Talk:Hex (board game)

message: OK, I moved this from Hex (game) to here as some anon IP did it by cut and paste. Rather than argue, I just deleted that and moved it properly. This does seem an acceptable place, ie we have Go (board game)... Evercat 21:16, 31 Aug 2003 (UTC)
thread_title: Move

message: is there a hex server somewhere on the net?
for example, on [], they have go, chess, checker, reversi, chinese checker.... and there's lots of go servers around. But never seen a hex server.
P0lyglut 07:35, 2003 Nov 27 (UTC)
You can play Hex turn-based on []. Reiner Martin 19:20, 27 Nov 2003 (UTC)
replies: text: See [] —Kri (talk) 00:19, 22 January 2012 (UTC)
replies: text: Please don't post gaming related links in wikipedia - Wikipedia is not a gaming site. Sbalfour (talk) 23:32, 24 January 2017 (UTC)
thread_title: Servers

message: I don't understand the connection between PSPACE and EXPTIME with the level of difficulty. Perhaps this should be made clearer in the article. --Johnleemk 14:05, 3 May 2004 (UTC)
thread_title: PSPACE vs. EXPTIME

message: Why can the game never end in a tie?  It seems plausible, but how does one prove it?   pstudier 06:52, 2004 May 27 (UTC)
OK, suppose the game is over, and neither player won.  Then the whole board is filled with your stones and your opponents stones, or the game wouldn't be over.  Now consider one of your home edges, and all of your stones connected to that edge.  That mass of stones doesn't reach your other home edge, or else you would have won.  So consider the frontier of that mass of stones.  All of the frontier must be either your opponent's stones, or your opponent's edges, because the whole board is filled.  That frontier must connect your opponent's two home edges (a topological fact unless the board has holes).  But that means he must have won: a contradiction.  Therefore the original assumption that the game was a tie is false.  This isn't a formal proof, but it may be enough for informal conviction. --Fritzlein 19:44, 28 May 2004 (UTC)
replies: text: The problem with this argument is that it would imply that a board made of squares would also not end in a draw. But, if you imagine a board filled in like a checkerboard, you'll see that the square version can end in a draw. I've added a sketch of David Gale's proof that Hex always has a winner, which requires the geometry of hexagons to work. --2606:6000:6107:4500:4ED4:BF52:CF56:5082 (talk) 11:01, 14 November 2018 (UTC)
thread_title: Tie games

message: Is the giant Go board really necessary on this page?
This should be describing the game Hex itself, not the way a particular image of a board has been created.
--ambience 04:16, 9 Jan 2005 (UTC)
replies: text: Hrm, I somehow missed the other one showing up and being removed. Doesn't yours have too many spaces? And the way it looks it could be a square board in perspective. Regarding the orientation of the graphic currently there, it's a top view, not a view from where someone playing would be sitting... players don't hover 5 feet above the board when they play either way, right? DreamGuy 18:59, Mar 4, 2005 (UTC)
How many spaces is too many? It's a 19x19 grid. That's not too many for the 282 players who have enjoyed playing 19x19 on Little Golem. Should I repeat myself? There are six lines radiating from each interior vertex. Perhaps "the way it looks" depends on how closely you look at it. Either you like it or you don't, I guess. No reason is necessary.
Yes, the current graphic is a top view. So are the graphic displays on Little Golem, Kurnik, and all the other Hex servers, both real-time and turn-based. All of them show the board oriented so the long diagonal is either horizontal or 30 degrees off horizontal. That's how the vast majority of Hex games are played these days: on the Internet. These vertically oriented images are, well, disturbing. In my opinion they do not describe the game of Hex, as it is played by so many people, as well as it would if they were rotated back.
--Twixter 14:29, 8 Mar 2005 (UTC)
thread_title: Game board graphic

