The Newcomb Problem

Quote: Wizard

My point being that just because Newcomb was 100% in the past, doesn't mean he will get YOU right.

Is the Newcomb Being success rate bassd on the past or is it a Fact?

Quote: Wizard

A being, who you believe to have superior predictive powers, makes you an offer. Before you are two boxes, identical in appearance. Within one box, let us call it 'Box A', there is either one million dollars or nothing. Within the other box, 'Box B', there is definitely one thousand dollars.

The being, whom in deference to tradition we will call the Newcomb Being, will allow you to either take both boxes, or just Box A.

Twenty-four hours ago, the Newcomb being made a prediction about what you would choose. At this point, it placed the money in the boxes. If the Newcomb Being predicted that you would take both boxes, it left nothing for you in Box A and the $1000 in Box B. If the Newcomb Being predicted that you would only take Box A, it would leave the million dollars in it, as well as the thousand dollars in Box B. If the being predicts you will base your choice on a random event (like flipping a coin), it will leave Box A empty.

Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.

Do you choose box A only, or both?

Wording above taken from greylabyrinth.com.

SciFi or In reality, the Facts is still the same.

Look at the Facts:
success rate on predictions = 90% (Don't need to know how he does it and does not matter went he placed the money in the boxes).
There for:
choose box A only = (million dollars 90% of the time) and (nothing 10% of the time).
choose both boxes = (thousand dollars 90% of the time) and (million+thousand dollars 10% of the time).

So if you choose box-A 100 times (It does not matter went, how & why you choose box-A), in average you will get million dollars 90 time and nothing 10 time, right.

Now, work it out.

Perhaps you missed the point that it is impossible to maintain a prediction accuracy of exactly 90% if you continue to make predictions. After N predictions with a record of 90%, the very next prediction will turn out to either be right or wrong, giving a new accuracy rate of ((.9N+0.5±0.5)/(N+1))x100%. Which is not 90%. Your assumption that an accuracy rate of exactly 90% is some kind of perpetual "Fact" invalidates the remainder of your analysis.

If you allow that the accuracy fluctuates up and down hovering around 90%, then perhaps we have some basis for discussion. At that point, we will probably need to address the issue that the original problem says that the being makes you "an" offer. It doesn't say you are allowed to play the game numerous times. Then if we agree that this is a one-time event, perhaps we can make some progress on resolving our disagreement.

Edit: When I originally made this post, I entered the formula for the new accuracy rate incorrectly. I think I have it right this time. Sorry.

Quote: Doc

Perhaps you missed the point that it is impossible to maintain a prediction accuracy of exactly 90% if you continue to make predictions. After N predictions with a record of 90%, the very next prediction will turn out to either be right or wrong, giving a new accuracy rate of ((.9N±1)/(N+1))x100%. Which is not 90%. Your assumption that an accuracy rate of exactly 90% is some kind of perpetual "Fact" invalidates the remainder of your analysis.

If you allow that the accuracy fluctuates up and down hovering around 90%, then perhaps we have some basis for discussion. At that point, we will probably need to address the issue that the original problem says that the being makes you "an" offer. It doesn't say you are allowed to play the game numerous times. Then if we agree that this is a one-time event, perhaps we can make some progress on resolving our disagreement.

Ok, make it accuracy of around 90% an is a one-time event.

The Formula (Equation) still the same.

The Facts: success rate on predictions = about 90% (Don't need to know how he does it and does not matter went he placed the money in the boxes).
There for:
choose box-A only (It does not matter why, how & went you choose box-A) = (million dollars about 90% of the time) and (nothing about 10% of the time).
choose both boxes (It does not matter why, how & went you choose both boxes) = (thousand dollars about 90% of the time) and (million+thousand dollars about 10% of the time).

One-time event: Do you choose box A only, or both?

Thank you for your reply -- I think we can have a discussion now.

Unfortunately, I am not yet ready to accept your "Facts", and we need to consider them a little further before my answer will do anything more than extend our divergent views of this problem. At this point, I disagree with your statement, "...does not matter when he placed the money in the boxes."

I need to understand your perspective on the following issue: At the time that I am to make my final decision and choice of box A only or both boxes, is the amount of money in each box already definitely established for this particular event? My viewpoint is that there is a fixed, unknown, specific amount of money already on the table, in each of the boxes, before I actually have to make my decision, and it doesn't matter to me personally how much money might be on the table the next thousand times some other persons might have the opportunity to make such a choice.

I assume you can see where I am going with that, but until I understand your perspective a little better, I don't know how to continue the discussion productively.

Quote: Doc

"...does not matter when he placed the money in the boxes."

Regarding the time he placed the money in the boxes befor you make your choose.
eg: hour ago, 24 hours ago, 2 days ago, months ago etc...

