Talk:WikiJournal of Science/A card game for Bell's theorem and its loopholes
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Vandegrift, G; Stomel, J.
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 Wright State University Lake Campus, Celina, Ohio, 45822
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DOI: 10.15347/wjs/2018.005
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Vandegrift, G; Stomel, J (2018). "A card game for Bell's theorem and its loopholes". WikiJournal of Science 1 (1): 5. doi:10.15347/wjs/2018.005. ISSN 24706345. https://en.wikiversity.org/wiki/WikiJournal_of_Science/A_card_game_for_Bell%27s_theorem_and_its_loopholes.
License: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction, provided the original author and source are credited.
Author comments
Why I am placing this in draft space
 The primary reason is that Josh and I want sole credit for creating this resource. Others will be able to edit this after it has been accepted by the WikiJournal of Science. (Note that the license permits anybody to copy and develop a parallel page on any wiki).
 At the moment (and subject to change) my opinion is that virtually everything on Wikiversity should eventually be in Draft space. This is a radical idea, but none of the WMF wikis have peerreviewed content. Perhaps the WikiJournals will evolve to fill this need. Perhaps Wikipedia will even create a peer reviewed namespace (see this discussion for yet another example of why the WMF needs something that supports peer review . See also ♠ for where peer reviewed documents might be situated on Wikiversity.)
 Finally, some people might whine when their articles are moved to draft space. There is nothing wrong with draft space. I have this article in draft space right now and it causes me no pain, concern, or discomfort.Guy vandegrift (discuss • contribs) 20:33, 17 February 2018 (UTC)
 FYI, according to Wiktionary, "whine" when referring to "a complaint or criticism" is considered "derogatory". Marshallsumter (discuss • contribs) 16:25, 12 March 2018 (UTC)
 Point well taken. I regret the uncivil tone of my comment. My only excuse is that since nobody has "whined" (or complained or objected) about being in draft space, nobody is the target of that remark. On the same topic, there are three plausible approaches to this problem: One is to highlight the best efforts (e.g. with WikiJournals or guilds); another is to place "drafts" in draftspace. Finally, the third plausible approach is to ignore the problem. I will never interfere with anybody's effort to implement any of these solutions. But, I have no idea which one is the best.Guy vandegrift (discuss • contribs) 18:40, 12 March 2018 (UTC)
Plagiarism check
Pass. WMF copyvio tool using TurnItIn. Trivial hits to the version hosted on a private wiki (link) and author's CV were found. Otherwise no plagiarism was detected. T.Shafee(Evo﹠Evo)^{talk} 11:48, 22 February 2018 (UTC)
A reference that needs to be added
Bojić, Alan. "A new quantum game based on CHSH game." Journal of Information and Organizational Sciences 37.1 (2013): 1522. https://bib.irb.hr/datoteka/868224.02.pdf
 I just found out about this. In many ways a better paper, especially for the more advanced reader. The card game still has advantages though.Guy vandegrift (discuss • contribs) 21:36, 13 March 2018 (UTC)
First peer review
Review by
Franck Laloë , Centre national de la recherche scientifique (CNRS)
This review was submitted on , and refers to this previous version of the article
As the text itself makes it clear, this is not a research article, since it contains nothing really new. It is rather a pedagogical contribution proposing a method to explain the Bell theorem to students, nicely illustrated with figures and drawings. I have never taught this part of quantum mechanics, and I cannot judge if this approach is the best to treat the subject. Personally, I would think that the traditional (more algebraic method) is not more difficult to follow, maybe even easier. Personally I did not find that easy to understand all the rules of this card game, and all these diagrams in the 13 pages, but this is just my personal taste.
In the field of fundamental quantum mechanics, one can enter endless discussions on the way to phrase ideas. So, I do not want to bother the authors with my own personal views, but I nevertheless with to express some disagreements.
The sentence "To some experts, a loophole is a constraint on any hidden variable theory that might replace quantum mechanics" is, to me, a very bad introduction to the notion of "loophole". A loophole is a logical possibility to evade the Bell inequalities by rejecting one of the (explicit or implicit) assumptions of the EPR paper and its continuation by Bell. It has nothing to do with hidden variable theory specifically, since it actually does not refer to any specific sort of theory. I would strongly recommend not to introduce the ideas of loopholes to students in this way.
Figure 1 is confusing for someone who is familiar with quantum optics. The text says that is shows two entangled photons but, with photons, it is impossible to have devices filtering three polarizations at 120 degrees as shown in the figure. The space of states of photon polarizations is 2dimensional, and the filters shown in the figure will necessarily leak since they have three outputs.
Nicolas Gisin, in his recent book "Quantum chance", discusses something similar, which he calls "Bell's game" I believe.The authors might wish to include a reference to this book.
Please note that the first and last lines of several pages are missing in the pdf file you sent me, for some technical reason.
My conclusion is that, if this articles comes as a complement of another more traditional introduction to the Bell inequalities, it may probably be useful to some teachers. I would nevertheless not recommend it as the only introduction to the inequalities, but maybe just as a nice illustration of the Bell theorem once the students understand its logic.
Second peer review
The following review was transferred from the American Journal of Physics with permission from the reviewer. It refers to the version of the manuscript as submitted to the previous journal and so may not take account of changes that have already been made between submissions. T.Shafee(Evo﹠Evo)^{talk} 22:47, 22 March 2018 (UTC)
Review by
anonymous peer reviewer , Physics lecturer
This review was submitted on , and refers to this previous version of the article
I have read the manuscript "A card game for Bell's theorem and its loopholes". The goal of the paper is to present a simple card game from which students can learn the impossibility of achieving the sorts of correlations that are forbidden according to Bell's theorem... and perhaps also understand, by figuring out how to "cheat" to win the game, several loopholes associated with the theorem and/or the associated experiments. I enjoyed reading the paper and applaud the general concept of trying to convey Bell's theorem to students in the form of a simple game. But I do have several reservations about the paper.
First, there is a lot of confusion, in the physics literature generally, about what Bell's theorem means/proves, and (at best) this paper doesn't help address those confusions. (At worst, it adds to the inertia of the confusions.) I have in mind here things like the paper's first sentence, which says (vaguely and noncommitally) that Bell's theorem proves "that the laws of physics are not constrained to obey ... intuitive or common notions." There is confusion/controversy, though, about what notions those are, and I would expect newlypublished papers on Bell's theorem to be more explicit about this. Another similarly offputting remark is the following: "Since entanglement is so successfully modelled by quantum mechanics, one can argue that there is no need for a mechanism that 'explains' it." The difference between a mere "model" and an "explanation" is not exactly clear. But the frustrating thing here is again just that the authors remain completely vague about what is at stake. Is it, as many have claimed, the concept of determinism? Or "hidden variables" generally? Or "local causality"? The fact that the authors don't take (and, as necessary, defend) a position on the meaning of Bell's theorem is not necessarily a fatal flaw with the paper since that is not what the paper is all about, but the fact that the ultimate implications of the idea illustrated by the game remain completely unspecified, does seem to significant detract from the authors' aims (and, in particular, would seem to undermine students' motivation to care about the topic).
Another point that detracts from the pedagogical value of the recommended game, at least for me, is that it is not perfectly parallel to the physics experiments (testing Bell's inequalities) that it is supposed to illuminate. The authors acknowledge this, e.g., when they explain that "the card game reverses roles regarding probability: Instead of the investigators attempting to ascertain the photons' socalled hidden variables, the players are acting as particles attempting to win the game by guessing the measurement angles." Similarly: "a penalty must be deducted from the partners' score whenever they are caught using a forbidden strategy..." Again, the fact that the game doesn't perfectly mirror the structure of the real experiments is not necessarily a fatal flaw, but the differences do detract from the ability of the game to really illuminate, for students, what it's meant to illuminate.
Third, I worry that the things about Bell's theorem (and the associated experiments) that are actually difficult to understand (by which I largely have in mind the questions, referred to above, about exactly what minimal set of assumptions gives rise to Bell's inequality, but then also various details about the structure of the experiments and how those relate to the assumptions) are not illuminated by the card game. Instead, the card game focuses exclusively on the purely statistical aspects of deriving the inequality  aspects which, in my experience, are the least controversial and easiest for students to understand properly. The authors seem to sort of acknowledge this when they write, in explaining the solitaire version of the game, that "It is evident that the player has a 2/3 probability winning a round." I agree, it is evident, and I think even students can understand clearly and easily why this is the case. But then, why bother with the game?