message: The Rules as currently stated here are not wrong, but IMO they could be stated more clearly. For example, emphasis is made on completing your path before your opponent completes theirs. This may mislead readers into thinking this is a pattern-forming game like Gomoku. Such games have a "racing" aspect to them. Hex is a blocking game, not a racing game. The only way to form your path is to block your opponent's path. Once you have created a pattern which blocks the opponent, there will be nothing they can do to stop you from completing your path.
Another reason I want to re-word the rules has to do with comparisons to Go. Many Go adherents claim that their game has the highest "ratio" of emergent game complexity to rules complexity. While I personally agree that 19x19 Hex is probably not as deep as Go, the rules to Hex are significantly simpler. One benchmark I like to use when arguing my case is how the rules to these two games are stated in Wikipedia. The Go rules currently consist of eight sections (including the beginning of the rules) and eight diagrams. Here is my proposal for the rules of Hex. It restates information already provided at the beginning of the article (which I do not propose to change,) as well as a description of the pie rule which is available in the provided link, but I want to put the complete rules from scratch in a single contiguous block, to show that they are still much simpler than the Go rules.
The board is a hexagonal grid of cells, traditionally in the overall shape of a rhombus. The cells could be represented as a grid of hexagons, where stones are placed in the hexagons, or as triangles, where stones are placed on the intersections. The rows of cells around the edges are called border rows. Each of the four corner cells are part of both adjacent borders. Two players have their own color collection of stones, for example black versus white. Before the game starts, the board is empty, and each pair of opposite border rows is designated as belonging to a specific player. With one exception, each move consists of placing a single stone of your color in any vacant cell. The object is to make a continuous path of your color stones which connects your border rows.
There is one more rule, called the pie rule, or the swap rule, or one-move equalization. Suppose black moves first. At the point in the game when black has placed the first stone on the board, the second player has the option to swap. There are two possible ways to implement this swap move. The second player could exchange their container of stones with the opponent. This is called swapping colors. The player who placed the first stone on the board as black becomes white, and makes the next move. Alternatively, the white player could place a white stone in a cell which is in a mirror image location to the black stone's cell, reflected across the nearest board diagonal, either the short diagonal or the long diagonal (which does not consist of contiguous cells.) If black's first stone is on a board diagonal, the white stone could replace the black stone there. Then the black stone is returned to black's container. This is called swapping the first stone. In terms of game play, this is effectively the same as swapping colors. Swap may be done only once per game. If the second player chooses to place a stone instead of swapping after the first stone is placed, then swap may not occur at all in that game. This rule makes Hex much more fair and deep. It is called the pie rule because it is like when two people want to share the last of the pie. One person cuts the pie into two slices, and the other chooses which slice to eat. Of course either player is allowed to resign before a winning path is completed. A drawn position can never occur, but several online servers allow agreed draws.
I am certain the creator of the previous image would not object, because that person is me. I welcome all feedback. Nit picking is encouraged. I want to get this right. My plan is to wait a couple months before I edit the main page. I don't want to enter into an editing battle.
--Twixter (talk) 20:39, 4 April 2019 (UTC)
thread_title: Re-word the rules section? And replace the image there?

message: In sect. Theory and Proofs one reads
 An important consequence of the determinacy of hex is the Brouwer fixed-point theorem which
 was shown by David Gale.
I'm not sure I fully understand what is meant, but it is clear that the Brouwer fixed-point theorem is not a consequence of the hex game (and this theorem was not "shown by Gale" but by Brouwer) ; maybe the other way round ? — MFH:Talk 12:20, 24 October 2006 (UTC)
replies: text: I had the same question but it checks out; I read through a summary of the results in the cited article (American Mathematical Monthly) on MathSciNet.  Gale's proof was certainly not the first nor the most important, but he does show equivalence of the two theorems.  The fixed-point theorem in n dimensions requires a different but related n-player game.  I've tried to make this clearer in the article.  Tracy Hall 17:55, 22 March 2007 (UTC)
thread_title:  Brouwer fixed-point theorem 

message: I'm a new contributer to wikipedia, so I'm still trying to learn the nuances of what other contributers believe the purpose of wikipedia is.  I think it would be a good idea to add examples of some templates (at least 5 or 6 of the smaller ones) along with the analysis to explain why a template is connected.  I like one explanation I read (perhaps in Browne's book, I don't recall) of 2-connectedness.  The reason a template (or any winning position) works can usually be explained well in terms of being 2-connected.  I.e. "if he moves there, then I move here to stay 2-connected."
Do others agree that this would be a useful addition?  If so, does anyone have ideas about a good way to create the images of the templates.  I could probably write up a decent explanation, but it wouldn't do much good without pictures.  What do people think?
--Ptrillian 21:55, 1 January 2007 (UTC)
thread_title:  Examples and more details for Template Section 

