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## Question

Sorry if this one has already been posted, but no results came up in my search.

There is a predictor that predicts the likelihood of events with %100 accuracy.

Today, you are presented with two boxes. You may open only Box B, or you may open both boxes.

Box A contains \$1000.

Box B may or may not contain \$1,000,000, depending on what the predictor predicted you would do.

It made this prediction yesterday.

If it predicted you would only open Box B, it has placed \$1,000,000 in Box B.

If if predicted you would open both boxes, then Box B is empty.

Should you open both boxes, or only Box B?

At first glance, it seems that opening only Box B is the best answer. Though I believe this, there is also an argument for opening both boxes:

The amount of money in the boxes isn't going to change now. It is a previously set amount. If you open Box B and it contains \$1,000,000, wouldn't it be sensible to open Box A in order to gain \$1000 more?

Of course, the predictor has predicted this course of action, so Box B contains no money. You should open Box A so you at least have \$1000. Then again, if you just open Box B, it should contain \$1,000,000. Right?

Personally, I love this paradox. Enjoy.

## Recommended Posts

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Well I eat one bite at a time..put my pants on one leg at a time..dated girls one at a time..ect..so the seer should think that I'd only want one cup...so he should just go ahead and throw that million under cup B...but since he does'nt know my secrets, he won't know that I would actually like to do some things more than once, and take things more than once at a time..so then I'll walk away with a \$1,001,000...

but why try figuring out what this 'seer' knows and thinks about you, and risk it...take the gauranteed \$1,000..

if it's like any other 'higher beings'(or whatever) that I know of, they'll be wrong more than right..

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would anyone who goes in intending to only take B, and then finds nothing, not take A? I wouldnt i guess, so the seer would be right either way

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would anyone who goes in intending to only take B, and then finds nothing, not take A? I wouldnt i guess, so the seer would be right either way

I think i would intend only to take B. Knowing everything i kno, if the seer is a great observer, he sould see that. Shouldn't he?

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but what if u did take B, and then realise the seer got it wrong? would u not take A? isnt \$1000 better than proving the seer wrong? And when u do take A, the seer was right and u only deserved \$1000

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I would not consider this a paradox. You control fate either way; you make the final choice. To me, a paradox controls its own fate. Unless we're going around that predetermination concept again. Let me simplify this out for everyone.

Choice 1. 2:1 ratio (50/50). \$1,001,000 (winner). \$1,000 (loser).

Choice 2. 2:1 ratio (50/50). \$1,000,000 (winner). \$0 (loser).

Choice 1 is the biggest profit win as well as the biggest profit loser. However, you should see that the seer is trying to sell you on singly choosing B within the description. Sadly, so many scams are set up this way (where you would pay \$2,000 to play this "game"). The lottery and most casinos run on a variant of this very same thing.

Edited by ybom
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I vote for thirty xanatos pileup.

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the logical choice would be cup A .as with first impresions they are normally correct. plus a free \$1000 bucks sounds pretty sweet to me

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if the seer knows me then i'm screwed either way

i'd better just pick a

Edited by DDMJ
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choices: Both cups or just the "B" cup. I like all or nothing. but if there is nothing, do I get to keep the cup?

I choose the B cup, today

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this is a repost, but one i thought worth considering.

in a book on symmetry, i read that John Conway knows the u.s. quarter so well that he can consistently get it to come up on the side of his choice.

so, let's say the being is Conway, and he explains his ability to you. he calls heads, flips a coin and it is indeed is heads. then he flips the other coin, calls heads and catches it in his hand. he says you have two choices. you can take only the unopened coin, and if it is heads, you get 1,000,000, if tails nothing. or you can take both coins. the one already showing being worth 1,000, and if the unopened coins shows tails you get 1,000,000.

basically your objective is to determine if Conway is honest or not, both about his ability and the state of the coin.

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When worded as it is in this thread (where the "Seer" is NOT omnipotent), this problem is NOT a paradox. Rather, it is a silly question about the assumptions involving this Seer's ability to predict your choice of cups.

On the other hand, if you say that there is a 100% guarantee that the "Seer" will correctly predict what cups you will pick up (B, or A and B), then there is an alleged paradox (I said "alleged" because I disagree that it actually is a paradox). The alleged paradox is that the "Seer" decided whether or not there should be a million dollars under Cup B ahead of time (before you entered the room and made your cup selection) and yet apparently you still have a choice of whether you want to cause the million dollars to be under Cup B or not (the choice is in whether or not you choose to take Cup A also). So the alleged paradox is: Who decides whether there is a million dollars under Cup B or not? The "Seer" or you with your choice of cups? The problem says that it is the "Seer," but it also says that you get to choose too.