Finally, I felt like the discussion of the three "loopholes" did not quite live up to what I was hoping for based on the beginning of the paper. Re: the communications loophole, the authors state that "Alice and Bob could win every round of the partners' version if they cheat by communicating with each other after seeing their question cards in phase 2." This is true (although I find it extremely confusing to describe this as a "loophole"  surely "locality" is one of the central premises in the derivation of Bell's inequality.) But I was disappointed that the authors just say this but then all the subsequent discussion is about why superluminal communication is problematic vis a vis special relativity. (Incidentally, there are problems with this discussion. For one, there is really no meaningful notion of "nearly infinite speed". Any fasterthanlight influence will appear to propagate with infinite speed in some inertial frame. Also, the whole argument is circular and unconvincing. If Bell's theorem and the associated experiments provide evidence that there is some nonlocality in nature  and I think they do  then we can hardly just assume any longer that special relativity, as ordinarily understood, is true. The same kind of theory that one might contemplate to reconcile Bell's result  say, a theory in which the usual relativistic metric is supplemented with some additional structure such as a dynamically privileged spacetime foliation  will automatically prevent the sorts of paradoxes discussed here. But my main point here isn't to complain about the content of this discussion of the relation between relativity and superluminal communication. Instead, I mean only to complain that this discussion is basically disconnected from the card game. It's the kind of thing one would find in any random website or popular book about Bell's theorem.)
I feel similarly about the second "loophole" discussed  the "superdeterminism loophole". This is almost completely unrelated to the card game and is instead just a (not very good) discussion of the idea of superdeterminism. (The authors seem slightly confused about what the "super" in "superdeterminism" adds to mere "determinism". It does add something  i.e., "superdeterminism" is not merely the idea that "nothing happens by chance". It is instead the idea that not only are the "randomly" or "freely" chosen measurement settings in the experiments determined, but that they are determined to be correlated in certain ways with the ("hidden variable") states of the photon pairs that are being tested. The idea is that there is a kind of cosmic conspiracy  things that we have no reason to think should be correlated, and indeed things that experimentalists take explicit pains to ensure are not correlated, are nevertheless correlated in a conspiratorial way that, in effect, fools us into seeing violations of Bell's inequality. But again, my point here is not to complain about the content of the discussion, even though I find it somewhat wanting. Instead, I am just pointing out that it is somewhat disappointing that the discussion doesn't really relate to the card game at all.)
I liked the discussion of the 3rd loophole much more, since it is actually what I thought I was getting: a way of cheating at the game that helps me understand one of the Bell loopholes!
To summarize, what I thought I would find in the paper was a card game that closely paralleled the structure of the experiments testing Bell's inequality  a game that would allow students to understand Bell's theorem itself by figuring out, after playing for a while, why they can never win... and which might also allow them to appreciate certain "loopholes" by finding creative ways to win the game (by stretching or violating the rules). I think I would really enjoy (and support the publication of) a paper that did that, and I enjoyed this paper to some extent because it did some of that. But at the end of the day I feel like it doesn't live up to that promise. It leaves too much of what's important about Bell's theorem (namely, understanding exactly what assumptions generate the inequality so one can understand what's at stake in the experiments) too obscure, the game is really only vaguely analogous to the relevant (local hidden variable) theories and experiments rather than perfectly reflecting them, and only one of the three loopholes really interacts significantly with the card game. If I was going to teach Bell's theorem and wanted to do so using a kind of "game", I would probably just keep it simple and do something that is more exactly parallel to the real experiments: make up 3 yes/no questions, have the students pair up and then answer one randomlyselected question at soundproofed stations on opposite ends of the room. Challenge them to find a strategy that will allow them to reproduce the QM correlations and see what happens... (Let them figure out that they cannot do it unless they carefully arrange to refuse to answer under certain conditions, or they somehow rig the question selection so it is not random at all but correlated with their answerstrategies on a given run, or if they simply use their cell phones to text each other and update their strategies after seeing what questions they're asked.)
Anyway, I think this paper has some value and I support its publication at the WikiJournal, but hopefully the above critical discussion will be useful for some readers and/or the authors.Where and when do author's respond?
Is this the time and place for authors to respond? If the WJS has already answered this question, I'm sure that whatever format has been chosen will suit my needs. If no policy has been established, perhaps individuals can put their thoughts, almost in a blog format in subpages? I have taken the liberty of creating such a subpage, with the understanding that it can be easily moved or deleted. See:
 Draft:A card game for Bell's theorem and its loopholes/Guy vandegrift. Guy vandegrift (discuss • contribs) 15:48, 23 March 2018 (UTC)
 Typically, the authors respond on the same page as the reviewers, however that is usually for the 'final version' of a response, as would be submitted to a journal during peer review. This can either be pointby point, or as a new section below the reviewer comments (example). Having reviewer comments and author responses collated together on one page can make them easier to track. However you're certainly welcome to use a subpage to draft unstructured / inprogress thoughts. T.Shafee(Evo﹠Evo)^{talk} 01:13, 24 March 2018 (UTC)
 Thanks. I started to construct my response here.Guy vandegrift (discuss • contribs) 18:27, 24 March 2018 (UTC)
 Typically, the authors respond on the same page as the reviewers, however that is usually for the 'final version' of a response, as would be submitted to a journal during peer review. This can either be pointby point, or as a new section below the reviewer comments (example). Having reviewer comments and author responses collated together on one page can make them easier to track. However you're certainly welcome to use a subpage to draft unstructured / inprogress thoughts. T.Shafee(Evo﹠Evo)^{talk} 01:13, 24 March 2018 (UTC)
Third peer review
Review by
Natalia Sanchez Kuntz , Institut für Theoretische Physik der Universität Heidelberg
This review was submitted on , and refers to this previous version of the article
Reviewer comments provided as annotated manuscript PDF (A) and further comments provided in additional PDF (B).
Author's initial responses
First, I thank the referees (including two who reviewed this manuscript in the American Journal of Physics.) All five reviews were expertly and carefully written, and quite frankly put to shame any referee report I have written. A theme common to all five reviews was concern about the loose and informal use terms such as Loophole, Hidden variable, Superdeterminism, and even Bell's theorem. Our target audience is far less sophisticated than one typically associates with the study of Bell's theorem, and my coauthor and I both struggled with the need to find language that is both precise and simple. Both of us had previously seen an entry level textbook that used a messy bedroom to illustrate entropy. I still don't know if making your bed in the morning changes the room's entropy. Nor do I care  we both consider that analogy to be pedagogically useless. To illustrate the difficulty we face in trying to bring Bell's theorem to this level, consider how WP defines hidden variable theory.
 "A local hidden variable theory in the w:Interpretations of quantum mechanics is a w:hidden variable theory that has the added requirement of being consistent with w:local realism. It refers to all types of the theory that attempt to account for the probabilistic features of w:quantum mechanics by the mechanism of underlying inaccessible variables, with the additional requirement from local realism that distant events be independent, ruling out instantaneous (i.e. w:fasterthanlight) interactions between separate events."
 Wikipedia:Hidden variable theory describes a hidden variable theory as
 (a hypothetical) "w:complete theory" would "provide descriptive categories to account for (all observable behavior and thus avoid any w:quantum indeterminacy".
My main point is that these definitions might serve those familiar with quantum mechanics, we need to explain it differently to the nonexpert.Guy vandegrift (discuss • contribs) 13:24, 6 April 2018 (UTC)
Author's response to First Review
The card game is not easier to follow than an algabraic proof
As the text itself makes it clear, this is not a research article, since it contains nothing really new. It is rather a pedagogical contribution proposing a method to explain the Bell theorem to students, nicely illustrated with figures and drawings. I have never taught this part of quantum mechanics, and I cannot judge if this approach is the best to treat the subject. Personally, I would think that the traditional (more algebraic method) is not more difficult to follow, maybe even easier. Personally I did not find that easy to understand all the rules of this card game, and all these diagrams in the 13 pages, but this is just my personal taste.
My response Guy vandegrift (discuss • contribs) 21:19, 14 May 2018 (UTC) 