message: That board is just like a go board except with diagonal lines drawn in one of two directions. Does this mean hex can be played with a go board?
68.7.25.121 (talk) 06:38, 28 July 2008 (UTC)
thread_title:  board representations 

message: The article said: [Cameron Browne]] wrote a book entitled Hex Strategy: Making the Right Connections, which covers Hex strategy at a greater level of detail than any preceding work. However, some Hex players feel that this book contains many factual errors and advocates questionable strategieshttp://maarup.net/thomas/hex/hex3.pdf page 83http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=38.
However, if we check the sources, they say e.g. Players have questioned some of the advice given. This is completely different to his book contains many factual errors and advocates questionable strategies. The other source says basically that there are things Browne does not mention. That is even less support for the wording.
I have taken the whole paragraph out and replaced it with a pointer to the existence of Hex strategy books. Going beyond that is hardly relevant. -- Zz (talk) 16:39, 15 November 2008 (UTC)
thread_title:  Cameron Browne's book 

message: Did Hein and Nash invent not only Hex but the entire sub-genre of connection games which require side-to-side connections to win (Hex, Twixt, Gonnect, etc)?  —Preceding unsigned comment added by 207.102.64.208 (talk) 07:17, 15 February 2009 (UTC)
thread_title: Nash and Connection games sub-genre

message: Did Nash ever give any reason for why he considered 14x14 the optimal size?  —Preceding unsigned comment added by 70.182.69.205 (talk) 03:33, 8 May 2010 (UTC)
thread_title: 14x14?

message: The claim that Nash thought the winner of Go was determined by chance and not strategy is in serious need of a credible reference; Go is quite obviously a game that involves an enormous amount of strategy - a fact well known among computer programmers and laypersons alike.  I will be very surprised if the man who invented game theory held such an obviously fallacious opinion about Go.  Failing the addition of a credible citation, this claim (pardon the pun) needs to Go! Spiral5800 (talk) 10:22, 18 February 2011 (UTC)
replies: text: Indeed it requires a citation! But note (1) that game theory has little to do wth games like go and hex (which of course doesn't mean that Nash wouldn't be aware that go is a strategy game with perfect information), and (2) go is - unlike hex - so complex, so far outside what any supercomputer could analyse, that among roughly equal players (or players matched with a suitable number of handicap stones), the outcome at the end of a long game has for all practical purposes a substantial element of randomness. I'm not saying the claim in the article is right, or that the claimed claim by Nash is right - but that it might be, in a sense.--Nø (talk) 11:57, 18 February 2011 (UTC)
replies: text: Certainly seems unlikely to have been worded in these terms. I would see little problem with you removing the comment and cleaning up the history section. Especially since "invented indepedently" is not the same as inventing the game.Tetron76 (talk) 18:33, 1 March 2011 (UTC)
thread_title:  Go strategy 

message: Who has the winning strategy when the pie rule is used? (My guess would be the second player, since he can "become" the first player if he wants, and he has a winning strategy wherever the first stone is placed for him.) If anyone knows could they add it to the article?  — Preceding unsigned comment added by 92.27.55.215 (talk) 21:10, 23 May 2012 (UTC)
replies: text: You are correct: the second player can win under the 'pie' rule.  The first player can make a move in either of two sets: moves which maintain his winning advantage, and those that do not.  If both players play perfectly, and the first player makes a winning move, the second player will swap the board; if the first player makes a losing move, the second player will let him keep it. However, no players are good enough to play perfectly.  The real purpose of the rule is to cause the first player to make a weak but plausable move, to equalize the winning changes of (imperfect) players.  Sbalfour (talk) 19:45, 20 January 2017 (UTC)
thread_title:  First-player strategy 

message: The first to prove that HEX is PSAPCE complete were Shimon Even and Robert Tarjan.
The proof was published in 
S. Even and R. E. Tarjan. 1976. A Combinatorial Problem Which Is Complete in Polynomial Space. J. ACM 23, 4 (October 1976), 710-719. DOI=10.1145/321978.321989 http://doi.acm.org/10.1145/321978.321989 
--79.176.112.80 (talk) 21:20, 15 October 2013 (UTC)
thread_title: first proof of PSPACE completeness

