Talk:Tic-tac-toe

Who goes first?

It seems that the world is split in terms of whether O plays first, X plays first or there's no standard. As a child, I was taught that O plays first.

But the external links are slanted towards X having first move, albeit varying in whether they claim it's a basic rule, what usually happens in practice or just a wlog assumption for mathematical analysis.

Still, there ought to be something we can find online about the whole debate, but I can't seem to find anything apart from this.

Moreover, it seems odd that the "X moves first" rule seems to have caught on and yet we call the game "noughts and crosses" not "crosses and noughts" - I don't suppose anyone here can find anything on how that happened? -- Smjg (talk) 23:47, 13 September 2010 (UTC) (post was lost in previous edit, but re-added by--Nø (talk) 07:48, 22 September 2010 (UTC)

Well, that depends on the language, for example in Russian the game is called "crosses-noughts" (without "and"), but I in childhood was taught there is no rule. - 89.110.14.218 (talk) 23:31, 5 January 2015 (UTC)

Yes everything is true Nkalane (talk) 14:55, 22 June 2018 (UTC)

Nkalane Nkalane (talk) 14:55, 22 June 2018 (UTC)

Another strategy error

Quoting the article "Player O must always respond to a corner opening with a center mark". This clearly false, for if Player X responds in the opposite corner he wins. Here is the position.

. . X
. 0 .
X . .

Now Player X has two opportunities to create a fork, namely moves a and b below.

a . X
. O .
X . b

The correct move for O is to play in another corner.
—Preceding unsigned comment added by 129.175.5.43 (talk) 16:10, 26 November 2010 (UTC)

No, you missed something. Player O moves after figure 1. Player O can move to one of the side spots like this now:

. . X
O O .
X . .

Now, if Player X decides to fork:

. . X
O O .
X . X

Then Player O can just win:

. . X
O O O
X . X

Avindratalk / contribs 18:02, 26 November 2010 (UTC)

the move for o (centre then side) above is the only valid means of preventing a loss as x can force a win if o goes in any corner: x goes in space 1,1:

if o takes the centre and then a non-forcing move they loose as explained above

if o takes the opposite corner (3,3) then x can take 3,1, forcing o to block in 3,2. x then takes 1,3 forcing a fork (as they can win on 2,2 or 1,2). This can also be played the opposite way round (x taking 1,3 first)

if o takes a different corner (3,1) then x can take 3,3 forcing o to play 2,2. x can then play 1,3 creating a fork (as they can win on 1,2 or 2,1).

therefore x can always force a win — Preceding unsigned comment added by 165.120.146.48 (talk) 14:45, 22 September 2018 (UTC)

On O's second move

I wrote my program based on the article. The guy who played it hadn't read the article ☺ and played a side-center followed by the adjacent side center. It looked like this

---
-OX
-X-

Of the six moves available to O, 3 are bad and 3 are good. A second move for O to a side center is in the bad group. It looks to me that the best move for O here is lower right, though lower left and upper right also force the draw. My program lost ;-( JMOprof (talk) 13:18, 11 April 2012 (UTC)

The "Strategy" section

I have removed the strategy section of this article because that was only a guide of how to prevent forks, how to block forks, and how to respond to moves; such guides are not permitted as per WP:NOTGAMEGUIDE and WP:GAMETRIVIA. — Forgot to put name (talk) 08:29, 3 February 2013 (UTC)

Think about it ... a slippery slope ... Many many chess articles involve "how to" advices. (Will you remove *all* chess "best move" recommendations!?) Ihardlythinkso (talk) 13:58, 3 February 2013 (UTC)

Read WP:NOTGAMEGUIDE and WP:GAMETRIVIA again. It clearly mentions that concepts and "walkthroughs" are not permitted. I think your argument is WP:OTHERSTUFFEXISTS which is not a good argument. — Forgot to put name (talk) 05:53, 4 February 2013 (UTC)

I'm familiar w/ those policies. And I wasn't making an argument [for keeping the material], I was inquiring if you'd thought this through. (And, you answered. Good.) Ihardlythinkso (talk) 06:53, 4 February 2013 (UTC)