I agree. Nothing is simpler than the Venn diagram proof shown above. But my experience is that the typical high school graduates has no understanding of "proof". A card game they cannot win is immediately grasped, even if they cannot "prove" it to be unwinnable. Also, I recently showed this game to undergraduate science students (trigbased intro physics), and they could play the solitaire game directly from the paper, which I handed out to them. See also #Article_would_serve_a_complement_to_traditional_introduction below. Regarding the length, I propose to remove the appendix from the article and place it into this supplementary subpage 
Definition of "loophole"
In the field of fundamental quantum mechanics, one can enter endless discussions on the way to phrase ideas. So, I do not want to bother the authors with my own personal views, but I nevertheless with to express some disagreements.
The sentence "To some experts, a loophole is a constraint on any hidden variable theory that might replace quantum mechanics" is, to me, a very bad introduction to the notion of "loophole". A loophole is a logical possibility to evade the Bell inequalities by rejecting one of the (explicit or implicit) assumptions of the EPR paper and its continuation by Bell. It has nothing to do with hidden variable theory specifically, since it actually does not refer to any specific sort of theory. I would strongly recommend not to introduce the ideas of loopholes to students in this way.
I agree that it is a bad introduction, I tried to change the wording to illustrate the fact that we will instead view a loophole as analogous to a way to cheat. The problem is that a loophole and Bell's theorem need to mean different things to different people. I am looking for the entrylevel understanding but felt obligated to tell the reader that this is not how experts might view it. I added an entire section "Conundrum" to help clarify
Figure 1 is confusing
Figure 1 is confusing for someone who is familiar with quantum optics. The text says that is shows two entangled photons but, with photons, it is impossible to have devices filtering three polarizations at 120 degrees as shown in the figure. The space of states of photon polarizations is 2dimensional, and the filters shown in the figure will necessarily leak since they have three outputs.
Response: I don't understand this comment, and can only guess it means one of two things: 