message: This external link is down:
We currently have some problems with the database. Please come back in a few daysweeks. The provider has been unable to fix his database for the last three months.
Does it take long? How do i got the documentation back?  — Preceding unsigned comment added by Bart veurink (talk • contribs) 14:37, 4 January 2014 (UTC)
replies: text: Your promotional link to an external wiki unrelated to Wikipedia has been deleted (apparently), and properly so.  Wikipedia is not responsible for that site, and the talk page of this article is not a forum for general discussion of hex or playing hex.  It is solely for discussion of content and editing of the article. Sbalfour (talk) 21:53, 24 January 2017 (UTC)
thread_title: HexWiki a wiki dedicated to Hex

message: https://boardgamegeek.com/blogpost/59630?commentid=6742048#comment6742048
If true, a lot of references to Hex across the Internet, not just this page, would need some serious editing. But the above reference is not solid enough for that IMO. If you, dear reader, happen to know more about this, or can afford to access the ICGA journal, 38:2, pp.126-7, any verifiable detail would be appreciated.
--Twixter (talk) 08:11, 1 January 2017 (UTC)
replies: text: I'd play this like newspaper sourcing: stories, especially sensational ones, must have at least a second corroborating source. Sbalfour (talk) 19:54, 20 January 2017 (UTC)
thread_title:  John Nash apparently did not independently invent Hex 

message: These games aren't really derivatives or variants of Hex; the nature of their connectivity is different (hex is 6-connected, Shannon's game is 4-connected generally) and this gives rise to profound differences in proofs and strategy: the Shannon game is representable as a binary matroid, and is solved. Hex is not a binary matroid; the strategy is very much more complex.  I think I'm going to pull Gale/Bridg-It into a separate article, or merge these subsections into the article on the Shannon switching game, which they ARE closely related to, as in synonymous.Sbalfour (talk) 15:33, 15 January 2017 (UTC)
replies: text: Agreed they're (it?) are not variants of Hex. Or derivatives — possibly. (But David Gale *was* around Princeton and knew John Nash when Hex was invented.) Nevertheless, they are very closely related kinds of topological / combinatorial games. For this reason, Bridg-It et al. might best be included toward the end of this article under a section called Related games.  If the material got to be too large, it would merit its own article/s.2600:1700:E1C0:F340:597F:5057:E89D:168E (talk) 01:05, 30 April 2019 (UTC)
thread_title:  Shannon switching game/Gale/Bridg-It 

message: The Strategy section is bare bones, more like an example section, like showing a castled king position or checkmate position in chess.  It borders on WP:ORIGINAL RESEARCH.  We might be able to cite Cameron Browne's book. But if we go much further, we'll have a WP:GAMEGUIDE. Take a look at historical versions of the TwixT article for what NOT to do.  I'm at a loss for how to make this section useful as well as terse and scholarly.  In chess, there's openings, endings, combinations and position play.  Maybe that'd be a good outline here.Sbalfour (talk) 21:54, 17 January 2017 (UTC)
thread_title:  Strategy section 

message: The argument has been badly botched.  Consider for example the simple statement that if it's been proven that the game can't end in a draw, then one player or the other has a winning strategy.  Suppose that the markers are placed on the board alternately by lot.  By the time the 121st marker has been placed, one player or the other MUST have won.  But neither player has a winning strategy!  That is, neither player can FORCE a win.  Sheeesh.  The argument either needs to be deleted entirely (just say it's been proven that the first player can win), or write that argument in correct prepositional logic.Sbalfour (talk) 23:40, 17 January 2017 (UTC)
thread_title:  Theory and proofs: strategy stealing agument 

message: If John Nash said or proved something, it must be sourced - a citation to a peer-reviewed professional journal.  Otherwise, the statement cannot remain in the article. I'm removing all such unsourced or improperly sourced statements.Sbalfour (talk) 06:05, 18 January 2017 (UTC)
thread_title: John Nash said?