This alleged paradox can be summed up in a simpler problem:

There is a cup. Somebody (a Seer) decides whether or not he is going to put a million dollars under the cup, and then puts the money under the cup if he decides to. Then, you are brought over to the cup and get to decide whether or not there is a million dollars under the Cup by choosing whether or not you are going to flip over some other cup.

So the problem is just saying that both you and the Seer get to decide whether or not there is a million dollars under Cup B. Some people think this is a paradox, but I can resolve it by saying that this problem's world is deterministic and so there really aren't two "possibilities" of cups that can be picked up. In other words, you don't actually have a choice of cups to pick up (you are told that you are given a choice between either Cup A or Cup A and Cup B, but in reality you don't have the free will to make the cup choice that you won't end up choosing) and will causally end up pick up the cup(s) that the omnipotent Seer saw that you would pick up. Thus, the problem is not forcing a paradox. Rather, it is forcing a deterministic world without free will. It can be assumed that the person given the choice of cups is not omnipotent and thus he believes that he is being given a choice of cups, but in reality his "choice" is causally determined and thus it can be assumed that the "Seer" foresaw the choice that he would make allow for the Seer to correctly predict what "choice" of cups the person would make without a paradox.

If you want to say that there IS a choice of cups (one with free will) there is a paradox, but I see no reason to assume that the person in the problem has free will, especially seeing as I don't see how free will would make sense in a world where rational agents grow out of irrational matter. Thus, I don't consider the problem a paradox.

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I'd kinda like to change my answer to pick only cup B.

here's why.

i see the problem this way now.

if you pick both cups, you get a guaranteed 1,000, with a small chance of getting 1,000,000.

for if the seer see you as someone would would take a sure thing, he would know ahead of time your likely to take both cups.

if you take only cup b. you get 1,000,000 with a high probability.

for if the seer know you don't mind some risk for great reward, he would know your likely to go for cup b only.

here's basically a simulation i would suggest.

every time player 2 picks both, decrease the probability of 1,000,000 in cup B.

every time player 2 picks only cup B increase the probability of 1,000,000 in cup B.

now which would be a better strategy, always taking cup B, always taking both, or a mixed?

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I'd kinda like to change my answer to pick only cup B.

here's why.

i see the problem this way now.

if you pick both cups, you get a guaranteed 1,000, with a small chance of getting 1,000,000.

for if the seer see you as someone would would take a sure thing, he would know ahead of time your likely to take both cups.

if you take only cup b. you get 1,000,000 with a high probability.

for if the seer know you don't mind some risk for great reward, he would know your likely to go for cup b only.

here's basically a simulation i would suggest.

every time player 2 picks both, decrease the probability of 1,000,000 in cup B.

every time player 2 picks only cup B increase the probability of 1,000,000 in cup B.

now which would be a better strategy, always taking cup B, always taking both, or a mixed?

Again, I think the "paradox" part of this is that the seer decided whether or not to put a million dollars under cup B BEFORE you enter the room and make a choice. Thus, the question is whether the choice of cups that you decide on affects whether or not there is money in cup B? Either no, your choice doesn't affect it because the seer already (in the past) decided to put the money in the cup and thus you should pick both A and B or else yes, your choice does affect whether or not there is money in the cup because the Seer is omnipotent and you don't have free will and thus you should pick just cup B to get a million dollars, because taking A also would cause there to NOT be a million dollars under cup B.

So to clarify, your choice of cups depends on whether or not your choice affects whether or not there is a million dollars in the cup. If your choice does affect it, then take cup B only. If your choice doesn't affect it, then take both cup A and cup B.

To help understand this you might want to imagine that there is a third person in the problem who witnesses the Seer put a million dollars under the cup. This third person has X-ray vision and can see through the cups to see whether or not there is a million dollars under cup B while the main person is deciding which cups to take. Imagine that there IS a million dollars under cup B. Then, obviously the person should take both cups A and B because its not like his choice will cause the money to disappear. Unless the Seer IS omnipotent, then either choosing cup B also will be am impossibility or else choosing Cup A also will result in the million dollars under Cup B disappearing before the person flips it over.

Edited by Use the Force
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I would just go with cup B because

1.I would get 1,000,000 and go merrily on my way.

or

2.I get nothing and am left where I started.

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vipe, the argument is, if you take both cups, you most certainly get 1,000, and since whether or not the million dollars was put there before hand, you lose nothing by going for both.

to me however, it's not the only paradox. another paradox comes in from determining whether we can see the likely consequences of our, and other peoples, actions or not. if i observed the someone was generally easy to anger, i can predict with fairly good accuracy that if he got into a crash he would get very angry. does my observation prevent them from not getting angry? of course not. now imagine a watched you for years. i made a prediction based on these observations, as to whether to put that million in the cup. i ran the same simulation with other people and got accurate predictions. does my decision affect your decision? not directly. you can chose one or the other. can i make an accurate prediction? almost certainly.

for me, i would take only cup B. if someone told me that they would put a million dollars under that cup if i only took it, and not both, clearly taking only that cup is the right choice.

