the box loading machine has predicted this and loaded the boxes accordingly. If it turns out that I choose both boxes then I will only get $1,000. If it turns out that I choose just box A then I will get $1,000,000. So I should try to choose box A (if this is possible) and I will be guaranteed $1,000,000".

If you are not convinced yet and think "both boxes" is still the right answer then suppose you had given this advice one year ago. By the premises of the puzzle the machine is always observed to get it right and there has never been a single instance where it has got it wrong, including cases just like this. And so for the past year the people who took your advice only got $1,000 and the people who ignored your advice and chose just box A always got $1,000,000. Some people come to you and ask that if there is anything about this that would make you change your advice, and if not why do you expect something to change and advice which has proved disastrously wrong for the past year will start being sound.

What would you say?
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Last edited by Robin; 27th April 2017 at 08:28 PM.
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Old 27th April 2017, 08:25 PM   #2
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Incidentally, I may not participate in this for a few days (other than to answer clarifications). That is not because I am doing a hit and run, rather I am interested in the responses of others.

Just remember you are answering the question about the hypothetical world described by the premises of the puzzle, not the real world.
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Old 27th April 2017, 08:30 PM   #3
marplots
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Originally Posted by Robin View Post
Undoubtedly this has come up before, but I want to pose this puzzle in a particular way.

You have two closed boxes and there is money in one of them. You have a choice of opening one box or both boxes and you get to keep any money you find. You are informed that the machine which loaded the money was able to predict your choice and has put $1,000,000 in box A if it predicted you chose just box A and $1,000 in box B if it predicted you chose both boxes.

You check and find that this machine has always made perfect predictions in the past, including in situations just like this. You have done your homework sufficiently to be sure there has been no trickery.

The question is, do you open just one box, or do you open both?
Neither. I sell the rights to the choice for $500,000 and let someone else make the call.
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Old 27th April 2017, 09:07 PM   #4
Robin
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Remember, by the premises of the puzzle the machine has always got the predictions right and never even once got it wrong even in cases just like this.

Anyone who answers both, please tell me what your answer would be when someone says: "But someone said 'both boxes' was the right answer 1 year ago and since then every single time someone chose both they only got $1,000 and every single time someone just chose box A they got $1,000,000. Given that this advice was wrong one year ago, what makes you think the situation will change and the machine will break its perfect record?".

Answering "both" implies that you think the machine's perfect record will end when you make a choice. Why do you think that?
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Last edited by Robin; 27th April 2017 at 09:08 PM.
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Old 27th April 2017, 09:13 PM   #5
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Why are you assuming everyone will choose both boxes?

I choose Box A. Now, where's my million dollars?
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Old 27th April 2017, 09:16 PM   #6
Robin
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Originally Posted by theprestige View Post
Why are you assuming everyone will choose both boxes?

I choose Box A. Now, where's my million dollars?
I am not assuming everybody would choose both boxes. But in a survey of nearly 2,000 academics only one fifth said that "one box" was the correct answer and over 30% choose "two boxes", so I am assuming that I will get some who answer that way.
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Old 27th April 2017, 09:19 PM   #7
marplots
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Originally Posted by Robin View Post
Answering "both" implies that you think the machine's perfect record will end when you make a choice. Why do you think that?
The accuracy of the machine's prediction is irrelevant because I don't know what the machine predicted until after I make my choice.

If machine predicts A and I pick A, I get $1m. If machine predicts A and I pick both, I still get $1m.

If machine predicts both and I pick A, I get nothing. If machine predicts both and I take both, I get $1,000.

Whatever the machine predicts, I get the most money by taking both.
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Old 27th April 2017, 09:21 PM   #8
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This sounds a lot like the god's-foreknowledge-free-will problem.
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Old 27th April 2017, 09:32 PM   #9
marplots
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Originally Posted by Fudbucker View Post
This sounds a lot like the god's-foreknowledge-free-will problem.
Yes. Coincidentally, I've just heard a nice podcast on this problem, centered around Scotus, Ockham (he of the razor), and Bradwardine - a debate dating back to the fourteenth century.

https://historyofphilosophy.net/fore...predestination

Quite good.
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Old 27th April 2017, 09:43 PM   #10
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I don't really care about the God's foreknowledge and predestination stuff.