message: Trying to ref the Variants section, it appears that someone perused the IG Games website and copied all the Hex-like games to here.  Easy effort, no scholarship. The list isn't unduely long; the issue is the notability of the items on it.  Wikipedia isn't an almanac or gamesite.  I propose the following criteria for including/excluding items from the list:
Inclusion criteria (at least one of):
*1. there is a published book devoted to the game, or at least a whole chapter in a book devoted to the game
*2. there is at least one paper in a peer-reviewed professional journal devoted exclusively to the game
*3. there is a commercially published game product
*4. there's a registered patent, trademark or copyright for the game even if it isn't published
*5. there's regulated national or international level competition in the game
*6. there's a wikipedia article for it (somewhat dubious - there's a lot of wiki articles on non-notable things)
*7. it's listed on the Game Geek website (somewhat dubious)
Exclusion criteria (any single one excludes)
*1. games that aren't direct descendants of Hex (i.e. Shannon switching game)
*2. if there are fewer than three online descriptions of the game
*3. games not structurally similar (i.e. not a maker-breaker positional game, not planar, etc)
Three, possibly four, of the items currently on the list would be excluded applying these criteria.  What I suggest for these, is to provide a link in the external links section to gamesite(s) where hex variants can be found for gamers (when THAT section overflows with gaming website links, we'll have a separate issue).
Sbalfour (talk) 19:13, 18 January 2017 (UTC)
thread_title:  Variants section 

message: The article has only 3 images, and two of them are dubious: the one illustrating a winning chain doesn't look anything like a chain in an actual game, and may be deceiving (the distribution of stones isn't like that, and Hex is seldom played to the state of a complete chain, just as chess is seldom played to checkmate). The picture of hex on a go board doesn't depict a standard or common playing surface (how about a picture of a 1947 Con-Tac-Tix board, or a 1952 Parker Brothers Hex game board and pieces?)
I find it challenging to imagine what the pattern configurations for path, template and especially ladder look like without a picture, and I'm a hex player.  It's like trying to play chess blindfold.  I also think we need one or more examples of how these patterns are combined into chains.  A few 3 or 4 move opening patterns to illustrate potential connection to templates would also be an appropo addition.  
It might also be useful to illustrate how the game develops on 2x2 thru 5x5 boards, because the utility of the patterns is immediately apparent there.  This gets to be more of a "magazine" type presentation rather than a scholarly one, so need to keep it concise.
It also seems almost essential to illustrate the asymmetry of the pairwise 2-connectivity paradigm with an obtuse position showing how a play in one area of the board may result in a response in another seemingly unrelated area.
Sbalfour (talk) 17:33, 23 January 2017 (UTC)
thread_title:  Embellish article with images 

message: I discovered a website that contains an interactive hex game where the computer goes first and always wins. Here it is: http://ec2-34-227-158-207.compute-1.amazonaws.com/fldb/hex99.html
How can this be implemented and is it necessary? I felt like it could be an important resource on this article
--IForgot321 (talk) 03:28, 27 January 2019 (UTC)
thread_title:  Online hex 9x9 winning strategy demonstration 

message: Under the section Theory and proofs, this passage appears:
"John Nash was the first to prove (c. 1949) that Hex cannot end in a draw, a non-trivial result colloquially called the "Hex theorem", which we now know is equivalent to the Brouwer fixed-point theorem"
Since this does not state what is meant by the "Hex theorem", we can only guess. But readers should not have to guess. 
Does this refer to the impossibility of two winners? The impossibility of zero winners? Or both?  All three have been referred to by mathematicians as the "Hex theorem".2600:1700:E1C0:F340:597F:5057:E89D:168E (talk) 00:54, 30 April 2019 (UTC)
thread_title:  The "Hex theorem" is ... what? 

message: "One such pattern, analogous to the bridge, is shown in diagram 2. " Teheres no diagram 2 in the article.  — Preceding unsigned comment added by 89.134.199.32 (talk) 20:13, 15 September 2019 (UTC)
thread_title:  diagram2 

message: "The game has deep strategy, sharp tactics and a profound mathematical underpinning" this sound more like a marketing slogen to increase apetite to buy this game than a factual desription of the game. 89.134.199.32 (talk) 20:15, 15 September 2019 (UTC)
thread_title:  is this encyclopedical? 