User:Forgot, I agree the way the material was written makes it seem inconsistent with WP:NOTAGAMEGUIDE; however, I'm not sure it really is (game guide), and, subtle editing could change that aspect easily enough. The fact that "best move" recommendations fill up chess articles, is not a comparison you can knock down as "not a good argument" by simply referencing WP:OTHERSTUFFEXISTS. (Have you read that essay? It supports consistency over all WP articles. It cautions against invalid comparisons being used as argument, and in this case, comparing to chess articles containing best move recommendations, isn't invalid. The chess articles and the nature of their contents has been around a long time; the WP:OTHERSTUFFEXISTS essay respects precedent in addition to consistency. Have you read that essay in detail? I have.) Ihardlythinkso (talk) 08:03, 8 February 2013 (UTC)

You are taking these rules too far. Tic Tac Toe, like Chess and many other classic games, is of academic interest, particularly in the artificial intelligence field. I have been writing a Tic Tac Toe AI for one my classes, and the strategy section was very helpful. This is not the sort of knowledge that is only of interest to a select number of enthuiasts, and it is not the sort of thing you can look up on a publisher's website (because tictactoe does not have a publisher). I am going to revert your change. Linkminer (talk) 05:59, 8 February 2013 (UTC)

And furthermore, both of the policies that you just cited are intended to apply to VIDEO GAMES. Linkminer (talk) 06:08, 8 February 2013 (UTC)

I also feel the removal of content here was heavy-handed. (I noticed some time ago too, as you mention, the refs to video games in those policies ... I'd always assumed this was an oversight or omission, but, thinking about it now ... that would mean quite big oversights/omissions! Those policies s/ probably clarify what they don't apply to.) Anyway, I support the content restoration you've done. Ok, Ihardlythinkso (talk) 08:17, 8 February 2013 (UTC)

The first diagram includes errors, and is erroneously labeled as "Optimal strategy for player X if starting in middle." instead of starting in the corner. As an example of its errors, look at the left side entry, which erroneously shows X on the top as the "optimal" move. The optimal second move after O on the side should actually be X in the top right corner, forcing one block with O in top center and followed by forking X in bottom right corner. This entire diagram should be removed, due to these problems.136.181.195.29 (talk) 19:06, 19 January 2023 (UTC)

"Initiative in start game"?

Since June 16, 2011, there has been a figure labeled "Initiative in start game" that is unreferenced within the body of the article and has essentially no information on the image page itself. What exactly is it showing? I think it has something to do with the relative strength of certain moves, but that's just a stab in the dark. While typing this out, I think I figured it out. It is the number of directions you can win from any square. This should probably be added to the caption.72.179.171.130 (talk) 23:18, 15 August 2014 (UTC)

xkcd graphic

A graphic similar to the on appearing the xkcd site originally appeared in Ian Stewart's "Mathematical Recreations" section of Scientific American http://www.ncbi.nlm.nih.gov/pubmed/10914406 Which in turn was based on "Fractal Images of Formal Systems," The Journal of Philosophical Logic 26: 181-222, 1997 http://www.pgrim.org/fractal/index.html It was certainly popularized by xkcd who deserves credit for that. — Preceding unsigned comment added by 129.49.17.164 (talk • contribs) 17:32, 8 December 2014