Quote: Doc

Unfortunately, I am not yet ready to accept your "Facts"

I think that's probably the crux of the paradox. Some people are willing to accept the premise, while others refuse to (or have trouble with it). If you don't buy into the premise that some being has supernatural predictive abilities -- and the conclusions that flow from that premise related to free will, etc. -- then the choice between just A or both is not as straightforward.

Quote: MrCasinoGames

Is the Newcomb Being success rate bassd on the past or is it a Fact?

It is based on the past.

Quote: MrCasinoGames

The Facts: success rate on predictions = about 90% (Don't need to know how he does it and does not matter went he placed the money in the boxes).

I would amend that to success rate on PAST predictions = 90%. It is critical to the problem that he put the money in the boxes before approaching you. It doesn't have to be exactly 24 hours. I would think of Newcomb as like a very good poker player who is outstanding at reading people, but is not psychic.

Quote: Wizard

It is based on the past.

Hmm, I'm not convinced about that. I believe the premise was that you have reason to believe that the NB *has* a 90% accuracy rate, not that he *had* one. Of course, that's going to be part of the interpretation of the setup that influences your view on the result.

Let me ask this: if you accept that the NB does have, and will have, a 90% success rate with predictions -- and all the ramifications of that -- is the answer to the puzzle obvious?

Quote: Wizard

It is based on the past.

If I have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.

then I will use The Formula (Equation) below.

I have grounds to believe: success rate on predictions = about 90% (Don't need to know how he does it and does not matter went he placed the money in the boxes).
There for:
choose box-A only (It does not matter why, how & went you choose box-A) = (million dollars about 90% of the time) and (nothing about 10% of the time).
choose both boxes (It does not matter why, how & went you choose both boxes) = (thousand dollars about 90% of the time) and (million+thousand dollars about 10% of the time).

One-time event: Do I choose box A only, or both?

Quote: MrCasinoGames

Regarding the time he placed the money in the boxes befor you make your choose.
eg: hour ago, 24 hours ago, 2 days ago, months ago etc...

OK, I can go with that. I don't care how long ago it was so long as it was in the past and a definite, fixed, action was taken at that time.

Can you explain your perspective on the question I asked above? It might help me move to the next step.

Quote: MathExtremist

I think that's probably the crux of the paradox. Some people are willing to accept the premise, while others refuse to (or have trouble with it). If you don't buy into the premise that some being has supernatural predictive abilities -- and the conclusions that flow from that premise related to free will, etc. -- then the choice between just A or both is not as straightforward.

That is perhaps true. I don't have any problem with the concept of a being having high ability (less than 100% accurate) to predict the future, but I do have a lot of problem with the concept of those predictions controlling what happens in the future.

Quote: MathExtremist

Hmm, I'm not convinced about that. I believe the premise was that you have reason to believe that the NB *has* a 90% accuracy rate, not that he *had* one. Of course, that's going to be part of the interpretation of the setup that influences your view on the result.

Let me ask this: if you accept that the NB does have, and will have, a 90% success rate with predictions -- and all the ramifications of that -- is the answer to the puzzle obvious?

Let's examine the original wording from the Grey Labyrinth:

"A being, who you believe to have superior predictive powers, makes you an offer."

"Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%."

The word I would focus on is "predictive." Predict means to make an educated guess. The "has" in "has a success rate" to me obviously refers to past predictions. If I were to say that Felix Pie has a batting average of 0.255 it would be obvious that it is based on past games, and not a guarantee of future results. I don't think anybody would say that proper English would be to say that he "HAD a batting average of 0.255," unless he was already retired from baseball.

It is hard for me to answer your question. It begs the question of how it is that he will be exactly 90% with me. That implies that omniscience is possible, which is hard for me to swallow.

It seems everyone is analyzing this as if there is a "right" and a "wrong" answer.

Aren't both answers equally correct given different context? For example, if the object is to maximize your possible return, choosing box A appears to be the correct choice. If the object is to walk away with the maximum amount of guaranteed money, then both boxes appears to be the correct choice.

The problem is that the objective is never stated.

Quote: Doc

OK, I can go with that. I don't care how long ago it was so long as it was in the past and a definite, fixed, action was taken at that time.

Can you explain your perspective on the question I asked above? It might help me move to the next step.

At the time that you to make my final decision and choice of box A only or both boxes, is the amount of money in each box already definitely established for this particular event?
Yes, the amount of money in each box already definitely established for this particular event?

My viewpoint is that there is a fixed, unknown, specific amount of money already on the table, in each of the boxes, before I actually have to make my decision, and it doesn't matter to me personally how much money might be on the table the next thousand times some other persons might have the opportunity to make such a choice.

I see your point.
But If (and is a big if) I have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.

then I will use The Formula (Equation) below.

I have grounds to believe: success rate on predictions = about 90% (Don't need to know how he does it and does not matter went he placed the money in the boxes).
There for:
choose box-A only (It does not matter why, how & went you choose box-A) = (million dollars about 90% of the time) and (nothing about 10% of the time).
choose both boxes (It does not matter why, how & went you choose both boxes) = (thousand dollars about 90% of the time) and (million+thousand dollars about 10% of the time).

