The analysis fail to recognize the most overlooked aspect: this is a highly superior being from another part of the galaxy.

So this raises new problems. Is it US currency? Canada, Australia, New Zealand, Bahamas, Barbados, Bermuda, Fiji, Hong Kong, Jamaica, and Singapore use 'dollars'.(List in not necessarily all inclusive or completely accurate.) So depending on which, this could extremely diminish the value.

Is it alien currency? If so does it have any value to me. Where the hell am I going to get it exchanged?!

Where did the alien get this money? Was it legally acquired? Is this money going to disappear into the galactic court system?

Doesn't he have cattle to mutilate and people to abduct?

What kind of boxes does he have? Are the from earth or another planet? I might really want two.

Is there any certainty the being is a "he"?

I'd let him keep the money if he could get me off this planet. But can I get BoingBoing away from Earth...

Here's my analysis:

Either the alien has predicted that I will take the closed box (Pc), or he's predicted that I'll take both boxes (Pb). I don't know the relative probabilities of Pc and Pb.

Either I will take only the closed box (Tc), or I'll take both boxes (Tb).

So we have four combinations:
Pc + Tc = $1,000,000 for me.
Pb + Tc = $0 for me.
Pc + Tb = $1,001,000 for me.
Pb + Tb = $1000 for me.

It seems pretty clear to me that unless I believe that Tc => Pc, then whatever the relative probabilities of Pc and Pb, it's best for me to choose Tb and take both.

Now, if the alien is smart, he'll have done the same analysis, so he knows that the best thing for me to do is choose to take both. It's quite plausible that the last 999 humans did so, as predicted; much more plausible than the hypothesis that nobody took the risk-free money. So I should break the chain, and take just the closed box.

Then again there are no such things as aliens. So, what appears to be the alien is probably Dick Cheney in a nice alien suit. He probably picked 999 greedy people who he used to work with, so naturally they went after the million. Cheney probably has a shotgun hidden in the alien suit, and he probably shot all 999 before you got there. So I'd either run like hell or shoot first.

The superior being has predicted what I will choose. He does this either by scientific reasoning (As one can predict with scientific accuracy that a pencil will fall downwards if it rolls off a desk) OR by some kind of supernatural, psychic power.

The first is based on scientifically sound data (Perhaps he has been observing me my whole life and knows me - and those other 999 people - that well) OR in the latter case, he recieved information that travelled back in time from the moment I make my decision.

Because of this, I would choose the single box, and I would get my million, because by choosing the single box I am either acting in a way that can be, and indeed has been, acurately predicted OR by choosing the single box, I send information back in time on which the being in the past bases his decion.

If you can find fault with my thinking (I am labourer, not any kind of professional thinking man), please let me know at jjnnww@gmail.com

Edited by author 12-14-2006 08:30 PM
The alien can predict the future. He says that he HAS possibly put a million dollars in the closed box. Even your second rate magician could make the money vanish as soon as he opened the closed box. Why is a "superior being" traveling around the galaxy teasing us. He is obviously up to no good. I would say just take both boxes (they might be made of some cool alien material), don't worry too much about the money, and try not to get beat up by some alien punk looking for a fight. You still go $1000 his money, right? Anyway, the odds are even, so you have a better chance of getting his money by dressing up as a different person, conning him into asking you again.

The human in the experiment knows nothing about the alien, save that it has a 100% success rate at predicting human behavior. However when the experiment is done, the alien does not have a 100% chance of predicting what the human will do. For instance if you accurately predict the result of 999 coin tosses your chance of predicting the 1000th toss correctly is still 50%.

This means there is a 50% chance that the closed box will contain a $1,000,000. So the best choice would be to take both boxes as this will result in $1,000 and the 50% chance, whereas choosing the closed box only will result in the 50% chance only.

Wait a moment.

If the alien knows nothing about it's human subjects then it has achieved a 100% success rate through dumb luck alone. This is as likely as a human predicting 999 coin flips in a row. The alien must have engaged in a very in-depth analysis of the humans in order to predict their behavior with such accuracy. It probably knows them better than they know themselves.

Given this state affairs, I would choose the closed box as it is very unlikely that the alien has made it's only error in predicting my actions.

But if I did not know of the alien's predictive success I would have chosen both boxes. And the alien (if indeed it had studied me carefully) would no doubt have predicted this choice as well.

The problem has nothing to do with predictability or anything the alien says, just look at the physicality of it, the alien has already put the million dollars in the box (or not). Which box you choose therefore makes no difference to whether the million dollars is in the closed box or not, therefore it will always be better to take both boxes, in NO SITUATION is it better to just take the closed box, you'll either lose out on a $1000 and just get the million or get nothing.

just think of it this way, the 50/50 chance of getting the million is totally independant of whether you choose one or both boxes, because it has already been put in there before you made your descision, so always take both as you'll have the same chance of getting the million plus a gaurenteed thousand no matter what. this seems very simple to me, i hope someone can point out how i'm wrong.