1. The suggestion of "leaking" might be a reference to an old version of the figure that simultaneously presented the atom with three different filters, with only one lying in the path of the photon. To avoid cluttering Commons with outdated figures, I placed it here] 2. "Leaking" might refer to the loss of efficiency in using three symmetric angles of polarization when attempting to statistically establish violation of Bell's inequality. Bell's inequality is better established with filters at (0°, 22.5°, 45°). This lack of symmetry adds more steps to the analysis because one must analyze two pairs of orientations. This Venn diagram proof of Bell's inequality leads one to immediately grasp the (0°, 60°, 120°) case.Guy vandegrift (discuss • contribs) 13:29, 6 April 2018 (UTC) 
Reference to other efforts to create a Bell's theorem "game"
Nicolas Gisin, in his recent book "Quantum chance", discusses something similar, which he calls "Bell's game" I believe.The authors might wish to include a reference to this book.
Response 

Whew! First I need to look at the book. I also found another reference here: And I found Frąckiewicz, Piotr. "Application of the Eisert–Wilkens–Lewenstein quantum game scheme to decision problems with imperfect recall." Journal of Physics A: Mathematical and Theoretical 44.32 (2011): 325304. https://arxiv.org/pdf/1407.6757.pdfGuy vandegrift (discuss • contribs) 13:29, 6 April 2018 (UTC) 
First and last lines missing from pdf file
Please note that the first and last lines of several pages are missing in the pdf file you sent me, for some technical reason.
See draft:A card game for Bell's theorem and its loopholesGuy vandegrift (discuss • contribs) 13:29, 6 April 2018 (UTC)
Article would serve a complement to traditional introduction
My conclusion is that, if this articles comes as a complement of another more traditional introduction to the Bell inequalities, it may probably be useful to some teachers. I would nevertheless not recommend it as the only introduction to the inequalities, but maybe just as a nice illustration of the Bell theorem once the students understand its logic.
Author's response 