Other variants

• Other variants, which were deleted in January 2015, include:-
  • A more complex variant can be played on boards utilising higher dimensional space, most commonly 4 dimensions in a 3×3×3×3 board. In such games the aim is to fill up the board and get more rows of three in total than the other player or to play with 4 people and get 1 row of 3.
  • In Nine board tic-tac-toe, nine Tic-tac-toe boards are themselves arranged in a 3×3 grid. The first player's move may go on any board; all moves afterwards are placed in the empty spaces on the board corresponding to the square of the previous move (that is, if a move were in the upper-left square of a board, the next move would take place on the upper-left board). If a player cannot move because the indicated board is full, the next move may go on any board. Victory is attained by getting 3 in a row on any board. This makes the game considerably longer and more involved than Tic-tac-toe, with a definite opening, middle game and endgame.
  • Super tic-tac-toe is played like Nine board tic-tac-toe except that the game does not end when a player wins a game on one of the small boards. Instead, the position of the small board where that player won is marked on a 3×3 grid, and a player wins when they form 3-in-a-row on that grid.
  • In Tic-Tac-Chess, players play a game of chess and Tic-tac-toe simultaneously. When a player captures an opponent's piece, the player can make a play on the Tic-tac-toe board regardless if the other player has not yet made a play. The first person to get 3 Xs or Os in a row wins the game. This makes for a much more defensive game of chess.
  • Two players fill out a 3×3 grid with numbers one through nine in order of priority. They then compare their grids and play Tic-tac-toe by filling in the squares by the priority they listed before.
  • In the 1970s, there was a two player game made by Tri-ang Toys & Games called Check Lines, in which the board consisted of eleven holes arranged in a geometrical pattern of twelve straight lines each containing three of the holes. Each player had exactly five tokens and played in turn placing one token in any of the holes. The winner was the first player whose tokens were arranged in two lines of three (which by definition were intersecting lines). If neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.
  • Toss Across is a Tic-tac-toe game where players throw bean bags at a large board to mark squares.
  • Star Tic Tac Toe is Tic-tac-toe game where it is played with checkers like movable pieces on 3×3 board. Each player gets 3 pieces.The players move the pieces into empty cells until someone wins. This adds dynamism. In addition each player gets a special piece marked with a star. The stars can be swapped. This adds surprise.
  • Mojo, Mojo Too and Mojo 2 is a Tic-tac-toe game played on a 3×3 board with original and unique movable pieces and pawns – the latter is played for points. The players move the pieces and pawn(s) onto empty positions until someone wins.
  • The object of the fictional D'ni game of Gemedet is to get six balls in-a-row in a 9×9×9 cube grid.
  • The object of the fictional game Squid-Tac-Toad is to get four (or five) pieces in-a-row on a 4×4 or 5×5 checkerboard grid.
  • Some children play where getting a Y formation also counts as a win. This effectively guarantees a win, since all of the game scenarios feature some form of Y formation.
  • Another variation on Tic-tac-toe is played on a larger grid (say 10×10) where the object is to get 5 in a row. The increased amount of space creates a greater complexity.
  • There is a variation on Tic-tac-toe that is popular in Vietnam, in which the player has to get 5 in a row to win the game. Each player takes turns to mark "x" or "o" on the board. The strategy is to not only block the opponent, but create chances for yourself to form 5 in a row in any direction. The board is unlimited and has no boundary until one wins. See Go-moku
  • The game can also be varied by limiting the number of pieces and then allowing movement. The three-a-side then becomes Three Men's Morris (see Nine Men's Morris).
  • Memory tic-tac-toe is played with the same rules as standard Tic-tac-toe. However, instead of marking moves on a piece of paper, the games is played verbally, with each player calling out which locations they take. The most used naming convention is referring to the locations as points as their corresponding cardinal and ordinal points with ″center" referring to the middle piece. In addition to the standard win condition, an optional lose condition may be implemented for a player that "re-touches" an already occupied square. Due to both players trying to keep all the board positions in memory, it may be useful for a third person keep track of the game on paper out of view of the players.
    • Anthony Appleyard (talk) 11:25, 25 April 2015 (UTC)

Earliest reference for noughts and crosses

Hi,

The article states 1864 as the earliest reference in print for "noughts and crosses". Here's one from 1843: https://books.google.com/books?id=RvAKAAAAIAAJ&dq=noughts%20and%20crosses&pg=PA341#v=onepage&q=noughts%20and%20crosses&f=false Battling McGook (talk) 22:48, 3 May 2015 (UTC)

Move Vocabulary

Is it possible to call Move each player's turn? Because it's not like chess, we don't really move anything, we only write signs (glyph) on board or put some figure on it…

What is the specific TTT vocabulary to call this change of state?

I also want to link this discussion about cat's game / tie situation.

http://english.stackexchange.com/questions/155621/why-is-a-tie-in-tic-tac-toe-called-a-cats-game — Preceding unsigned comment added by 2A01:E34:EF23:5C50:C46F:458D:BCEE:5A29 (talk) 09:08, 30 June 2015 (UTC)

External links modified

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When X plays edge first, the best first move of O

1	2	3
4	5	6
7	8	9

When X plays edge (like 2) first, the best first move of O is taking a corner, not the center. (since if O take a corner as first move, O has a higher property to win)

In this article, we assume O is a perfect player (except the first move) (for example, X2 -> O1 -> X9 -> O4 -> X7 -> O8 -> X3 will not happen, since X can take 5 or 6 to win) but X only take a random empty position.

If X takes 2 as first move, and O takes the center (5) as first move, the following will happen:

When X takes 1 as second move:

• X2 -> O5 -> X1 -> O3 -> X7 -> O4 -> X6 -> O8 (9) -> X9 (8), this game will be draw.