It does interest me in how people reason about determinism, (ie hard determinism - exactly one next state).
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Old 27th April 2017, 09:46 PM   #11
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Seems to me that foreknowledge is in principle possible without a God or even without an astronaut pushing books off a bookshelf from a tesseract he conveniently found in a black hole.
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Old 27th April 2017, 09:50 PM   #12
theprestige
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Originally Posted by marplots View Post
The accuracy of the machine's prediction is irrelevant because I don't know what the machine predicted until after I make my choice.

If machine predicts A and I pick A, I get $1m. If machine predicts A and I pick both, I still get $1m.

If machine predicts both and I pick A, I get nothing. If machine predicts both and I take both, I get $1,000.

Whatever the machine predicts, I get the most money by taking both.
I'm pretty sure the machine predicted I would pick A, because that's where it put the money.
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Old 27th April 2017, 09:56 PM   #13
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So this is a question about free will? The money is just a convenient way to measure compliance.

God will guarantee you a great life if you live according to morals set A.
God will make no guarantees if you live in any other way.

I don't know. I don't like doing something just because I'm told I will, but I do enjoy money. The more you think about it, the more interesting it gets.
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Old 27th April 2017, 09:59 PM   #14
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Originally Posted by Robin View Post
Seems to me that foreknowledge is in principle possible without a God or even without an astronaut pushing books off a bookshelf from a tesseract he conveniently found in a black hole.
Sure. The same problem arises with anything that can predict what you're going to do with 100% accuracy, like the machine in the OP.
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Old 27th April 2017, 10:02 PM   #15
Robin
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Originally Posted by Loss Leader View Post
So this is a question about free will? The money is just a convenient way to measure compliance.

God will guarantee you a great life if you live according to morals set A.
God will make no guarantees if you live in any other way.

I don't know. I don't like doing something just because I'm told I will, but I do enjoy money. The more you think about it, the more interesting it gets.
The question is not about anything except what is mentioned in the question. It is definitely not about God.
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
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Old 27th April 2017, 10:03 PM   #16
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Originally Posted by theprestige View Post
I'm pretty sure the machine predicted I would pick A, because that's where it put the money.
Quite possibly, but it doesn't really matter for the purposes of the question.
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
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Old 27th April 2017, 10:11 PM   #17
Robin
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Originally Posted by Fudbucker View Post
Sure. The same problem arises with anything that can predict what you're going to do with 100% accuracy, like the machine in the OP.
If I asked a logic puzzle about a country where half the people always told the truth and half the people always lied and you couldn't tell which was which - would you be looking at the implications, or hesitating to answer because such a country is completely implausible or would you just answer the puzzle? (or perhaps not because you don't have the time or interest).
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
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Old 27th April 2017, 11:26 PM   #18
marplots
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Originally Posted by Robin View Post
If I asked a logic puzzle about a country where half the people always told the truth and half the people always lied and you couldn't tell which was which - would you be looking at the implications, or hesitating to answer because such a country is completely implausible or would you just answer the puzzle? (or perhaps not because you don't have the time or interest).
All of that. Implications are part of what make it interesting. For example, here is an interesting implication:

I do not have the boxes in front of me now. This is a thought experiment, or, as Pigliucci calls it, "an intuition pump." I must imagine the situation and place myself in it and see what I think my imaginary self would do.

However, I am not 100% certain what I would really do. I can only guess. Perhaps my future self has an epiphany and changes his mind, or picks otherwise just on a whim, or makes a mistake. No logic I can bring to bear now is capable of protecting me from an uncertain future. And that means the infallible machine is actually a better guesser of what I would do than I am myself. It has more insight into my actions than I do.

So the answer must be: "I don't know what I would do; ask the machine."

