# Are you a One-Boxer or a Two-Boxer? **URL:** \ **Category:** Great Debates\ **Created:** [August 15, 2013, 5:34am UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287 "2013-08-15T05:34:09Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 6:40pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/61 "2013-08-15T18:40:48Z")
To be even more clear: I am not trying to game the system to ensure I get $1,001,000. I am saying “There is a point, after the prediction but prior to me looking in the boxes, where whether or not I get the $1,000,000 is a settled question. At that point, all I can do is decide if I want an extra $1000 on top of whatever is in box B.” ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 6:43pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/62 "2013-08-15T18:43:39Z")
> [@Chronos](#): > > Henry having more men would make it more likely for him to win the battle, and you picking to open only the hidden box will make it more likely for the hidden box to contain the million. The latter is only true before the prediction has been made. After the prediction of whether you will pick box B is made, whether you get the million is locked in. You can’t change it with your subsequent actions. In contrast, there is never a point where the outcome of the battle is locked in, prior to fighting the battle. ---
**Author:** ![Cheshire\_Human](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Cheshire\_Human](https://boards.straightdope.com/u/Cheshire_Human)\ **Post date:** [August 15, 2013, 6:48pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/63 "2013-08-15T18:48:24Z")
> [@tim314](#): > > Either way, once the prediction is locked in, you should choose A & B. Without denying my assumptions above, how do you get around this? The Predictor predicted that you would change your mind, and locked in that prediction, or he’s not virtually infallible. You’ll only ever get 1000, never 1001000. Any other result violates the virtually infallible part of the hypothetical. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 6:56pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/64 "2013-08-15T18:56:20Z")
> [@Cheshire\_Human](#): > > The Predictor predicted that you would change your mind, and locked in that prediction, or he’s not virtually infallible. You’ll only ever get 1000, never 1001000. Any other result violates the virtually infallible part of the hypothetical. If he predicted that I’d change my mind, then it’s a good thing I did, because otherwise I’d get $0. If he didn’t predict that I’d change my mind, it’s a good thing I did, because I get $1,001,000 instead of $1,000,000. Once the prediction is made, I should stop letting that influence my decision, because A & B is always better. Here’s an equivalent restatement of the problem: The predictor says “I have put $1000 in box A. I may or may not have put $1,000,000 in box B, based on X”. Regardless of X, you can know for sure that _at that point_ there is more money in boxes A and B together than box B alone. You are being misled by the claim of “a virtually infallible prediction” to believe that the contents of B can _change_. They can’t change at that point, and X + $1000 is always greater than X. ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [August 15, 2013, 6:58pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/65 "2013-08-15T18:58:14Z")
Not if X is Zero, which is what it will be if you choose both boxes. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 7:02pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/66 "2013-08-15T19:02:02Z")
> [@Inner\_Stickler](#): > > Not if X is Zero, which is what it will be if you choose both boxes. In my statement above, X is a placeholder for the _reasoning_ the predictor uses. In the original problem, X = “a vitually infallible prediction of what you will choose…” My point is, it doesn’t matter. At some point, the boxes contain whatever they’re going to contain. It’s impossible at that point for one box to contain more than that box plus another box. ---
**Author:** ![Malthus](https://avatars.discourse-cdn.com/v4/letter/m/85f322/32.png) [@Malthus](https://boards.straightdope.com/u/Malthus)\ **Post date:** [August 15, 2013, 7:02pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/67 "2013-08-15T19:02:13Z")
> [@Steve\_MB](#): > > I don’t understand how this is controversial, either. If you take both boxes, you get $1000 more than if you take just the one box. It’s too late for your decision to take both boxes to change the contents of the opaque box, so you can’t possibly lose anything by doing so. > > Of course. If the odds are 10-1 against there being a million dollars in the other box, that’s all the more reason to take the sure $1000, since the decision to do so doesn’t _change_ those odds (the boxes are already set up). It sounds like you are betting against the hypothetical - that is, that you can outsmart the Predictor. ---
**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\ **Post date:** [August 15, 2013, 7:02pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/68 "2013-08-15T19:02:41Z")
> [@inner stickler](#): > > not if x is zero, which is what it will be if you choose both boxes. 0=0 0+1000=1000 1000\>0 ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [August 15, 2013, 7:04pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/69 "2013-08-15T19:04:38Z")