One-time event: Do I choose box A only, or both?

Quote: Wizard

Let's examine the original wording from the Grey Labyrinth:
"Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%."

You accept that the NB does have (you have grounds to believe), and will have, a 90% success rate with predictions -- and all the ramifications of that.

then the choice should be based on Newcomb Being has a success rate on predictions of about 90% (and not how, why or if).

Quote: scotty81

It seems everyone is analyzing this as if there is a "right" and a "wrong" answer.

Aren't both answers equally correct given different context? For example, if the object is to maximize your possible return, choosing box A appears to be the correct choice. If the object is to walk away with the maximum amount of guaranteed money, then both boxes appears to be the correct choice.

The problem is that the objective is never stated.

I think everyone here is assuming the object is to maximize the possible return. However, there is great debate in which option leads to that end.

Both I choose both

Quote: Wizard

It is hard for me to answer your question. It begs the question of how it is that he will be exactly 90% with me. That implies that omniscience is possible, which is hard for me to swallow.

So if you modify the premise to be "the NB is 100% omniscient, he's just intentionally wrong 10% of the time" then does your answer change?

In other words, if you *can* swallow the premise of omniscience, doesn't the answer become obvious? And if so, doesn't that really mean the problem is all about how you interpret the premise and not what the answer is?

Quote: MrCasinoGames

...then I will use The Formula (Equation) below.

I have grounds to believe: success rate on predictions = about 90% (Don't need to know how he does it and does not matter went he placed the money in the boxes).
There for:
choose box-A only (It does not matter why, how & went you choose box-A) = (million dollars about 90% of the time) and (nothing about 10% of the time).
choose both boxes (It does not matter why, how & went you choose both boxes) = (thousand dollars about 90% of the time) and (million+thousand dollars about 10% of the time).

One-time event: Do I choose box A only, or both?

MrCasinoGames:

OK, here is where I think we disagree. I think you are using the being’s predictive accuracy record to compute an expected value of what he would have placed in each box based on his prediction of what choice I would make.

My view is that whether he predicted correctly or not, he took a specific action with regard to putting money in the boxes. The amount of money available to me is no longer a stochastic amount with an expected value to be calculated with probability theory. It is a predetermined amount. There might only be a total of $1,000 available, or there might be a total of $1,001,000, depending on what he predicted. If the game were played numerous times, the amount would change and the choices would change and different players would receive either of those amounts or $0 or $1,000,000.

But on my one and only chance to make a choice, the amount in each box is already fixed. If he predicted I would choose both boxes, my options are $0 or $1,000. If he predicted I would choose box A only, my options are $1,000,000 or $1,001,000. No matter what he predicted and what action he took, I prefer the option of both boxes. I can’t do any worse by choosing both boxes than by choosing only box A. Whether I wind up with $1,000 or $1,001,000 depends upon what the being predicted my action would be, not upon the fact that I actually eventually chose both boxes.

If he knows me well, his prediction would be that I would choose both boxes, and I would wind up with $1,000. If I were to have a change of heart and choose box A only, I would get nothing. On the other hand, perhaps if he knows you well, he would predict that you would choose box A only. If you did so, you would get $1,000,000, but if you had a change of heart to my "dark" side, you would get $1,001,000. Both of us would come out better if, when the time for our final decision came, we chose both boxes.

Quote: Doc

If he knows me well, his prediction would be that I would choose both boxes, and I would wind up with $1,000. If I were to have a change of heart and choose box A only, I would get nothing. On the other hand, perhaps if he knows you well, he would predict that you would choose box A only. If you did so, you would get $1,000,000, but if you had a change of heart to my "dark" side, you would get $1,001,000. Both of us would come out better if, when the time for our final decision came, we chose both boxes.

See, that's where I disagree. I think the premise is intended to eliminate (with 90% certainty) the two outcomes where the NB predicts you pick both but you only pick one, and where the NB predicts you pick one but you pick both. The logic that says "I can't do any worse" implies that there is some equality in the likelihood of there being 0 vs. 1M in the box, which can't be true if you believe the premise. If you're the sort that believes in the predictive abilities of the NB, you'll act accordingly, pick one box, and get the 1M. If you're the sort that denies the predictive abilities of the NB, you'll act accordingly, pick both boxes, and get $1000. It's as if you are being punished for your lack of faith. :)

Put another way, the Wizard has repeatedly used the phrase "A vs. A+1000". I think that's where you're coming from too, but I dispute the interpretation that "A" is equivalent in both scenarios. With 90% likelihood, the truth is "A=1000000 vs. A=0 + 1000".

Quote: MathExtremist

Put another way, the Wizard has repeatedly used the phrase "A vs. A+1000". I think that's where you're coming from too, but I dispute the interpretation that "A" is equivalent in both scenarios. With 90% likelihood, the truth is "A=1000000 vs. A=0 + 1000".