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Could you please tell me more about the Seer?

Edit: Specifically are they trustworthy/untrustworthy

Edited by phaze
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vipe, the argument is, if you take both cups, you most certainly get 1,000, and since whether or not the million dollars was put there before hand, you lose nothing by going for both.

to me however, it's not the only paradox. another paradox comes in from determining whether we can see the likely consequences of our, and other peoples, actions or not. if i observed the someone was generally easy to anger, i can predict with fairly good accuracy that if he got into a crash he would get very angry. does my observation prevent them from not getting angry? of course not. now imagine a watched you for years. i made a prediction based on these observations, as to whether to put that million in the cup. i ran the same simulation with other people and got accurate predictions. does my decision affect your decision? not directly. you can chose one or the other. can i make an accurate prediction? almost certainly.

for me, i would take only cup B. if someone told me that they would put a million dollars under that cup if i only took it, and not both, clearly taking only that cup is the right choice.

Phillip, you have put yourself in the shoes of the Seer. Bravo. The seer is your peer, not some unapproachable deity on high. You understand that even a simple human mortal Seer can reliably control the outcome of this game and reward those who implicitly trust him/her. My personal interpretation of this: Each and every one of us holds the key to 'divine' influence on how the future of our universe plays out.

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Could you please tell me more about the Seer?

Edit: Specifically are they trustworthy/untrustworthy

Phaze - The zen of this paradox is crystalized in your question. Only you can answer it. Do not expect your mentor to help you because *your* answer defines your reward in this game, as in the larger game of life.

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Phaze - The zen of this paradox is crystalized in your question. Only you can answer it. Do not expect your mentor to help you because *your* answer defines your reward in this game, as in the larger game of life.

As it is *my* answer, I have control of what type of person the seer is.

Essentially the seer is a product of my imagination.

The amount of trust/trustworthiness/suspicion he portrays is a direct reflection of the trust/trustworthiness/suspicion I portray.

There is no way to take the reward from both cups

To optimize my reward I must choose only cup B and trust myself that I will not then be tempted to choose also cup A.

The real question is not is the seer trustworthy but am I trustworthy to myself.

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I'd hire someone trusted and give then strict instructions to return only what is in cup B. I would not explain the paradox to them only that I would know if he also looks under cup A and that his life is at stake if he does so.

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something like this is close to say...

you watching and recording a game,

then watching it with all your buddies,

you already know what's gonna happen,

and to them it seems as if it's live,

one would choose box b of course,

and in opening box a you would find:

1. 1,000 dollars

2. A contract thanking you for your participation and allowing you to keep all contents of box a, but none received from box b. since you opened box b first, it is now empty lol

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This is one of my favourite thought experiments.

I'd go with just opening box B, but can't really logically justify it at all.

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once again i feel just opening box B to be the correct choice. you cannot simutanously only pick box B, and pick box A and B. that is if you open only Box B and not both, you cannot now open Box A. therefore the million is garenteed to be there if you only pick box B. trying to pick both after picking box B negates the experiment, as you took an option that wasn't available.

yes the 1,000 is there. but by taking box A after only picking box B, you did something the predictor couldn't predict.

imagine you had a test and you have two options A or B. if you pick only one or the other your garenteed a 50/50 shot at getting it right. so you logically assume that by picking both, your garanteed to get it right. but how often on a scantron test is bubbling in all potentail answers the correct choice?

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the thing with this one is,

it's not a paradox,

anything you choose is correct,

no one would open B, find it empty, then refuse to open A.

anything you decided,

has already been predicted,

so it doesn't really matter,

besides,

the question is "Should you open both boxes, or only Box B?"

so the answer again, doesn't matter,

but pick B.

also,

just because he's been 100% up until now,

doesn't mean he will be 100% forever,

he may be wrong,

remember,

the items in the boxes is based on whatever HE PREDICTED.

not on what YOU WILL CHOOSE.

so obviously,

the only "safe" prediction is you will open both,

in making box B empty,

he's kinda forcing your hand so long as your greed is greater than your desire to prove him wrong

which again,

just because he's never been wrong before,

doesn't mean he can't be...

besides,

do you EVEN KNOW about the prediction?

or are you just presented with 2 boxes and told "you may open just one, or open both, whichever you choose, you may keep the contents of either the one or both"

because if that's the case,

then 99.99% of people will choose to open both and keep both.

It's only logical.

so basically just reiterating,

the safe prediction is both boxes.

People are curious, if you allow them to see the other box,

most will choose to do so.

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The amount of money in the boxes isn't going to change now. It is a previously set amount.

Not true. By the OP, it's tied to your choice. It can't be "a previously set amount" unless your choice has previously been set. If your choice has previously been set, there's no question to answer.

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