> [@tim314](#): > > To be even more clear: I am not trying to game the system to ensure I get $1,001,000. I am saying “There is a point, after the prediction but prior to me looking in the boxes, where whether or not I get the $1,000,000 is a settled question. At that point, all I can do is decide if I want an extra $1000 on top of whatever is in box B.” However you posit the predictor getting the success rate that it has (by checking your phone metadata and e-mail traffic, contacting your family, whatever), the _fact remains that it has a success rate of 100-epsilon percent_. So, whatever the non-causality-violating method it has, when I show up it thinks “That **RitterSport** seems like a nice simple guy. He will just choose B.” When you show up, it thinks “That **tim314** is too clever by half. He looks like the type to think B is the right choice, then waffle a bunch of times, finally choosing A+B.” ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 7:05pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/70 "2013-08-15T19:05:13Z")
Basically, I think the 1-boxers are implicitly denying causality even if they think they aren’t. You’re saying “You shouldn’t open box A (even after both boxes are filled with whatever they’re going to be filled with” because if you do, then box B will be empty." If you believe the future can’t affect the past, then _once the boxes are filled_ you shouldn’t worry about the impact your choice has on the contents of box B, because it can have no impact. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [August 15, 2013, 7:07pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/71 "2013-08-15T19:07:15Z")
> [@tim314](#): > > Regardless of whether or not the predictor is nearly infallible, at some point he will have made a prediction. > > We can split this prediction into two cases: > > 1. He picked A & B. > 2. He picked B. > > I am asking anyone to present an argument why, at that point, in either of those cases, I shouldn’t switch to A & B. > > If you are saying that a nearly infallible predictor precludes me from switching to A & B in case 2, then it seems to me that you are denying that I have free will. If you’re the kind of person who thinks this way, you’ll end up with $1K. Go ahead and think that way, though! It makes the game more fun for the rest of us. > [@Mr\_Shine](#): > > Another two-boxer here. I can’t explain it better than **tim314** ’s posts. The question boils down to "Would you like $X or $X+1000? I can’t tell you what X is but I can tell you that X is a fixed amount, **and cannot _now_ be changed."** To such a question the only appropriate response is that you would like the X+1000 See the above. You’re dead right in your logic, but your logic nets you $1K. I walk out with $M. Enjoy! > [@Cheshire\_Human](#): > > It seems to me that the reason 2 boxers are 2 boxers is because they are rejecting the premise of a virtually infallible predictor. Bingo. > [@Inner\_Stickler](#): > > Not if X is Zero, which is what it will be if you choose both boxes. Bingo. Let’s look at the last 10 contestants, and see how they did! 5 were the type who figured X + 1000 \>= 1000 and picked two boxes. How much did they leave with? $1K each 5 were the type who figured that picking B only would net them $1M. They all walked out with $1M. Which category do you want to be in? There are no other categories, based on the premises. So, there are the guys who get $1M and the guys who don’t. I know which I’d choose. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 7:10pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/72 "2013-08-15T19:10:03Z")
> [@RitterSport](#): > > However you posit the predictor getting the success rate that it has (by checking your phone metadata and e-mail traffic, contacting your family, whatever), the _fact remains that it has a success rate of 100-epsilon percent_. > > So, whatever the non-causality-violating method it has, when I show up it thinks “That **RitterSport** seems like a nice simple guy. He will just choose B.” > > When you show up, it thinks “That **tim314** is too clever by half. He looks like the type to think B is the right choice, then waffle a bunch of times, finally choosing A+B.” OK, fine. I accept that as a stipulation of the problem. I am saying, there is a point where he has made that decision, and filled the boxes. At that point, the $1,000,000 is off the table for me. So I should clearly also open box A, and get the $1000. As for you, the $1,000,000 is in box B. So at that point, if you open both, you get $1,001,000, which is even better. You are either saying: 1. **RitterSport** can’t choose to open both at that point. This denies your free will. 2. If **RitterSport** chooses to open both at that point, the $1,000,000 ceases to be there. That denies causality. ---
**Author:** ![Malthus](https://avatars.discourse-cdn.com/v4/letter/m/85f322/32.png) [@Malthus](https://boards.straightdope.com/u/Malthus)\ **Post date:** [August 15, 2013, 7:10pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/73 "2013-08-15T19:10:59Z")
> [@tim314](#): > > In my statement above, X is a placeholder for the _reasoning_ the predictor uses. In the original problem, X = “a vitually infallible prediction of what you will choose…” > > My point is, it doesn’t matter. At some point, the boxes contain whatever they’re going to contain. It’s impossible at that point for one box to contain more than that box plus another box. If you reason this through, your point is fighting the hypothetical. Of course the hypothetical is absurd, but what the hey. Of course the Predictor can’t change what’s in the boxes, but we know he uses some magic or juju to be very nearly infallible in his, her or its predictions as to what you will do. If you are the kind of person whio reasons as you do, the Predictor will know of it and all you can ever get is $1000. Put it this way: if you pick only box B and it is empty, the Predictor is fallible. ---
