Talk:Dots and Boxes

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Strategy games To-do:

This is usually called dots and boxes, isn't it? The linked gametheory.net page calls it such, and so does Richard's PBeM server, and even Elwyn Berlekamp (who has written a book on the game). So I think the page should be renamed. --Zundark 19:28 Dec 21, 2002 (UTC)

I've always known it as Boxes and obviously the same for the numerous previous contributors. Mintguy
I hope you're not really suggesting that anyone who edits a page without complaining about the title necessarily approves of the title. I've edited many pages with titles I don't approve of - complaining about them is usually just too much effort. --Zundark 10:13 Dec 23, 2002 (UTC)
Fair enough. If you want to move the page use move page from the menu or do it from here. Mintguy
Well. At least me and the user who wrote the article first then. Mintguy

Duplicate article, needs merging:

Dots and boxes is a popular children's game, at least among mathematicans. The rules are as follows: The board begins as a rectangular grid of dots; six by six is a common size. The two players alternate moves, connecting adjacent dots with a horizontal or vertical line. If a player completes the fourth side of a square ("box") then she receives a point and must move again. When no vertical or horizontal line is left the player with the most points wins.

Dots and boxes has been carefully studied by Berlekamp, Conway, and Guy. See their book Winning Ways for further information.

Contents

[edit] Java applet?

A few years ago I wrote a Java applet to play Dots and Boxes. What do you think: would it add to the article to have such an applet on Wikipedia? I don't know whether it's technically possible, but I don't see why not. I'll be happy to license it as GPL or even GFDL, but I want to find out what other people think first. dbenbenn | talk 16:55, 3 Feb 2005 (UTC)

Disagree - Although an external link to such an applet would be a useful addition. -Surturz 05:40, 8 January 2007 (UTC)

[edit] An Oddity of the Universe

Isn't it strange how you can be sat next to someone you've never met before, and draw a grid of dots on a bit of paper, put a line between two of them, and slide it over, and they'll know exactly what to do, whoever they are?

[edit] Chains?

I've seen the game before, but never really played much. The article doesn't really explain how a chain is defined. Obviously I don't know otherwise I'd add it myself, so could someone enlighten me and/or edit the article to say what exactly chains are? Thanks. --Ciaran H 19:37, 18 September 2005 (UTC)

[edit] Why doesn't B win 4-0?

According to the article, A player who completes the fourth side of a box earns one point and takes another turn. In step 8 of the example illustrated at the top of the article, B completes the upper-left-hand box, yet somehow A then takes a turn and completes three boxes in a row without B being allowed to take another turn. Once B completes one box in step 8, why does A get to move immediately afterward? It would seem that upon completing the first box, B could then complete the remaining three boxes in three successive moves. --Metropolitan90 07:03, 10 January 2006 (UTC)

If you look a bit closer, you'll notice that in step 8 B completes the box and then draws the line going from the centre to the middle-right dot. In fact, any move B could make would give A the remaining 3 squares (the 4x4 game is actually analysed a small amount in the novel Golem in the Gears by Piers Anthony). However, I would suggest this page needs a little clean-up, possibly giving the rules their own section rather than including it in the introduction. Confusing Manifestation 16:04, 30 January 2006 (UTC)
Thanks, I revised the description of the sample game per your explanation. --Metropolitan90 06:13, 10 February 2006 (UTC)

[edit] Good article?

Are there enough references for this to be a good article? --Jtalledo (talk) 20:15, 26 May 2006 (UTC)

[edit] 6x6?

Well, at least here in Brasil, when there's nothing better to do, this can be played in huge entire-paper board (with about 1cm x 1cm each box)... And it's not so rare to see this kind of play... 6x6 here is for begginers... The only major problem of this is after the game, when counting the boxes (with ending scores around 120 x 80)... 201.56.56.96 22:20, 24 June 2006 (UTC)

On the contrary, large boards are most often used by beginners, because their size diminishes the effect of a mistake. Smaller boards better lend themselves to analysis and strategic play. On a 20x20 board an expert can simply wait until most of the board has been filled and then establish the correct chain parity with any number of sacrifices because it will not affect the outcome. Also, many strategies become obsolete on the large boards, such as the use of quads, nibbling, and incorrect parity wins. Most competitions and tournaments will use either 5x5 or 6x6. Anyone could play pool with 140 balls, but 9 makes it a more challenging game of skill. —The preceding unsigned comment was added by 74.102.156.147 (talk • contribs) 15:45, 8 August 2007.

[edit] Solved?

Has this game been solved? For all size grids, or only up to a certain size?70.42.112.151 06:22, 31 October 2006 (UTC)

I imagine the game is only solvable up to a certain size. I calculate the number of moves in a game to equal (2cr − c − r) where c = number of dots across, r = number of dots down. I calculate the number of possible games equal to the factorial (2cr − c − r)! (actually you could probably divide that by 8 to account for rotations & reflections)
--Surturz 05:37, 8 January 2007 (UTC)

[edit] Double-cross strategy

Does anyone know who "officially" came up with the double-cross strategy of not completing the last few boxes in a chain? The reason I ask is that I thought of it circa 1990. I never published it or anything so I can't prove it (unless Julie Thompson, the girl at my high school to whom I showed the strategy, remembers my demonstration!), but I would like to know if I was the first, for my own ego. For all I know the strategy is hundreds of years old, of course --Surturz 04:45, 14 November 2006 (UTC)

The strategy has been around far longer than that, probably as long as the game itself. The concept relies on fairly simple reasoning, and is generally discovered by a player that reaches a certain level of sophistication and maturity with the game. Mindmatrix 13:54, 14 November 2006 (UTC)
Yes, I've discovered it myself too after playing for a while (Circa 1980). No big deal.
Fair enough. It would be nice to know the first recorded description of the strategy though. --Surturz 05:21, 8 January 2007 (UTC)
“Winning ways – Vol. 2: Games in Particular”, by E. R. Berlekamp and others, published in 1982, already mentions on the chapter dedicated to ths game (chapter 16) the double dealing strategy. -89.180.81.64 23:21, 12 November 2007 (UTC)

[edit] Improvements

I'm planning to bring this article up to wikipedia standard (eventually Featured!) What do people think is a sensible level of depth of strategy to go into? What topics should it cover?
Topics we might want to cover (bold if they're necessary):
.Intro
.Comment on popularity.
.Strategy
.Grid sizes.
.Computer analysis.
.Notable players (are there any?) and experts.
.Variants.

That's all I can think of.
To break down Strategy further:
.All but two trick. (is there a name for that?)
.""Chain rule""
.""Strings and coins""
.Nimstring.
.Ways of calculating nimbers quickly. (Up to vines?)
Computer analysis:
.Which grids have be analyzed.
.Computer sugested openings.
Specific grids:
3*3 Second player always wins.
4*4 Draw always attainable. Common openings. Importance of quads.
3*5 (?)
5*5 Common openings. (First player advantage?)

Clearly that's far too much depth, but which bits can be cut?

Sugestions please.
Macbi (talk) 18:39, 19 May 2008 (UTC)