Last edited by marplots; 27th April 2017 at 11:28 PM.
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Old 27th April 2017, 11:40 PM   #19
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I must be missing something here, I don't see how this is even remotely interesting. In the situation described in the OP, if I understand it correctly, I'd open box A and walk away with $1,000,000. Why would I or anybody do anything else?
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Old 27th April 2017, 11:59 PM   #20
marplots
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Originally Posted by Guybrush Threepwood View Post
I must be missing something here, I don't see how this is even remotely interesting. In the situation described in the OP, if I understand it correctly, I'd open box A and walk away with $1,000,000. Why would I or anybody do anything else?
Because if there is a million in box A, there is no penalty for taking both boxes. By the time you make your choice, the contents of the boxes are fixed.
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Old 28th April 2017, 12:03 AM   #21
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Originally Posted by marplots View Post
Because if there is a million in box A, there is no penalty for taking both boxes. By the time you make your choice, the contents of the boxes are fixed.
But the OP is quite explicit, this isn't happening in our world, but in a world that contains a robot with supernatural powers, why would I even think about trying to outsmart that at the risk of $999,000?
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Old 28th April 2017, 12:12 AM   #22
marplots
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Originally Posted by Guybrush Threepwood View Post
But the OP is quite explicit, this isn't happening in our world, but in a world that contains a robot with supernatural powers, why would I even think about trying to outsmart that at the risk of $999,000?
It does matter a little bit if a thousand dollars, in your circumstances, has significance. If we changed it to one dollar, who would care?

But the situation is that there are two boxes in front of you. Whatever is in them is in them and won't change. On what basis would you ever take less than both? If A has a million, you still get that million, no matter if you take just A or both.

It doesn't have anything to do with whether or not the machine is right or wrong. Two boxes sitting there and you can have one or both.
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Old 28th April 2017, 12:32 AM   #23
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Originally Posted by marplots View Post
Because if there is a million in box A, there is no penalty for taking both boxes. By the time you make your choice, the contents of the boxes are fixed.


The evidence of the machine's perfect predicting record implies that it really can predict. So the penalty for opening both boxes is that it changes what the machine predicted so you only get $1000.

In our world your approach is right because the machine's perfect record is just luck. In an imaginary world, that isn't necessarily true and the machine's perfect record might be down to something other than luck so, even if it were some kind of trick, just open A and take at least 99.9% of your possible winnings.
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Old 28th April 2017, 12:42 AM   #24
marplots
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Originally Posted by Jack by the hedge View Post
The evidence of the machine's perfect predicting record implies that it really can predict. So the penalty for opening both boxes is that it changes what the machine predicted so you only get $1000.

In our world your approach is right because the machine's perfect record is just luck. In an imaginary world, that isn't necessarily true and the machine's perfect record might be down to something other than luck so, even if it were some kind of trick, just open A and take at least 99.9% of your possible winnings.
But if there is no wiggle-room, then you aren't actually making a choice at all. You are merely playing out the script predicted by the machine. For a choice to exist, there must be the possibility of actually choosing, or the question, "What would you do?" makes no sense. What you will do is whatever the machine has predicted you will do, no matter how you happen to feel about it now. You play the same role as my computer does when I program it to act in some fashion in response to some input.

The problem is, at one point the situation requires a free choice (on your part), but then at another, it denies the existence of a free choice (to make the machine infallible). Can both those conditions be met? If not, if one must give, we can pick either equally and arrive at either answer. But the only one we can abandon and have the question make any sense is the "infallible prediction" condition - no matter how it seems to us, there must remain a possibility for the machine to guess wrong. It must, indeed, be a guess and not an infallible look into the future.

Last edited by marplots; 28th April 2017 at 12:44 AM.
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Old 28th April 2017, 12:53 AM   #25
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What if, in this imaginary world, the machine can see 2 days into the future?



More prosaically, what if your research into its 100% predicting record found it made a total of 3 predictions and each time it correctly predicted the person would open both boxes?
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Old 28th April 2017, 12:57 AM   #26
marplots
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Originally Posted by Jack by the hedge View Post
What if, in this imaginary world, the machine can see 2 days into the future?
Then screw the boxes, what are the winning powerball lottery numbers?

Last edited by marplots; 28th April 2017 at 12:59 AM.
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Old 28th April 2017, 01:18 AM   #27
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Originally Posted by Robin View Post
I am not assuming everybody would choose both boxes. But in a survey of nearly 2,000 academics only one fifth said that "one box" was the correct answer and over 30% choose "two boxes", so I am assuming that I will get some who answer that way.
That is because the way you posed the problem is incorrect. In the original newcombe, if you chose the opaque box and the machine predicted you would, then you get a fat zero. In order to maximize your chance at winning, you ask both box, which always has a minimum of 1000$ win.
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Old 28th April 2017, 01:21 AM   #28
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There is insufficient information in the initial statement of the puzzle. Do I know, in advance of opening any boxes, which is box A and which is box B?