And here lies our point of departure. What you're saying implies that what you choose now will affect your actions more than 24 hours in the past. That strikes me as absurd.

Where I have a hard time with this is that if both of us actually played this out, chances are you'd get $1,000,000, and I would get $1,000, but I still would say that you chose wrong and I chose right. It sounds a bit absurd too, but that's my story, and I'm sticking to it.

Quote: Wizard

And here lies our point of departure. What you're saying implies that what you choose now will affect your actions more than 24 hours in the past. That strikes me as absurd.

You've said that before, but I think it's inaccurate. I didn't act at all in the past, the NB did. The premise of the problem is that the NB knows what I'm going to pick, and in fact knew what I was going to pick 24 hours ago, and it was *his* actions -- not mine -- that were based on that knowledge.

Okay, here's a better way of looking at it that doesn't involve any sci-fi or suspension of disbelief (in reality, anyway).

You're minding your own business one Sunday afternoon when you're startled by a knock at the door. You open it and three black-suited men barge in, holding guns. One of them identifies himself as Agent Newcomb from NEGA (you Google this later and learn it stands for Non-Existent Government Agency). He sits you down in your kitchen and explains why he and his men are there.

Newcomb begins. "We're doing a top-secret military experiment in tactical prediction, and we've identified you as an ideal candidate to test our latest theories. Here's what's going to happen. You're going to make a choice in the near future that could significantly change your financial picture. You will be shown two boxes. One will either have $0 or $1M in it, the other will have $1000 in it. You can pick either the first box or both boxes, and you'll get to keep whatever is in them. You will be told this story about an advanced being with predictive powers that can guess with 90% accuracy whether you will pick one or both boxes, but here's the catch -- this being only put $1M in the first box if he predicted that you'd only pick the first box. If he predicted you'd pick both, the first box will be empty. But that's all crap because there is no advanced being.

Here's $1M in non-sequential $100 bills. Your task is to choose whether to put the $1M in the first box based on what you think you'll pick tomorrow. After you choose, we're going to inject you with this syringe which will knock you out for 24 hours. You won't remember any of this. We'll be back tomorrow to tell you the story about the being and then give you the choice of one or both boxes. If your choice tomorrow reflects your decision now, you get to keep whatever was in the box(es) that you picked. If not, we'll kill you. Got it?"

"Yes," you reply. "But wait - the 90% prediction rate... what does that mean?"

Newcomb grins. "Yeah, that. We've done this a few hundred times before. Roughly 9 out of 10 people have guessed right." He taps the syringe twice to prime it. "The other 10%, sadly, are no longer with us."

You won't know about the bit about death when you make your choice 24 hours from now, but you know it now.

Do you put the $1M in the box or not?

I think it is a matter that it is preferable to have the being believe and predict that you will choose only box A, but, whatever he predicts, it turns out better to choose both boxes. I don't think you actually have any control over what he predicts, though his knowledge of you and expectations about you will influence the prediction. You certainly don't have any control over his prediction two days after he makes it. All you can control is your choice of box(es) after the money is all in place.

Quote: MathExtremist

You've said that before, but I think it's inaccurate. I didn't act at all in the past, the NB did. The premise of the problem is that the NB knows what I'm going to pick, and in fact knew what I was going to pick 24 hours ago, and it was *his* actions -- not mine -- that were based on that knowledge.

Your use of the words "knows" and "knew" and other posts leads me to think that you think Newcomb has supernatural psychic powers. That is not my reading of the problem. I just see him as a good mentalist. Much like I can easily predict that if a random person calls the flip of a coin, he is more likely to call heads, or be more likely to throw rock in roshambo.

Quote: Doc

MrCasinoGames:
But on my one and only chance to make a choice, the amount in each box is already fixed. If he predicted I would choose both boxes, my options are $0 or $1,000. If he predicted I would choose box A only, my options are $1,000,000 or $1,001,000. No matter what he predicted and what action he took, I prefer the option of both boxes. I can’t do any worse by choosing both boxes than by choosing only box A. Whether I wind up with $1,000 or $1,001,000 depends upon what the being predicted my action would be, not upon the fact that I actually eventually chose both boxes.

I agree with Doc. No one has shown a better solution. Take both boxes.

Quote: Wizard

A being, who you believe to have superior predictive powers, makes you an offer. Before you are two boxes, identical in appearance. Within one box, let us call it 'Box A', there is either one million dollars or nothing. Within the other box, 'Box B', there is definitely one thousand dollars.

The being, whom in deference to tradition we will call the Newcomb Being, will allow you to either take both boxes, or just Box A.

Twenty-four hours ago, the Newcomb being made a prediction about what you would choose. At this point, it placed the money in the boxes. If the Newcomb Being predicted that you would take both boxes, it left nothing for you in Box A and the $1000 in Box B. If the Newcomb Being predicted that you would only take Box A, it would leave the million dollars in it, as well as the thousand dollars in Box B. If the being predicts you will base your choice on a random event (like flipping a coin), it will leave Box A empty.

Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.

Do you choose box A only, or both?

Wording above taken from greylabyrinth.com.

Think of it this way, based on what you accepted.
You accept (you have grounds to believe) that in such matters, the Newcomb Being has a success rate on predictions of about 90% (don't matter what the NB is or what powers he has etc...). Right?

There for you accept (believe):
Eventually choose box A only (It does not matter why or what make you choose box A) = (million dollars 90% of the time) and (nothing 10% of the time). Right?

Eventually choose both boxes (It does not matter why or what make you choose both boxes) = (thousand dollars 90% of the time) and (million+thousand dollars 10% of the time). Right?

If all the about is Right.

Do you choose box A only, or both?

Quote: Wizard

Your use of the words "knows" and "knew" and other posts leads me to think that you think Newcomb has supernatural psychic powers. That is not my reading of the problem. I just see him as a good mentalist. Much like I can easily predict that if a random person calls the flip of a coin, he is more likely to call heads, or be more likely to throw rock in roshambo.

Please see my update/edit of the post to which you replied, where the NB is actually you...

Quote: MrCasinoGames

Think of it this way, based on what you accepted.
You accept (you have grounds to believe) that in such matters, the Newcomb Being has a success rate on predictions of about 90% (don't need to know what supernatural psychic powers he have etc...). Right?

There for you accept (believe):
Eventually choose box A only (It does not matter why or what make you choose box A) = (million dollars 90% of the time) and (nothing 10% of the time). Right?

Eventually choose both boxes (It does not matter why or what make you choose both boxes) = (thousand dollars 90% of the time) and (million+thousand dollars 10% of the time). Right?

If all the about is Right.

Do you choose box A only, or both?

I am willing to accept the concept of a being that is about 90% accurate in his (perhaps numerous) predictions of the future.

At least at this point, I don't consider it even meaningful to say that he is 90% accurate in his one prediction about my one chance to choose the box(es). He either predicts correctly or incorrectly on that specific event. He doesn't get it right 90% of the time and wrong 10% of the time. There is only one time.

Thus, I answer "Yes" to your first "Right?" and "No" to the other two. And I still choose both boxes. It will turn out $1,000 better for me than if I just choose box A.

Quote: Doc

I am willing to accept the concept of a being that is about 90% accurate in his (perhaps numerous) predictions of the future.

At least at this point, I don't consider it even meaningful to say that he is 90% accurate in his one prediction about my one chance to choose the box(es). He either predicts correctly or incorrectly on that specific event. He doesn't get it right 90% of the time and wrong 10% of the time. There is only one time.

Thus, I answer "Yes" to your first "Right?" and "No" to the other two. And I still choose both boxes. It will turn out $1,000 better for me than if I just choose box A.

If my Formula (Equation) below is right, I will choose box A only, otherwise I will have to rethink about it.

The Newcomb Being has a success rate on predictions of about 90% (don't matter what the NB is or what powers he has etc...).

There for:
Eventually choose box A only (It does not matter why or what make you choose box A) = (million dollars 90% of the time) and (nothing 10% of the time).

Eventually choose both boxes (It does not matter why or what make you choose both boxes) = (thousand dollars 90% of the time) and (million+thousand dollars 10% of the time).

To summarize my disagreements with your formula:

(1) I believe you are doing the equivalent of calculating an expected value of a number that is not a random variable but instead a specific amount of money predetermined by the being. I don't consider the calculation to be meaningful.

(2) In calculating this expected value, you are treating the 90% and 10% figures as if the being will be making numerous predictions about numerous choices that you will be making when, in fact, there will only be one relevant prediction and one relevant choice of box(es).

Of course, if the being is aware of your line of thinking, he will likely predict that you will choose only box A, so he will place a lot more money in the box than if I were given a chance at the choice. :-) The being's prediction two days in advance is a much more important event than the actual process of choosing a box or boxes. The prediction makes $1,000,000 difference; the choice only makes $1,000 difference.

ME, I just read your story, but it doesn't change my answer. In that situation I would predict that I would choose both boxes.

Maybe it is a bad comparison, but this strikes me a bit like Pascal's Wager. With both you have to accept a ridiculous belief in exchange for a huge reward if its true. Sorry, but I can't accept that A>A+1000, and if that costs me $1,000,000, then so be it.

Quote: Wizard

ME, I just read your story, but it doesn't change my answer. In that situation I would predict that I would choose both boxes.

In that case, you would have put $0 in the box before being knocked out. That's okay - at least you're still alive with the $1000 to show for it. :)

Quote:

Maybe it is a bad comparison, but this strikes me a bit like Pascal's Wager. With both you have to accept a ridiculous belief in exchange for a huge reward if its true. Sorry, but I can't accept that A>A+1000, and if that costs me $1,000,000, then so be it.