message: "Once placed, stones are not moved, captured or removed from the board (ala, the game of go)"
this sentence seems wrong. 
case 1: if "ala" is supposed to mean "like" or "similarly to" then it is just unnecessary verbosity, since this game is not othervise likened to the game of go and the first part of the sentence already desribes the game clearly enough, so no need for a clarifying remark that does not add to the clarity.
case 2: if "ala" is supposed to mean "not like" or "in contrary" then it is just plain wrong since in go pieces need not to be removed, in practice are not removed but instead they become "dead" which means they become owned by the encircling opponent and thus count for the final score of the game.
89.134.199.32 (talk) 20:38, 15 September 2019 (UTC)
thread_title:  what the heck is "ala" 

message: Neither of the two pictures in the article showing game positions show anything like a realistic position between skilled players. Can we amend that?--Nø (talk) 17:07, 25 October 2019 (UTC)
thread_title:  Illustration 

message: — Assignment last updated by Dlopezramos (talk) 19:41, 22 February 2023 (UTC)
thread_title: Wiki Education assignment: Topicos en Ciencias Matematicas

message: At the end of the section Computed strategies for smaller boards, we state a conjecture that the center cell (2 in the case of n being even) is a winning move, uncited. I can find the conjecture in a reference; in fact, the assertion that any play on the short diagonal is a winning move appeared as early as Gardner's  1959 columns in Scientific American. The set of winning moves is in fact considerably larger than that for boards except n=2 and n=4. The number is between 1/2 and 2/3s of nxn. Figuratively, a random first move is most likely to be a winning move! The pattern of likely winning first moves is a critical component of swapping strategy - for very strong automata like we have now, if the first player makes a likely winning move, the second player will swap; otherwise it was a losing move, so the second player must have a winning move, and therefore plays it. So swap patterns, not merely conjectures about a few selected moves, would be an interesting addition to the article. Sbalfour (talk) 17:28, 20 June 2023 (UTC)
replies: text: I've adjusted this to say what we do know, based on solved board sizes, and cited Gardner's original stronger conjecture. Sbalfour (talk) 19:55, 20 June 2023 (UTC)
thread_title:  Conjecture about winning moves 

message: I have a first edition game, and the instruction manual says copyright 1950. I believe we should change the (uncited) date in the article to the copyright date, presumptively the date of first reease. Sbalfour (talk) 20:43, 20 June 2023 (UTC)
thread_title: Parker Brothers first edition "The Zig-zag Game Hex" copyright 1950

message: The Strategy section is a little anemic: assuming we create on the board various templates with virtual connections, what are we supposed to do with them - i.e. how does that translate into a win? Maybe it's patently obvious, that we must attempt to create an unbroken chain of templates and/or stones from one edge to the other?! Maybe that's why we don't say it. But it'd complete the argument that templates are useful to do so. If we do say that, is it necessary to have a source? If it's patently obvious so we don't say it, then it should be patently obvious when we do, i.e. no source needed. I'm not sure I entirely buy my own argument; I believe we should be able to find such a source that says it, or generally implies it. Sbalfour (talk) 20:02, 21 June 2023 (UTC)
replies: text: Additionally, I just saw that Seymour's book is also cited in Hayward, Ryan B. Hex: A Playful Introduction. Vol. 54 of Anneli Lax New Mathematical Library. American Mathematical Society, 2022. So now there are at least two independent reputable published sources who cite Seymour's self-published book as an authority on Hex strategy. I think this strengthens my argument that going forward, Seymour's book is not merely a blog. It is a source that other reliable authors rely on. WP:RS does not prohibit self-published material outright. It merely establishes a higher standard for assessing their reliability. Selinger (talk) 01:47, 11 January 2024 (UTC)
thread_title: Strategy section, redux

message: The Strategy section is not adequately sourced even if its sole source were valid. That source was . That source is by a non-credentialed author, self-published, online only, and not peer reviewed.  The content basically appears on a personal blog which is not allowed in Wikipedia. I have therefore removed it leaving the whole section unsourced. Unsourced content may be challenged and removed, and I have challenged it with an unsourced tag. In due time, if WP:RS sourcing does not appear, I will remove the section and revert it back to the previous rendition of 19 July, 2022. That rendition has issues also, but they were more repairable than the ones faced here.  Sbalfour (talk) 14:51, 26 June 2023 (UTC)
thread_title:  About a source