Quite to the contrary: Our goal is to make this a "stand alone" introduction for those who do not understand the logic. As such, this last comment will take a lot of work to address. But the referee and I agree on one point: The card game is a "nontraditional" approach. And, one should never mix two different approaches when introducing a subject. Advanced students should be taught the traditional approach, and then perhaps be shown the card game. If we are to bring Bell's theorem to a less sophisticated audience, we need this longer paper. The editors and referees need to make a decision: Is this a paper for the expert or the novice? If experts are the target, the paper can be drastically reduced in length in a way that will remove almost all issues raised. But I still think the article can be fixed so that novices can understand it. That is the purpose of Wkiversity/Wikipedia, right?Guy vandegrift (discuss • contribs) 21:45, 14 May 2018 (UTC) 
Author's response to Second Review
I enjoyed the paper (but have several reservations)
Referee's entire comment 

I have read the manuscript "A card game for Bell's theorem and its loopholes". The goal of the paper is to present a simple card game from which students can learn the impossibility of achieving the sorts of correlations that are forbidden according to Bell's theorem... and perhaps also understand, by figuring out how to "cheat" to win the game, several loopholes associated with the theorem and/or the associated experiments. I enjoyed reading the paper and applaud the general concept of trying to convey Bell's theorem to students in the form of a simple game. But I do have several reservations about the paper. 
I'm glad you enjoyed the paper and agree that your reservations have merit. The solution is to focus at the introductory level and make that clear to the reader at the beginningGuy vandegrift (discuss • contribs) 13:37, 6 April 2018 (UTC)
Confusion about what Bell's theorem means/proves
Referee's entire comment 

First, there is a lot of confusion, in the physics literature generally, about what Bell's theorem means/proves, and (at best) this paper doesn't help address those confusions. (At worst, it adds to the inertia of the confusions.) I have in mind here things like the paper's first sentence, which says (vaguely and noncommitally) that Bell's theorem proves "that the laws of physics are not constrained to obey ... intuitive or common notions." There is confusion/controversy, though, about what notions those are, and I would expect newlypublished papers on Bell's theorem to be more explicit about this. Another similarly offputting remark is the following: "Since entanglement is so successfully modelled by quantum mechanics, one can argue that there is no need for a mechanism that 'explains' it." The difference between a mere "model" and an "explanation" is not exactly clear. But the frustrating thing here is again just that the authors remain completely vague about what is at stake. Is it, as many have claimed, the concept of determinism? Or "hidden variables" generally? Or "local causality"? The fact that the authors don't take (and, as necessary, defend) a position on the meaning of Bell's theorem is not necessarily a fatal flaw with the paper since that is not what the paper is all about, but the fact that the ultimate implications of the idea illustrated by the game remain completely unspecified, does seem to significant detract from the authors' aims (and, in particular, would seem to undermine students' motivation to care about the topic). 
Gill, Richard D. "Statistics, causality and Bell's theorem." Statistical Science (2014): 512528. "quantum mechanics is incompatible with the principles of realism, locality and freedom". https://arxiv.org/pdf/1207.5103.pdf. I just don't see how this belongs in an introductory paperGuy vandegrift (discuss • contribs) 13:29, 6 April 2018 (UTC)
Game not perfectly parallel to the physics experiments
Referee's entire comment 

Another point that detracts from the pedagogical value of the recommended game, at least for me, is that it is not perfectly parallel to the physics experiments (testing Bell's inequalities) that it is supposed to illuminate. The authors acknowledge this, e.g., when they explain that "the card game reverses roles regarding probability: Instead of the investigators attempting to ascertain the photons' socalled hidden variables, the players are acting as particles attempting to win the game by guessing the measurement angles." Similarly: "a penalty must be deducted from the partners' score whenever they are caught using a forbidden strategy..." Again, the fact that the game doesn't perfectly mirror the structure of the real experiments is not necessarily a fatal flaw, but the differences do detract from the ability of the game to really illuminate, for students, what it's meant to illuminate. 
Author's responseGuy vandegrift (discuss • contribs) 21:36, 14 May 2018 (UTC) 

The discrepency between the game and actual experiments is unavoidable because we need they three fold symmetry of the polarizers to give the player(s) a concrete goal. How do you instruct card players to strive for certain correlations? In the system introduced in the paper, the players try to maximize the sum of three correlations with the understanding that all three are inherently negative I believe the referee and I have different students in mind. NonSTEM students cannot grasp the concept of an "impossible correlation". The fact that physicists didn't know these quantum correlations were impossible until 1964 illustrates the conceptual difficulties with the traditional way of introducing the topic Finally, I wrote two subpage supplements that bring both the experiment and theory up to a higher level: See Impossible correlations and Tube entanglement 
Paper ignores the difficult questions and focuses on the easiest to understand
Referees entire comment 