No, that's fine -- but if you cannot accept the premise of the problem then there's really no point in debating the answer. At least with the Newcomb problem (as originally stated), you can verify the answer before you die. Pascal's Wager is untestable.

Quote: MathExtremist

No, that's fine -- but if you cannot accept the premise of the problem then there's really no point in debating the answer. At least with the Newcomb problem (as originally stated), you can verify the answer before you die. Pascal's Wager is untestable.

I can accept the premise of the problem, just as I can accept the premise of the Newlywed Game. It is not far fetched to suggest someone can fairly accurately predict what others will do. Have you seen The Mentalist show here in Vegas? Either that guy is a con using audience stooges or he has a remarkable skill.

Please don't take this as a personal insult (ahem), but I think what we have here is a situation where those who make the correct decision get punished for it.

Quote: Wizard

Have you seen The Mentalist show here in Vegas? Either that guy is a con using audience stooges or he has a remarkable skill.

The Amazing Randi is still around and is still waiting to give away the million dollar prize to anybody who can prove their abilities. He's not worried.

If you put a different slant on it then (maybe) it shows how the math' is fallable, to some degree, in a problem like this.

For example, imagine that Box A contains $1,000 or $0 (instead of the $1m) and Box B contains the $1,000 still. I'm sure that everyone would go with both boxes as this would guarantee them $1,000 or $2,000. Just picking Box A wins them just $900 (on average) and boils down to either $0 or $1,000.

So, using a 'mathematical only' factor, let's assume that Box A now contains $1,250 and Box B still has $1,000. If you pick A then you have 90% of $1,250 = $1,125 and if you pick A + B then you have $1,000 + 10% of $1,250 = $1,125. So it would seem that 'mathematically' it makes no difference ... BUT ... I wonder how many would sway towards A+B as almost 90% of their possible win is locked up as a sure thing ???

So, possibly, as you increase the value of Box A then more people will be swayed towards picking just Box A - however, the Newcomb prediction rate remains the same - this would form some sort of contradiction in itself anyway.

The Newcomb will remain consistent regardless of whether there is $1,000 or $1,000,000 in box A but people will change their minds as the value of Box A increases despite the fact that it will not alter the prediction. The question is whether the amount in Box A should mathematically change a player's choice or whether the added $1,000 in Box B should point to that choice regardless (as The Newcomb will remain consistent then why shouldn't we ?).

Therefore, those who pick both boxes remain consistent (along with The Newcomb) and those that would change to Box A only are working on a mathematical overall result. Not sure which is quite correct as it's a bit of a paradox and arguements can be made for both sides - I'm still tending to lean to my first choice which is to stay with the 2 boxes.

Maybe the above will shed more light on the problem either way - not sure :-)

Quote: Doc

To summarize my disagreements with your formula:

(2) In calculating this expected value, you are treating the 90% and 10% figures as if the being will be making numerous predictions about numerous choices that you will be making when, in fact, there will only be one relevant prediction and one relevant choice of box(es).

Of course, if the being is aware of your line of thinking, he will likely predict that you will choose only box A, so he will place a lot more money in the box than if I were given a chance at the choice. :-) The being's prediction two days in advance is a much more important event than the actual process of choosing a box or boxes. The prediction makes $1,000,000 difference; the choice only makes $1,000 difference.

As I say:
If my Formula (Equation) is right, I will choose box A only, otherwise I will have to rethink about it.

By the way 90% of a (1-time event, 2-time event, 90-time event, 101-time event etc...) it is still 90%. Yes or No?
put it this way 100% of any-number-time event it is still 100%. Yes or No?

Don't for get,
the examine the original wording from the Grey Labyrinth:
"Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%."

The fact that you have accept that the NB does have (you have grounds to believe), and will have, a 90% success rate with predictions -- and all the ramifications of that. (then don't ask how the NB can have a success rate on predictions of about 90%, what kind of power he has, aware of your line of thinking, is he god? etc... this Questions should have been done befor you accept the 90% success rate) Yes or No?

If it is yes, Then your should make you choice based on the 90% (You accepted), (and not who the NB is, his power or were/how he get the power from ect...).

Quote: Wizard

Please don't take this as a personal insult (ahem), but I think what we have here is a situation where those who make the correct decision get punished for it.

Me? Never (and especially not here -- you're one of maybe 3-4 readers who even know me). Besides, in this particular case, I think it's reasonable to assess the correctness of the decision by the results. If the premise holds and there really is not much randomness involved, then 9 times out of 10 I'll end up with a million bucks while you'll end up with a thousand. I don't see mine as being an incorrect decision, not if money is the metric.

Quote: MathExtremist

Besides, in this particular case, I think it's reasonable to assess the correctness of the decision by the results. If the premise holds and there really is not much randomness involved, then 9 times out of 10 I'll end up with a million bucks while you'll end up with a thousand. I don't see mine as being an incorrect decision, not if money is the metric.

