Talk:Hex (board game)

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Untitled

Discussion follows, now in sections...

first proof of PSPACE completeness

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)

14x14?

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)

Move

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)

Servers

is there a hex server somewhere on the net?

for example, on games.yahoo.com, 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 Little Golem. Reiner Martin 19:20, 27 Nov 2003 (UTC)

There are three realtime Hex servers that you might be able to find an opponent on.

A relatively popular server these days is Board Game Arena which is based in France. BGA offers grid sizes 6x6, 11x11, 14x14, and 15x15.

Game Center (linked below) may have stronger players. If you start a game table in all three servers, you may be more likely to snag an opponent.

Ludoteka is Spanish. They have a new client which offers odd sizes from 9x9 to 15x15. English menus are available. The board is oriented like a diamond instead of "tipped over" on the other servers. On Wednesdays a real time tournament takes place if there are enough participants.

--Twixter (talk) 08:45, 1 January 2017 (UTC)

You can play Hex in real-time on igGameCenter. It supports different board sizes.

--artyomch 04:10, 21 Jun 2008 (UTC)

See HexWiki - Online playing —Kri (talk) 00:19, 22 January 2012 (UTC)

PSPACE vs. EXPTIME

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)

PSPACE and EXPTIME are terms in computational complexity that measure the difficulty of a problem (how long it takes to solve a generic instance of the problem in terms of the size of the input). I added a few sentences to clarify. Basically, it means that we know that generalized chess is at least as hard as generalized hex, but most experts think chess is probably harder. --Ptrillian 22:24, 1 January 2007 (UTC)

Tie games

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)

Another way to look at it (more informal than the version Fritzlein gave) is to try to build a tie in an actual board, or think what a tie must be. You'll see quite easily that it is impossible. RBerenguel 09:40, 9 November 2007 (UTC)

The article is underselling Nash's contribution. Nash showed that not only must the game have a winner (which is relatively easy to verify on these space filling games), but that there is a winning strategy for the first player. i.e. if player 1 plays a perfect game he will win. —Preceding unsigned comment added by 194.159.45.130 (talk) 15:09, 12 June 2009 (UTC)

Game board graphic

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)

First of all, that was a Hex board, not a Go board. Each internal vertex had six lines radiating from it, not four. The board was a diamond shape, not a rectangle. And did you see the border colors?

I apologize for including my description of how it was made. I apologize if the image was too large to suit you. I could make a smaller image if there is interest. Does anyone besides me think that such an image does indeed describe the game of Hex? Twixter 16:50, 27 Feb 2005

I don't have a problem with the image. It was kind of large when it was horizontal, so I rotated it a while back, but it seems appropriate. If it's still too large you could try specifying a certain pixel width in the article tag. Might make it less jaggy too. DreamGuy 04:44, Feb 28, 2005 (UTC)

DreamGuy, you and I are talking about two different images. I created a POV-ray perspective image of a Hex board. It has been removed. You can see this image in the previous revisions of the Hex (board game) page. I now have a smaller version of the image:

I would be glad to include it on the main page for Hex, without the extraneous discussion I foolishly added the first time. But first, I would like to know if anyone would be interested in it besides me.

And regarding what you did to the other image, I'm sure you meant well, but when two players sit down for a face to face game, they don't orient the board like that. An image serves other purposes than simply fitting on the page well. Some players might like to rotate the board 30 degrees from horizontal, since that is how several servers display it, but not 90 degrees for heaven's sake! That vertical image is disturbing to the eyes of any Hex player. I urge you to rotate it back again.

--Twixter 17:57, 4 Mar 2005 (UTC)

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)

I think we lack a user-box capable graphic, in my user page I just put a hexagon, but it lacks some visual appeal. Does anybody mind adding some kind of Piet Hein problem (the one 3x3 would be dear) to this page? This way we could use it to create an user box. RBerenguel 16:24, 9 November 2007 (UTC)

Brouwer fixed-point theorem

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)

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)

Examples and more details for Template Section

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)

Certainly 2-connectedness is a very basic concept which is essential to nearly all Hex strategy. I would prefer not to submit any more images to Wikipedia, but it shouldn't be difficult for someone else to use a Hex tool such as Jhex or Ohex, an image capture tool, and an image editor to show whatever patterns or templates you wish to. Please be sure to verify that your image is your own creation and that you release it to the public domain, when you upload it.--Twixter 02:50, 12 February 2007 (UTC)

Future FA?

I think this article has much room for adding new things. I can imagine tons of different images and mathematical information. I feel that it has the potential to be an FA. Compare with chess, a featured article. Below are the subtopics from the chess article and how a corresponding section could be made for hex.

• Rules - got that.
• History - easy to expand. The current article does not include information about anything past the year 1952, except for the mention of Cameron Browne's Hex Strategy.
  • predecessors - Hmm...
  • origins - Hmm...
  • birth of a sport
  • post-war
• Place in Culture - well... Place in Mathematical Culture?
• Notation for Recording Moves - Easy to add.
• Strategy and Tactics - enough info about this out there, I believe
  • fundamentals of strategy - doable.
  • fundamentals of tactics - I think templates, ladders, and such belong here.
  • opening - easy to add, already have some external links
  • middle game
  • endgame - I think the closest thing to an endgame in hex is where one player realizes he/she has a winning connection. But I still think it's possible to write a blurb about that.
• chess composition - there are a few problems on HexWiki that are usable
• competitive play
  • organization of competitions - mention online playing sites like kurnik, boardspace, littlegolem; mention the ICGA
  • Titles and rankings - well... according to HexWiki, "champion" on littlegolem is currently the most prestigious title
• Mathematics and computers - mention programs, algorithms; solutions for the game without the swap-option...
• psychology - nothing.
• Variants - got that

Anyone agree?

Leon math 18:25, 9 April 2007 (UTC)

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) This mechanism in itself, one gathers, is totally original and unprecedented, but this has never been stated clearly in anything I have read. —Preceding unsigned comment added by 207.102.64.208 (talk) 07:23, 15 February 2009 (UTC)

board representations

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)srn347

Cameron Browne's book

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 strategies.

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)

I think there is only one book specifically dealing with Hex strategy, and although it may not be perfect, I'd like to see its name or some way for user to find it via wikipedia (of course one could google "hex book"). --Halladba (talk) 15:38, 18 November 2008 (UTC)

Ok. A game matures when books about it hit the market. I am not against mentioning it anymore. -- Zz (talk) 19:14, 20 November 2008 (UTC)

Go strategy

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)

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)

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)

First-player strategy

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)

John Nash apparently did not independently invent Hex

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)