When X takes 4 as second move:

• X2 -> O5 -> X4 -> O1 -> X9 -> O3 (6, 7, 8) -> X7/8 (7/8, 3/6, 3/6) -> O8/7 (8/7, 6/3, 6/3) -> X6 (3, 8, 7), this game will be draw.
• X2 -> O5 -> X4 -> O3 (7) -> X7 (3) -> O1 -> X9 -> O8 (6) -> X6 (8), this game will be draw.

When X takes 7 as second move:

• X2 -> O5 -> X7 -> O1 -> X9 -> O8 -> X3 (6) -> O6 (3) -> X4, this game will be draw.
• X2 -> O5 -> X7 -> O3 -> X1 -> O4 -> X6 -> O8 (9) -> X9 (8), this game will be draw.
• X2 -> O5 -> X7 -> O3 -> X4 -> O1 -> X9 -> O8 -> X6, this game will be draw.
• X2 -> O5 -> X7 -> O3 -> X6 -> O1 (4, 8, 9) -> X8/9 (8/9, 1/4, 1/4) -> O9/8 (9/8, 4/1, 4/1) -> X4 (1, 9, 8), this game will be draw.
• X2 -> O5 -> X7 -> O3 -> X8 -> O9, then O can take 1 or 6 to win.
• X2 -> O5 -> X7 -> O3 -> X9 -> O8 -> X1 (4) -> O4 (1) -> X6, this game will be draw.
• X2 -> O5 -> X7 -> O4 -> X6 -> O3 -> X8 (9) -> O9 (8) -> X1, this game will be draw,
• X2 -> O5 -> X7 -> O4 -> X6 -> O9 -> X1 -> O3 -> X8, this game will be draw.
• X2 -> O5 -> X7 -> O6 -> X4 -> O1 -> X9 -> O8 -> X3, this game will be draw.

When X takes 8 as second move:

• X2 -> O5 -> X8 -> O1 -> X9 -> O7, then O can take 3 or 4 to win.

Thus, the win property of O is ${\frac {2}{7}}\cdot {\frac {1}{5}}+{\frac {1}{7}}={\frac {2}{35}}+{\frac {5}{35}}={\frac {7}{35}}={\frac {1}{5}}$.

(${\frac {2}{7}}$ = "X takes 7 or 9 as second move", when X take 7 (9) as second move, O should take 3 (1) as second move, ${\frac {1}{5}}$ = "X takes 8 as third move (when X takes 7 (9) as second move and O takes 3 (1) as second move)", ${\frac {1}{7}}$ = "X takes 8 as second move")

However, if O takes 1 as first move, the following will happen:

When X takes 3 as second move:

• X2 -> O1 -> X3 -> O4 -> X7 -> O5, then O can take 6 or 9 to win.

When X takes 4 as second move:

• X2 -> O1 -> X4 -> O5 -> X9 -> O3 (6, 7, 8) -> X7/8 (7/8, 3/6, 3/6) -> O8/7 (8/7, 6/3, 6/3) -> X6 (3, 8, 7), this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X3 (7) -> O5 -> X9 -> O7 (3)/8 (6) -> X8 (6)/7 (3), this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X3 (7) -> O7 (3) -> X5/8 (6) -> O8 (6)/5 -> X9, this game will be draw,
• X2 -> O1 -> X4 -> O6 (8) -> X3 (7) -> O8 (6) -> X5/7 (3) -> O7 (3)/5 -> X9, this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X5 -> O8 (6) -> X3/7 -> O7/3 -> X9, this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X7 (3) -> O9, then O can take 3 (7) or 5 to win.
• X2 -> O1 -> X4 -> O6 (8) -> X8 (6) -> O5 -> X7 (3)/9 -> O9/7 (3) -> X3 (7), this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X9 -> O5 -> X7 (3)/8 (6) -> O8 (6)/7 (3) -> X3 (7), this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X9 -> O7 (3) -> X5/8 (6) -> O8 (6)/5 -> X3 (7), this game will be draw.
• X2 -> O1 -> X4 -> O6 (8) -> X9 -> O8 (6), then this game can only be draw.