That is a valid point that if we use money as the metric of success, then you would probably be right. However, I would like to think that if producing a logical answer is the goal, then I would be right. Thanks for the personal insult immunity, by the way ;-).

As an aside, I'm surprised nobody suggested randomizing your decision. If I had a coin to flip, that is what I would use to determine my decision. However, I think for purposes of the exercise, we can rule out that option.

Quote: EvenBob

Sounds supernatural to me.

Then you'd love the show. And be more skeptical.

Quote: Wizard

As an aside, I'm surprised nobody suggested randomizing your decision. If I had a coin to flip, that is what I would use to determine my decision. However, I think for purposes of the exercise, we can rule out that option.

That was explicitly ruled out in the premise, wasn't it? If you use a randomizing element, you only get $1000.

Quote: MathExtremist

That was explicitly ruled out in the premise, wasn't it? If you use a randomizing element, you only get $1000.

You're right, I forgot about that rule.

Quote: MrCasinoGames

As I say:
If my Formula (Equation) is right, I will choose box A only, otherwise I will have to rethink about it.

By the way 90% of a (1-time event, 2-time event, 90-time event, 101-time event etc...) it is still 90%. Yes or No?
put it this way 100% of any-number-time event it is still 100%. Yes or No?

For 90%, my answer has to still be "No." What is even the meaning of being correct 90% of the time in a single prediction? You either get it right or get it wrong; you can't be 90% right.

If we allowed the possibility of 100% accuracy, then yes, you could get the prediction 100% correct, but we have already shown that an absolute certainty of 100% accurate predictions leads to the elimination of free will and the absurdity of even analyzing what you should do, so the 100% figure is irrelevant.

Quote: MrCasinoGames

You accept that the NB does have (you have grounds to believe), and will have, a 90% success rate with predictions -- and all the ramifications of that. (and not how the NB can have a success rate on predictions of about 90%, what kind of power he has, aware of your line of thinking, is he god? etc... this Questions should have been done befor you accept the 90% success rate) Yes or No?

If it is yes, Then your should make you choice based on the 90% (You accepted), (and not who the NB is, his power or were/how he get the power from ect...).

I interpret the 90% accuracy as applying to numerous predictions. I don't really care how he tends to be so good predicting the future. Maybe he just makes predictions in situations where he can "read" people well (see the recent comment by the Wizard). If he reads me well, I would wind up with $1,000. If by stating your case as above quite firmly and frequently you were able to convince the being to predict that you will go with just box A, then you would wind up with $999,000 more money than I would, but you would be an additional $1,000 better off if you went against your analysis and took both boxes. Both of us would be better off by taking both boxes than by taking just box A.

Posts about the Mentalist show have been moved to The Mentalist Live.

Quote: Doc

For 90%, my answer has to still be "No." What is even the meaning of being correct 90% of the time in a single prediction? You either get it right or get it wrong; you can't be 90% right.

If we allowed the possibility of 100% accuracy, then yes, you could get the prediction 100% correct, but we have already shown that an absolute certainty of 100% accurate predictions leads to the elimination of free will and the absurdity of even analyzing what you should do, so the 100% figure is irrelevant.

I interpret the 90% accuracy as applying to numerous predictions. I don't really care how he tends to be so good predicting the future. Maybe he just makes predictions in situations where he can "read" people well (see the recent comment by the Wizard). If he reads me well, I would wind up with $1,000. If by stating your case as above quite firmly and frequently you were able to convince the being to predict that you will go with just box A, then you would wind up with $999,000 more money than I would, but you would be an additional $1,000 better off if you went against your analysis and took both boxes. Both of us would be better off by taking both boxes than by taking just box A.

Based on what the examine the original wording from the Grey Labyrinth:
"Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%."

The fact that I have accept that the NB does have, and will have, a 90% success rate with predictions -- and all the ramifications of that. (don't need to know how the NB can have a success rate on predictions of about 90%, what kind of power he has, aware of your line of thinking, is he god? etc... this Questions should have been done befor I accept the 90% success rate).

There for I accept (believe):
It does not matter why or what make me choose box A (Eventually choose box A only) = (90% of the time million dollars) and (10% of the time nothing).

It does not matter why or what make me choose both boxes (Eventually choose both boxes) = (90% of the time thousand dollars) and (10% of the time million+thousand dollars).

I will choose box A only.

Based on what the examine the original wording from the Grey Labyrinth:
"Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90% (Eventually choose)."

The fact that I have accept that the NB does have, and will have, a 90% success rate with predictions (My Eventually choose)."-- and all the ramifications of that.
(don't need to know how the NB can have a success rate on predictions of about 90%, what kind of power he has, aware of my line of thinking, is he god? etc... this Kind of Questions should have been ask, befor I accept the 90% success rate).

There for I accept (believe):
For what every reason, If I Eventually choose box A only then (90% of the time I get million dollars) and (10% of the time I get nothing).