Third, I worry that the things about Bell's theorem (and the associated experiments) that are actually difficult to understand (by which I largely have in mind the questions, referred to above, about exactly what minimal set of assumptions gives rise to Bell's inequality, but then also various details about the structure of the experiments and how those relate to the assumptions) are not illuminated by the card game. Instead, the card game focuses exclusively on the purely statistical aspects of deriving the inequality  aspects which, in my experience, are the least controversial and easiest for students to understand properly. The authors seem to sort of acknowledge this when they write, in explaining the solitaire version of the game, that "It is evident that the player has a 2/3 probability winning a round." I agree, it is evident, and I think even students can understand clearly and easily why this is the case. But then, why bother with the game? 
I have two good responses:
1. I like to emphasize technical writing skills and have used that as an excuse to have students read the procedures for both the solitary and partner's game. They routinely grasp the solitaire game. But it is not unusual for a student to say they never really understood the partner's game. As I have already stated, the intended audience for this paper includes those who need the solitaire game. That's why I focused on the easy questions.
2. See the two supplements. This derives the CHSH inequality without calculus, and the this uses Maluss' law to explain much of what happens in a semiclassical way, with the introduction of a simple 2particle system to get the 100% correlation (or anticorrelation) that seems to be possible only in a full quantum model.
The fasterthanlight loophole (or not a loophole?)
Referee's entire comment 

Finally, I felt like the discussion of the three "loopholes" did not quite live up to what I was hoping for based on the beginning of the paper. Re: the communications loophole, the authors state that "Alice and Bob could win every round of the partners' version if they cheat by communicating with each other after seeing their question cards in phase 2." This is true (although I find it extremely confusing to describe this as a "loophole"  surely "locality" is one of the central premises in the derivation of Bell's inequality.) But I was disappointed that the authors just say this but then all the subsequent discussion is about why superluminal communication is problematic vis a vis special relativity. (Incidentally, there are problems with this discussion. For one, there is really no meaningful notion of "nearly infinite speed". Any fasterthanlight influence will appear to propagate with infinite speed in some inertial frame. Also, the whole argument is circular and unconvincing. If Bell's theorem and the associated experiments provide evidence that there is some nonlocality in nature  and I think they do  then we can hardly just assume any longer that special relativity, as ordinarily understood, is true. The same kind of theory that one might contemplate to reconcile Bell's result  say, a theory in which the usual relativistic metric is supplemented with some additional structure such as a dynamically privileged spacetime foliation  will automatically prevent the sorts of paradoxes discussed here. But my main point here isn't to complain about the content of this discussion of the relation between relativity and superluminal communication. Instead, I mean only to complain that this discussion is basically disconnected from the card game. It's the kind of thing one would find in any random website or popular book about Bell's theorem.) 
As per previous comments, I need to be explicit about the focus on elementary pedagogy. The (valid) suggestion that there might be something wrong with special relativity "as normally understood" would confuse the target audience.
Once the target audience is recognized, perhaps the reviewer will reconsider the relevance of the spacetime diagram in this paper. It is not easy to explain why most things cannot travel faster than light, and this argument using the two trains with "magic phones" is the most convincing and direct argument that I know. The argument is based on the two postulates of relativity (with the nonexistence of a preferred frame used to argue that a magic phone would operate on the same way on train as on earth.) A more sophisticated person might be satisfied with the velocity transformation rule, which says that superluminal messages travelling from Alice to Bob will be viewed as travelling in the opposite direction by a moving observer. But first, that requires an equation, and second, the velocity transformation rule requires that the reader understand that a message delivered to the past to a remote observer causes a paradox.
For evidence that we need a simple explanation of why superluminal communication is impossible, look at the current version of Wikipedia:Fasterthanlight_communication.
Many years ago, the parent of a physics major told me they never understood special relativity until they learned about the light clock. Though the explanation for the violation of causality associated with superluminal communication is a bit more involved, it is also based on something that can be visualized as a geometry problem. I recently introduced Bell's theorem to instructor who teaches introductory college chemistry, and their first reaction is that the particles might be in "communication". For Bell's theorem, we don't need proof that all superluminal communication is impossible, just that "nearly infinite" communication is impossible (or at least inconsistent with special relativity.) If anybody is concerned that "nearly instantaneous communication" is an artificial concept, I point out that "quasistatic equilibrium" is also an idealism designed to simplify things."Guy vandegrift (discuss • contribs) 13:29, 6 April 2018 (UTC)
Superdeterminisme "loophole"
Referee's entire comment 

I feel similarly about the second "loophole" discussed  the "superdeterminism loophole". This is almost completely unrelated to the card game and is instead just a (not very good) discussion of the idea of superdeterminism. (The authors seem slightly confused about what the "super" in "superdeterminism" adds to mere "determinism". It does add something  i.e., "superdeterminism" is not merely the idea that "nothing happens by chance". It is instead the idea that not only are the "randomly" or "freely" chosen measurement settings in the experiments determined, but that they are determined to be correlated in certain ways with the ("hidden variable") states of the photon pairs that are being tested. The idea is that there is a kind of cosmic conspiracy  things that we have no reason to think should be correlated, and indeed things that experimentalists take explicit pains to ensure are not correlated, are nevertheless correlated in a conspiratorial way that, in effect, fools us into seeing violations of Bell's inequality. But again, my point here is not to complain about the content of the discussion, even though I find it somewhat wanting. Instead, I am just pointing out that it is somewhat disappointing that the discussion doesn't really relate to the card game at all.) I think I repaired this by removing the confusing talk about superdeterminism. The goal (as with the previusley relativitycausalitycommunication loophole) is to get students to analyize position versus time diagrams in a critical way. It also points out that while (classical) wave equations are determinisitic, they can be used to model the nondeterministic nature of quantum mechanics in a way that does not seem to be contradicted by Bell's inequality or theoremGuy vandegrift (discuss • contribs) 22:00, 14 May 2018 (UTC) 
Liked the 3rd loophole
I liked the discussion of the 3rd loophole much more, since it is actually what I thought I was getting: a way of cheating at the game that helps me understand one of the Bell loopholes!
Summary
Extended content 