When X takes 5 as second move:

• X2 -> O1 -> X5 -> O8 -> X3 -> O7, then O can take 4 or 9 to win.
• X2 -> O1 -> X5 -> O8 -> X4 -> O6 -> X3 (7) -> O7 (3) -> X9, this game will be draw.
• X2 -> O1 -> X5 -> O8 -> X6 -> O4 -> X7 -> O3 -> X9, this game will be draw,
• X2 -> O1 -> X5 -> O8 -> X7 -> O3 -> X4 (6) -> O6 (4) -> X9, this game will be draw.
• X2 -> O1 -> X5 -> O8 -> X9 -> O3 -> X4 (6) -> O6 (4) -> X7, this game will be draw.
• X2 -> O1 -> X5 -> O8 -> X9 -> O4 -> X7 -> O3 -> X6, this game will be draw.
• X2 -> O1 -> X5 -> O8 -> X9 -> O6 -> X3 (7) -> O7 (3) -> X4, this game will be draw.
• X2 -> O1 -> X5 -> O8 -> X9 -> O7 -> X4 -> O6 -> X3, this game will be draw.

When X takes 6 as second move:

• X2 -> O1 -> X6 -> O7 -> X4 -> O5, then O can take 3 or 9 to win.

When X takes 7 as second move:

• X2 -> O1 -> X7 -> O5 -> X9 -> O8 -> X3 (6) -> O6 (3) -> X4, this game will be draw.
• X2 -> O1 -> X7 -> O8 -> X3 -> O5 -> X9 -> O6 -> X4, this game will be draw.
• X2 -> O1 -> X7 -> O8 -> X4 -> O3 -> X5 (6) -> O6 (5) -> X9, this game will be draw.
• X2 -> O1 -> X7 -> O8 -> X5 -> O3 -> X4 (6) -> O6 (4) -> X9, this game will be draw.
• X2 -> O1 -> X7 -> O8 -> X6 -> O3 (4, 5, 9) -> X4/5 (3/9, 9, 5) -> O5/4 (9/3, 3, 4) -> X9 (5, 4, 3), this game will be draw.
• X2 -> O1 -> X7 -> O8 -> X9 -> O3, then this game can only be draw,
• X2 -> O1 -> X7 -> O8 -> X9 -> O5 -> X3 (6) -> O6 (3) -> X4, this game will be draw.
• X2 -> O1 -> X7 -> O8 -> X9 -> O6 -> X3 (5) -> O5 (3) -> X4, this game will be draw.

When X takes 8 as second move:

• X2 -> O1 -> X8 -> O5 -> X9 -> O7, then O can take 3 or 4 to win.

When X takes 9 as second move:

• X2 -> O1 -> X9 -> O5 -> X3 -> O6 -> X4 -> O7 (8) -> X8 (7), this game will be draw,
• X2 -> O1 -> X9 -> O5 -> X4 -> O3 (6, 7, 8) -> X7/8 (7/8, 3/6, 3/6) -> O8/7 (8/7, 6/3, 6/3) -> X6 (3, 8, 7), this game will be draw.
• X2 -> O1 -> X9 -> O5 -> X6 -> O3 -> X7 -> O8 -> X4, this game will be draw,
• X2 -> O1 -> X9 -> O5 -> X7 -> O8 -> X3 (6) -> O6 (3) -> X4, this game will be draw.
• X2 -> O1 -> X9 -> O5 -> X8 -> O7, then O can take 3 or 4 to win.
• X2 -> O1 -> X9 -> O7 -> X4 -> O5 -> X3 -> O6 -> X8, this game will be draw,
• X2 -> O1 -> X9 -> O7 -> X4 -> O6 -> X5 (8) -> O8 (5) -> X3, this game will be draw.
• X2 -> O1 -> X9 -> O8 -> X3 -> O6 -> X5 (7) -> O7 (5) -> X4, this game will be draw.
• X2 -> O1 -> X9 -> O8 -> X4 -> O3 -> X5 (6) -> O6 (5) -> X7, this game will be draw.
• X2 -> O1 -> X9 -> O8 -> X4 -> O5 -> X3 (6) -> O6 (3) -> X7, this game will be draw.
• X2 -> O1 -> X9 -> O8 -> X4 -> O6, then this game can only be draw.
• X2 -> O1 -> X9 -> O8 -> X5 -> O3 -> X4 (6) -> O6 (4) -> X7, this game will be draw,
• X2 -> O1 -> X9 -> O8 -> X5 -> O4 -> X7 -> O3 -> X6, this game will be draw.
• X2 -> O1 -> X9 -> O8 -> X5 -> O6 -> X3 (7) -> O7 (3) -> X4, this game will be draw.
• X2 -> O1 -> X9 -> O8 -> X5 -> O7 -> X4 -> O6 -> X3, this game will be draw.