The answer seems simple and the key is that the alien isn't guessing what you're going to do - according to the premise, the alien knows what you're going to do. All you have to do, therefore, is decide to go for the million dollar option. As you will choose this option, the alien will have predicted you would do so, and have stuffed the box with the million dollars.

This is truly a paradox, in the classic sense of Zeno's paradox, Epimenides' paradox, and the Barber's paradox. (_Not_ in the sense of the Monty Hall "paradox", which has a logical, mathematically correct solution, but people will still argue endlessly about it, because the correct solution can appear counter-intuitive and is difficult to understand.) That is, the question per se contradicts itself, with the result that neither of its mutually exclusive answers is more correct than the other. The only real way to "solve" it is to point out the flaw in the reasoning of the problrm stated.

Which is this: On one hand, the "highly superior being" always predicts your decision and makes sure you cannot get away with over a million dollars. If the "highly superior being" already knows that you will take both boxes, before you even meet, then the million-box will be empty. On the other hand, the problem states that if there is money in both boxes, you could conceivably take them both. This is logically inconsistent, hence paradoxical.

From a scientific perspective, it's pointless to try to solve the puzzle, as it doesn't make sense to begin with. If it is worth contemplating at all, then as a philosophical question: Would you believe the story the "highly superior being" told you and attempt to take the box with the million dollars? Or would you be more of a realist, don't buy the crazy story that apparently violates the laws of nature, play it safe, and take all the boxes you are offered?

No matter which choice you make, you cannot prove that it really is better. A proof must be based on axioms that are part of the same formal system, but if the formal system is meaningless, then theorems inferred from it are meaningless, too. The answer "take both boxes" is not more meaningful or correct than the answer "fruit salad".

This is not a paradox in the normal sense. In a true paradox, there is a lack of internal consistency -- like "What happens when an irresistable force meets an immovable object?". The answer to which is, if one exists the other by definition cannot -- the question asserts the existence of a logically impossible condition -- so it is simply a non-sensical question.

Newcomb's "paradox" is not a paradox in that sense; it is just a brain teaser. The key to Newcomb's is to consider the possible combinations of what the alien knows, and how it chooses to load the boxes based on that knowledge (or lack thereof); and to determine what is your optimal strategy based on these combinations of what the alien might be able to know & do.

Scenarios

1/A -- the alien IS able to accurately predict what you will select, and places the million-dollar bill in the SAME way he said he would.

1/B -- the alien IS able to accurately predict what you will select, and places the million-dollar bill in the OPPOSITE way he said he would

2/A -- the alien is NOT able to accurately predict what you will select, and RANDOMLY puts the million-dollar ball in the box or not based on a coin flip or other random process, or a non-random process you are not privy to

2/B -- the alien is NOT able to accurately predict what you will select, and NEVER puts the million-dollar bill in the box

2/C -- the alien is NOT able to accurately predict what you will select, and ALWAYS puts the million-dollar bill in the box

2/D -- the alien is NOT able to accurately predict what you will select, and puts the million-dollar bill in the box or not based on what most of the prior 999 people did in a way that favors you getting the million

2/E -- the alien is NOT able to accurately predict what you will select, and puts the million-dollar bill in the box or not based on what most of the prior 999 people did in a way that favors you NOT getting the million

... and any other variation you can think of. This works out better if you can define the scenarios in ways that are mutually exclusive & exhaustive.
 

The optimal strategy is obvious in each case --

1/A >>> Choose the closed box only

1/B >>> Choose both boxes

2/A >>> Flip your own coin

2/B >>> Choose both boxes

2/C >>> Choose both boxes

2/D >>> Ask the prior people what they did if you can; if not, then think of what an "average" person would do (which is not the same as the current analysis -- the average person isn't all that logical :) and do what that hypothetical person would do. Call this the "Family Feud" analysis :)

2/E >>> Opposite conclusion from 2/D


Your job is to figure out which is most likely. Just because the other player is an alien doesn't mean it actually has amazing powers, or is telling the truth. Maybe it is just a weird guy in a rubber mask :) You can choose one scenario if you feel strongly it is correct; or you can assign relative probability to each scenario and generate a random number to decide which of these to select (likelihood of selection weighted by the probability you assigned). This is the "utility function" approach and is actually the general case, because if you are absolutely sure one scenario is accurate it gets 100% of the probability in this utility function.

Or maybe there are other factors you aren't aware of that change the whole situaion -- maybe the alient always puts the million-dollar bill in the box, but has the super-power of being able to take the million-dollar bill out of the box psychokinetically if you grab the closed box :) Maybe your friends think you are a retarded monkey for believing in aliens in the first place and set you up for an embarassing Candid Camera segment.