To summarize, what I thought I would find in the paper was a card game that closely paralleled the structure of the experiments testing Bell's inequality  a game that would allow students to understand Bell's theorem itself by figuring out, after playing for a while, why they can never win... and which might also allow them to appreciate certain "loopholes" by finding creative ways to win the game (by stretching or violating the rules). I think I would really enjoy (and support the publication of) a paper that did that, and I enjoyed this paper to some extent because it did some of that. But at the end of the day I feel like it doesn't live up to that promise. It leaves too much of what's important about Bell's theorem (namely, understanding exactly what assumptions generate the inequality so one can understand what's at stake in the experiments) too obscure, the game is really only vaguely analogous to the relevant (local hidden variable) theories and experiments rather than perfectly reflecting them, and only one of the three loopholes really interacts significantly with the card game. If I was going to teach Bell's theorem and wanted to do so using a kind of "game", I would probably just keep it simple and do something that is more exactly parallel to the real experiments: make up 3 yes/no questions, have the students pair up and then answer one randomlyselected question at soundproofed stations on opposite ends of the room. Challenge them to find a strategy that will allow them to reproduce the QM correlations and see what happens... (Let them figure out that they cannot do it unless they carefully arrange to refuse to answer under certain conditions, or they somehow rig the question selection so it is not random at all but correlated with their answerstrategies on a given run, or if they simply use their cell phones to text each other and update their strategies after seeing what questions they're asked. Anyway, I think this paper has some value and I support its publication at the WikiJournal, but hopefully the above critical discussion will be useful for some readers and/or the authors. 
Author's final (?) response begins here.
I have now digested the three reviews shown here, which have a lot in common with two additional reviews from my original submission to AJP. A common theme among all five reviews was expressed by an AJP reviewer who wrote
“  ...I worry that the things about Bell's theorem (and the associated experiments) that are actually difficult to understand ... are not illuminated by the card game. Instead, the card game focuses exclusively on ... aspects which, in my experience, are the least controversial and easiest for students to understand ...  ” 
This was a valid criticism that inspired me to write the supplement Draft:A card game for Bell's theorem and its loopholes/Guy vandegrift. I will refer to that document as I go through each review and edit accordingly. I begin with the third review because that person meticulously proofread the document.Guy vandegrift (discuss • contribs) 20:51, 2 May 2018 (UTC)
Third review
I begin with part 1 at File:Preprint  A card game for Bell's theorem and its loopholes (Reviewer 3).pdf
Done: "Abstract" and "A simple Bell theorem expt" 

Abstract
A simple Bell's theorem experiment

Done: The solitaire cardgame 

The solitaire cardgame

Done: The game for entangled partners 

The game for entangled partners

Done: Cheating at cards and Bell's theorem "loopholes" 

Cheating at cards and Bell's theorem "loopholes"

Done: Magic phones: Communications loophole 

Magic phones: Communications loopholeI wrote: Alice and Bob could win every round of the partners' version if they cheat by communicating with each other after seeing their question cards in phase 2. In an actual experiment, this loophole is closed by making the measurements far apart in space and nearly simultaneous, which in effect requires that these communications travel faster than the speed of light. Referee#3 commented: If this loophole is closed, there is not a "communication loophole" anymore. There is not such thing as a "superluminal communication loophole" given that loopholes are designed to explain the violation of Bell's inequality by experiments in a way that is consistent with Special Relativity...Then, this section is devoted to explain what would happen to causality if we were to violate the limit c, within the causal structure of Special Relativity. Not to the discussion of the loophole and its benefit to Bob and Alice. My response: First I must confess that my understanding of the word "loophole" is largely based on Wikipedia. Given that the intended audience for the paper includes those with minimal understanding of Bell's theorem, this might not be so bad. The current version of w:Loopholes in Bell test experiments vaguely states that the word "loophole" refers to any problem of experimental design or setup that affect the validity of the experimental findings. It is clear from this article's context that to "close" a loophole is to repair this flaw in the experimental design (and in the process verify the predictions of Quantum mechanics in a way that violates Bell's inequality). I don't see how "closing a loophole" implies that it no longer exists. All I am trying to do in this section is explain why it was considered so important to ensure that the two remote measurements are designed to occur at nearly the same time. And key to this explanation is the fact that fasterthanlight communication is inconsistent with special relativity due to issues with causality.
Finally, I don't understand what was meant by "the loophole and its benefit to Bob and Alice". To me, a "loophole" in a Bell's test experiment involves an effort by the experimentalist to change the outcome by tinkering with the experimental design (this outcome is predicted by QM but violates Bell's inequality). A "loophole" in the card game is an effort by Bob and Alice to win the game, presumably by cheating (since I seriously doubt that two human beings can achieve quantum entanglement.)
Also, the apparent typos involving commas in "simultaneity, which" and "January, as" seem to be flaws in the wikitexttopdf conversion. ♦ R3 seen