**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\ **Post date:** [August 15, 2013, 7:11pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/74 "2013-08-15T19:11:00Z")
> [@Malthus](#): > > It sounds like you are betting against the hypothetical - that is, that you can outsmart the Predictor. There are 2 ways of looking at it: 1. You \*\*can’t ever ever ever \*\* outsmart the predictor. This is identical to a complete lack of free will, and yes in this case you should take only box B. But have you really decided anything? 2. Nobody has ever outsmarted the predictor. Yoy personally believe he has a chance \<100%, possibly as high as 99.999999999% of “reading” you. This defaults to the assumption “there are now 2 boxes here, I’m taking box B regardless, I cannot now change the contents of box B, would I like an extra grand?” ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [August 15, 2013, 7:12pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/75 "2013-08-15T19:12:35Z")
If he opens both, then there was never a million in it in the first place. ---
**Author:** ![Malthus](https://avatars.discourse-cdn.com/v4/letter/m/85f322/32.png) [@Malthus](https://boards.straightdope.com/u/Malthus)\ **Post date:** [August 15, 2013, 7:14pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/76 "2013-08-15T19:14:17Z")
> [@tim314](#): > > OK, fine. I accept that as a stipulation of the problem. I am saying, there is a point where he has made that decision, and filled the boxes. > > At that point, the $1,000,000 is off the table for me. So I should clearly also open box A, and get the $1000. > > As for you, the $1,000,000 is in box B. So at that point, if you open both, you get $1,001,000, which is even better. > > You are either saying: > > 1. **RitterSport** can’t choose to open both at that point. This denies your free will. > 2. If **RitterSport** chooses to open both at that point, the $1,000,000 ceases to be there. That denies causality. All you are really saying is that the Predictor can’t really be the Predictor. Which is true, but we are taking it as a fact that it is. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 7:19pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/77 "2013-08-15T19:19:38Z")
> [@Inner\_Stickler](#): > > If he opens both, then there was never a million in it in the first place. At some point, the million is there, or it’s not. Does he still have the power to make a choice at that point? If so, the choice can’t make the million go away. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [August 15, 2013, 7:21pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/78 "2013-08-15T19:21:52Z")
> [@Great\_Antibob](#): > > Then, you’re back to a coin flip situation, and in the absolute worst case, it doesn’t matter which strategy you use. So single box in that case, too. Loved your math, thanks! Made perfect sense. But I didn’t follow this last bit. If the “predictor” uses a coin flip, I’m picking both boxes, regardless of the (nonnegative) prize values. Am I wrong? ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [August 15, 2013, 7:22pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/79 "2013-08-15T19:22:43Z")
> [@Malthus](#): > > All you are really saying is that the Predictor can’t really be the Predictor. Which is true, but we are taking it as a fact that it is. I’ve never said “The predictor will be wrong”. At some point, the predictor has made his choice. At that point, the better choice for me is to take both boxes. You can say, “Well, you won’t ever make that choice if the $1,000,000 is in Box B.” But that’s a statement of what I _will_ do, not what I _should_ do. If the $1,000,000 is in box B, I still _should_ take both boxes. If the predictor is infallible, then for some reason I won’t take both boxes. But that’s the wrong choice. If the $1,000,000 is not in box B, I should also take both boxes. And if the predictor is infallible, then I will. ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [August 15, 2013, 7:23pm UTC](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287/80 "2013-08-15T19:23:11Z")
> [@Mr\_Shine](#): > > 1. You \*\*can’t ever ever ever \*\* outsmart the predictor. This is identical to a complete lack of free will, and yes in this case you should take only box B. But have you really decided anything? As much as anybody does in this universe. Free will may not exist anyway. > [@Mr\_Shine](#): > > This defaults to the assumption “there are now 2 boxes here, I’m taking box B regardless, I cannot now change the contents of box B, would I like an extra grand?” Not really. By taking that extra box, you are potentially going from $1M to $1000 only. You are banking on the 0.0000000…1% chance the predictor is wrong and still leaves $1M in box B. There are four cases here: Case 1: Predictor correct, you choose B - Net $1M Case 2: Predictor correct, you choose A+B - Net $1000 Case 3: Predictor incorrect, you choose B - Net $0 Case 4: Predictor incorrect, you choose A+B - Net $1,001,000 You are focusing only on cases 3 and 4. The other side on cases 1 and 2. But in trying to argue for the “extra” $1000, you are now comparing cases 1 and 4. And that’s the crux of the paradox. You have to make some assumption about the predictor. If you don’t like the idea of an infallible predictor, you are limited to cases 3 and 4. If you imagine such a predictor exists, you are limited to cases 1 and 2. The arguments that are the most fallacious in this thread are the ones trying to mix the cases, e.g. comparing case 1 to 4. [Previous page](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287.md?page=3) [Next page](https://boards.straightdope.com/t/are-you-a-one-boxer-or-a-two-boxer/666287.md?page=5)