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Old 28th April 2017, 02:12 AM   #29
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I would open box A, take my $1,000,000 and leave the other box in case I've misinterpreted the question and opening the second box means losing my $1,000,000 for a measly $1,000.

Last edited by JesseCuster; 28th April 2017 at 02:14 AM.
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Old 28th April 2017, 02:30 AM   #30
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Originally Posted by JesseCuster View Post
I would open box A, take my $1,000,000 and leave the other box in case I've misinterpreted the question and opening the second box means losing my $1,000,000 for a measly $1,000.
This.

Oh damn I've won a measly million dollars when I could have had a whole One million one thousand dollars. Woe is me.
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Old 28th April 2017, 02:33 AM   #31
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Originally Posted by Hungry81 View Post
This.

Oh damn I've won a measly million dollars when I could have had a whole One million one thousand dollars. Woe is me.
You should change it so that the box randomly gifts you $1000 or $1000000 if you just open one box it has predicted whereas if you open both boxes when it has predicted you will do so you have a chance at $1100000 or nothing. Then it creates incentive for people to try and break away from the boxes percieved omnipotence.

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Old 28th April 2017, 03:27 AM   #32
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With my luck, I'd open the box with the dead cat.
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Old 28th April 2017, 03:58 AM   #33
Robin
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Originally Posted by Dave Rogers View Post
There is insufficient information in the initial statement of the puzzle. Do I know, in advance of opening any boxes, which is box A and which is box B?

Dave
Yes. They are marked A and B
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Old 28th April 2017, 04:10 AM   #34
Robin
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Originally Posted by JesseCuster View Post
I would open box A, take my $1,000,000 and leave the other box in case I've misinterpreted the question and opening the second box means losing my $1,000,000 for a measly $1,000.
Do you mean you have chosen to open just boz A and then after finding the million you want to change your choice to "both boxes"? No you have to make your choice "Just box A, just box B or both boxes.
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Old 28th April 2017, 04:12 AM   #35
Meadmaker
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As presented, I choose box A.
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Old 28th April 2017, 04:17 AM   #36
JesseCuster
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Originally Posted by Robin View Post
Do you mean you have chosen to open just boz A and then after finding the million you want to change your choice to "both boxes"?
No, that's not what I mean. I mean I'd just choose box A and forget about box B.
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Old 28th April 2017, 04:29 AM   #37
Robin
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Originally Posted by marplots View Post
The accuracy of the machine's prediction is irrelevant because I don't know what the machine predicted until after I make my choice.

If machine predicts A and I pick A, I get $1m. If machine predicts A and I pick both, I still get $1m.

If machine predicts both and I pick A, I get nothing. If machine predicts both and I take both, I get $1,000.

Whatever the machine predicts, I get the most money by taking both.
If the machines predictions are inaccurate you will get most by picking both boxes.

By the premises the machine has been accurate every single time and never made a mistake. By the premises you have done your homework and made sure this is the case.

So if you think that opening both boxes will be the best strategy you must think that the machine's perfect record will stop and it will start making mistakes. Why do you think that?
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
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Old 28th April 2017, 04:34 AM   #38
Robin
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Originally Posted by Aepervius View Post
That is because the way you posed the problem is incorrect. In the original newcombe, if you chose the opaque box and the machine predicted you would, then you get a fat zero. In order to maximize your chance at winning, you ask both box, which always has a minimum of 1000$ win.
Do you have a cite for this? I have never seen this version. Not saying you are wrong, I've just never heard that version.
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
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Old 28th April 2017, 07:01 AM   #39
Fudbucker
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Originally Posted by marplots View Post
With my luck, I'd open the box with the dead cat.
I lol'd
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Old 28th April 2017, 07:16 AM   #40
Jack by the hedge
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Originally Posted by Meadmaker View Post
As presented, I choose box A.
Would that change if you learned that the total number of predictions the machine had made was, say, fifty and on every single occasion the player had opened both boxes?
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