Done: Referee collusion:Determinism loophole 

Referee collusion:Determinism loopholeMore than one referee raised concerns about comments I made, and in retrospect, I decided to delete many of them. I did include the recent reference to 600 year old cosmic photons, and retained the use of figure 5 to discuss the deterministic nature of quantum mechanics in that it does predict probabilities. While there is no practical value in pondering a deterministic theory of the entire universe, students should recognize that any theory that predicts probabilities is is some sense deterministic. I removed most references to "superdetermisim" and "hidden variables" (but retained the references in the footnotes). The deleted section is archived at special:permalink/1865381. ♦ R3 seen ♠ GV seen. 
Done:The Rimstock cheat: Detector error loophole  

table
The Rimstock cheat: Detector error loophole

Done:Pedagogical issues 

Pedagogical issues
♠ GV: We seem to be OK here. 
Appendix
 Figure 8: question>answer Done!
 ♦ R3: A typo still remains. Please see comments in the new PDF commented file.
 ♠ GV@R3: Is this the typo I already fixed?
 Confusion about Alice announcing alpha and Bob not following clarified. ♦ R3 seen
 Done (with all three reports Guy vandegrift (discuss • contribs) 22:03, 14 May 2018 (UTC))
I think it's time to talk about subpages
In response to referee comments, I have created three "official" subpages with supplementary material. And I created a fourth subpage that begins an educational effort aimed at nontechnical students. It is my guess that the educational effort should be moved into Wikiversity mainspace, but that is something for the WJS editor and/or board to decide without my input (see Wikipedia:COI.)
But as author, I wish to argue the case for the three supplementary pages already linked already present: One subpage, The car and the goats is the proof of equation 1 for the penalty for giving different answers. One referee commented that this material was not easy to understand. Moreover, it is not required for the firsttime reader (which is why it was placed in an appendix). The other two Impossible correlations and Tube entanglement) were in response to referee remarks to the effect that very little was actually explained in the article. As a college teacher with many years of experience with introductory students, I can assert that "conceptual overload" is a serious problem. I wanted to focus the article on the card game, and state without proof or much explanation that it is isomorphic to experiments that involve quantum mechanics. This mismatch between the intended reader and the reviewers has motivated most of the recent edits to this article (see also https://www.ee.ucl.ac.uk/~mflanaga/thresholds.html.) I think the introduction of three subpages helps with this quite a bit.
Finally, some of the most recent comments by referee 3 cannot be resolved without going beyond the intended scope of this article. I suggest the future creation of "subpages" (official or unofficial) to resolve these issues. Personally, I consider the ability to freely append and comment upon journal articles to be a fascinating and largely unexplored aspect of the WikiJournal concept.
Before I go into Referee 3's latest comments, I need to clean up the subpage "Impossible correlations" by moving the practice quiz and discussion of Quizbank to a more appropriate location.Guy vandegrift (discuss • contribs) 11:45, 25 May 2018 (UTC)
 Done with the subpages Guy vandegrift (discuss • contribs) 21:42, 26 May 2018 (UTC)
 The article currently contains three "official" subpages and a fourth subpage that perhaps should be moved into Wikiversity namespace.
 The car and the goats was originally the appendix, but since students need not read it, it is better as a supplement (that even the ɫteachers don't need to fully understand).
 Impossible correlations resolves complaints that Bell test experiments don't use the geometry introduced by the card game. The asymmetries associated with actual experiments will render the scorekeeping of any game more complicated. Nevertheless, I did find the transition from the symmetrical to actual configurations to make for interesting instructional materials (see #4 in this list below)
 Tube entanglement allows us to use Schödinger's equation to achieve a primitive entanglement. Lower division physics majors with little or no experience in quantum mechanics might find this accessible. And, I found a way to introduce Dirac notation to such an audience.
 Conceptual is a work in progress that the WJS will likely want to move into Wikiversity mainspace. Nevertheless, it is relevant to the evaluation of this article as nontechnical introduction to the "spookiness" of Bell's theorem. Also, if at all possible I would like to invite a few readers of the article into the Quizbank effort (but understand that this decision must be made by the WJS with no input from me as a member of the board.). I will refer to this section often as I address the remaining referee comments.Guy vandegrift (discuss • contribs) 21:42, 26 May 2018 (UTC)
Editorial comment
Comments by Melanie Stefan
These comments were submitted on , and refer to this previous version of the article
The article is well written, but the beginning (both of the "abstract" and the actual article) is a bit abrupt and confusing to the nonexpert reader. Specifically, it does not explain what Bell's inequality is, what a card game has to do with it, what Bell's test experiments are and what the observed "spookiness" there is. I would suggest adding just a few introductory sentences of the following form: "Bell's inequality states that ... This is related to observations of ... We suggest a card game that can be used to teach the underlying concepts."
I agree with the need for more explanation early on. I think the best way to achieve this is to move material from the "Conundrum" section that starts the article and move it to the beginning of the "Abstract". I added a few "live" (not permalinks) to Wikipedia articles that are so well established that I think they are stable (I use permalinks to more quirky or obscure places that are likely to be edited.)Guy vandegrift (discuss • contribs) 01:35, 1 June 2018 (UTC)