For what every resion, If I Eventually choose both boxes = (90% of the time I get thousand dollars) and (10% of the time I get million+thousand dollars).

I will choose box A only.

The Wizard requested I give a story using a Newcomb Being and something did come to mind. I am about half way through. Figure it will be up by end of week.

For me the problem centers around the difference between the million and the $1000. There only has to be a .1% (divided by 90% to be exact) chance of the prediction being correct to be even money on the 2 choices. For me box A is a lock at those odds. Change it to $100,000 in box B and the choice is much more difficult.

Quote: Wizard

That is a valid point that if we use money as the metric of success, then you would probably be right. However, I would like to think that if producing a logical answer is the goal, then I would be right.

Logical, or I think "optimal", is all relative to the rules of the game. What if I turned the situation around and phrased the problem as:

Government agents come to your door. They tell you that they visited you yesterday, but they also tell you that after yesterday's visit they drugged you and you have no recollection of their visit. The agents make you an offer. Before you are two boxes, identical in appearance. Within one box, let us call it 'Box A', there is either one million dollars or nothing. Within the other box, 'Box B', there is definitely one thousand dollars.

The agents will allow you to either take both boxes, or just Box A.

Twenty-four hours ago, when the agents visited you the first time, they told you about today's visit, and you made a prediction about what you would choose. At that time, they placed the money in the boxes. If you predicted that you would take both boxes, they left nothing for you in Box A and the $1000 in Box B. If you predicted that you would only take Box A, the agents would leave the million dollars in it, as well as the thousand dollars in Box B. If you predicted you would base your choice on a random event (like flipping a coin), the agents will leave Box A empty.

Edit:
I forgot to add this part -- on your first meeting, the agents told you that if you guess wrong during the second meeting, they'll kill you. They do *not* tell you about this when they see you the second time, but you use knowledge of this threat to make your prediction the first time.

As above, you don't recall your meeting (or the threat), so you have only your understanding of yourself upon which to rely. Do you choose box A only, or both?

If it is what i think you mean.
This is what I will do.

Quote: MathExtremist

Twenty-four hours ago (the first visited), when the agents visited you the first time, they told you about today's visit, and you made a prediction about what you would choose. At that time, they placed the money in the boxes. If you predicted that you would take both boxes, they left nothing for you in Box A and the $1000 in Box B. If you predicted that you would only take Box A, the agents would leave the million dollars in it, as well as the thousand dollars in Box B. If you predicted you would base your choice on a random event (like flipping a coin), the agents will leave Box A empty.

At this time (the first visited), I will predicted that I would only take Box A, so the agents would leave the million dollars in it, as well as the thousand dollars in Box B.

Quote: MathExtremist

Twenty-four hours later (the second visited), you don't recall your meeting, so you have only your understanding of yourself upon which to rely. Do you choose box A only, or both?

At this time (Twenty-four hours later, the second visited)
choose box A only = million dollars
choose both boxes = million dollars + $1000

I will choose both boxes.

Quote: MathExtremist

Logical, or I think "optimal", is all relative to the rules of the game. What if I turned the situation around and phrased the problem as:

Government agents come to your door. They tell you that they visited you yesterday, but they also tell you that after yesterday's visit they drugged you and you have no recollection of their visit. The agents make you an offer. Before you are two boxes, identical in appearance. Within one box, let us call it 'Box A', there is either one million dollars or nothing. Within the other box, 'Box B', there is definitely one thousand dollars.

The agents will allow you to either take both boxes, or just Box A.

Twenty-four hours ago, when the agents visited you the first time, they told you about today's visit, and you made a prediction about what you would choose. At that time, they placed the money in the boxes. If you predicted that you would take both boxes, they left nothing for you in Box A and the $1000 in Box B. If you predicted that you would only take Box A, the agents would leave the million dollars in it, as well as the thousand dollars in Box B. If you predicted you would base your choice on a random event (like flipping a coin), the agents will leave Box A empty.

As above, you don't recall your meeting, so you have only your understanding of yourself upon which to rely. Do you choose box A only, or both?

If you phrased the problem as above.
I don't need to know what I predicted Twenty-four hours ago.

All I Need to know is:
If I choose box A only = (I get million dollars or I get nothing).
If I choose both boxes = (I get million dollars or I get nothing) + (I get thousand dollars).
Therefor I choose both boxes.
(In this case the predictions of my (Eventually choose) is not based on about 90%).

But if it is Based on what the examine the original wording from the Grey Labyrinth:
"Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90% (Eventually choose)."
The fact that I have accept that the NB does have, and will have, a 90% success rate with predictions (My Eventually choose)."-- and all the ramifications of that.
(don't need to know how the NB can have a success rate on predictions of about 90%, what kind of power he has, aware of my line of thinking, is he god? etc... this Kind of Questions should have been ask, befor I accept the 90% success rate).

I choose box A only.

A similar scientific study was performed years ago.

Details here:

http://www.gametheory.net/news/items/095.html