Personally, I would choose the closed box. Not making $1000 is a small let down but the possibility of earning 1000x more (a life-changing amount) is very attractive. If I thought there was more than a 1-in-1000 chance the alien was telling the truth, then I would choose just the closed box.

p.s. Just because a decision is hard to make doesn't make it a paradox.

We see that it's clearly not the case that everybody chooses the same course here, just from this thread. So the alien is not just lucky.

The confusion people have here is that they have an incorrect concept of what a choice is in the context of this problem. (Perhaps because they deny that there could ever be such an alien.)

In the context of this problem, you do not _make_ a choice. You _are_ a choice. The alien's accuracy suggests that a human's conclusion that she is weighing two options here is a false one. From the alien's viewpoint, you are no more likely to choose differently than the prediction than you will choose to suddenly freeze because of a bizarre entropic coincidence. (It could happen, but it's really unlikely.)

So there is no paradox. Predictable beings are presented with a problem and answer it just as predicted. The only paradox is in their illusion that they might do otherwise. The trick is the question asks you to decide which choice to take, when in fact the premise says you don't have that freedom.

We don't like the idea of being predictable and deterministic, of course, which is what vexes us.

But we can imagine ways in which we are slighly less predictable.

Imagine I present you with Uma Thurman and George Clooney, and you are completely heterosexual. I ask you to decide which one you want to have sex with. Now you might imagine that you could, if given an important enough reason, have homosexual sex, but in this puzzle you're completely heterosexual and find that unappealing or even repulsive. But that's really an illusion. Knowing you are straight, and knowing your sex, I can predict with extreme accuracy which of the two you will choose.

It's presented as a decision you can make, but in fact the decision is already inherent in your sexual orientation, and was before you entered the room.

We don't know how the alien managed to predict it (i.e. whether he used a special alien "make it be yesterday" device or just clever psychological analysis) but what we DO know is that he's predicted correctly on all prior attemps (all 999 of them) and although it's not stated explicitly, we should assume that the former participants had the same information as we do (ask the alien if needbe). There are those of us who think "the money's already been put in the boxes, so I have nothing to lose by opening both." To the alien, such people probably glow blue. One step ahead of you, no million in the box. Then there are those that think that out of those 999 people, at least some of them must have tried to second guess and trick the system. They all failed. Every one of them. For whatever reason, the alien was one step ahead of them. I too could risk 999 thousand dollars beliving that I can second guess better than they did for a potential gain of a measly 1 thousand dollars, or I could just assume that this alien is a lot cleverer than me and take the cool million. I'll make up the extra thousand in interest within a week if I invest cleverly (and maybe ask the alien financial advice, as he's clearly good at this type of thing). Such people to the alien probably glow red, so the million is prepared. Getting it right every time sounds relatively easy. Tricking the system sounds relatively hard as the sequential odds are against you, and your choices for tricking it are very limited.

Now if the numbers were more even, say 15 thousand dollars in one box and 50 thousand dollars in the other, and the alien only had a 70% success rate, then it would make for a more interesting problem.

Msg 49: "always take both as you'll have the same chance of getting the million plus a gaurenteed thousand no matter what. this seems very simple to me, i hope someone can point out how i'm wrong."

The alien knows you think that way, so it won't put $1 million in the box.

Edited by author 12-14-2006 11:35 PM
This is only a paradox if there is a causal link between your decision in the present moment and the alien's prediction at some past time. That this is the case is not necessary, or even obvious; I predict right now that "The sun will rise tomorrow," but just because I have made this assumption every evening with unerring accuracy for my entire life, it is not the case that my prediction was "caused" by tomorrow's sunrise.

The million is either there or it is not; the prediction, accurate or not, has been made. Opening both is the only rational choice.

I'm tired, and I think I missed something, but if the alien can only predict your own decision, then can't you just flip a coin to void his knowledge? Would the odds not be back at 50/50? A level playing ground?

Personally, I'd probably be happy playing with a box, they make great spaceships.

Allright, my assumption that this is truly a paradox in the classic sense is only correct if you consider the entire quote presented in post #1. As a whole, it contradicts itself, here: "Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only."

If you only consider the first three paragraphs, i.e. up to and including "what would you do?", it isn't paradoxical in the sense that the situation is actually impossible. The question is still a bit philosophical, and I'm still not sure that you could _prove_ that one answer is better, but it _is_ much clearer in this case: Would you risk a million dollars for one thousand dollars, even though the futility of this endeavor has already been demonstrated over and over? Would you go against all odds, in the hope that afterwards you could say, "a highly superior being offered me a million dollars as a gift, but I tricked it and increased my earnings by one tenth of a percent"?