Thus, the win property of O is ${\frac {3}{7}}+{\frac {1}{7}}\cdot {\frac {1}{5}}+{\frac {1}{7}}\cdot {1}{5}+{\frac {1}{7}}\cdot {\frac {1}{5}}={\frac {15}{35}}+{\frac {1}{35}}+{\frac {1}{35}}+{\frac {1}{35}}={\frac {18}{35}}$.

(${\frac {3}{7}}$ = "X takes 3, 6 or 8 as second move", ${\frac {1}{7}}$ = "X takes 4 as second move", when X takes 4 as second move, O should take 6 or 8 as second move, ${\frac {1}{5}}$ = "X takes 7 (3) as third move (when X takes 4 as second move and O takes 6 (8) as second move)", ${\frac {1}{7}}$ = "X takes 5 as second move", ${\frac {1}{5}}$ = "X takes 3 as third move (when X takes 5 as second move)", ${\frac {1}{7}}$ = "X takes 9 as second move", when X takes 9 as second move, O should take 5 as second move, ${\frac {1}{5}}$ = "X takes 8 as third move (when X takes 9 as second move and O takes 5 as second move)")

If O takes 7 as first move, the following will happen:

When X takes 1 as second move:

• X2 -> O7 -> X1 -> O3 -> X5, then X can take 8 or 9 to win.

When X takes 3 as second move:

• X2 -> O7 -> X3 -> O1 -> X4 -> O9, then O can take 5 or 8 to win.

When X takes 4 as second move:

• X2 -> O7 -> X4 -> O9 -> X8 -> O5, then O can take 1 or 3 to win.

When X takes 5 as second move:

• X2 -> O7 -> X5 -> O8 -> X9 -> O1 -> X4 -> O6 -> X3, this game will be draw.

When X takes 6 as second move:

• X2 -> O7 -> X6 -> O9 -> X8 -> O5, then O can take 1 or 3 to win.

When X takes 8 as second move:

• X2 -> O7 -> X8 -> O5 -> X3 -> O1, then O can take 4 or 9 to win.

When X takes 9 as second move:

• X2 -> O7 -> X9 -> O1 -> X4 -> O5 -> X3 -> O6 -> X8, this game will be draw.
• X2 -> O7 -> X9 -> O1 -> X4 -> O6 -> X5 (8) -> O8 (5) -> X3, this game will be draw.

Thus, the win property of O is ${\frac {4}{7}}$.

(${\frac {4}{7}}$ = "X takes 3, 4, 6 or 8 as second move")

Besides, both ${\frac {18}{35}}$ and ${\frac {4}{7}}$ are greater than ${\frac {1}{5}}$. (although if O takes 7 as first move, O may be lose, when and only when X takes 1 as second move, the property is only ${\frac {1}{7}}$) Thus, the best first move of O (when X plays edge first) is a corner, not the center! — Preceding unsigned comment added by 101.9.98.209 (talk) 17:10, 7 October 2016 (UTC)

Work in progress: Combinatorics

The section "Combinatorics" had a number of issues - sources, spelling, formatting, at least - and I think the lay reader is better served by having the section removed from the article until it is in a more polished state. PLEASE do not move all of it back "as is", but perhaps some parts of it were fairly OK; I'm not sure. Anyway, here is what I removed. Feel free to edit it here on the talk page, or discuss changes below.

Combinatorics

The first two plies of the game tree for tic-tac-toe. Once rotations and reflections are eliminated, there are only three opening moves – a corner, a side or the middle.

Despite its apparent simplicity, Tic-tac-toe requires detailed analysis to determine even some elementary combinatory facts, the most interesting of which are the number of possible games and the number of possible positions. A position is merely a state of the board, while a game usually refers to the way a terminal position is obtained.

Naive counting leads to 19,683 possible positions (3⁹ since each of the nine spaces can be X, O or blank), and 362,880 (i.e., 9!) possible games (different sequences for placing the Xs and Os on the board). However, two matters much reduce these numbers:

• The game ends when three-in-a-row is obtained.
• If X starts, the number of Xs is always either equal to or exactly 1 more than the number of Os.

The complete analysis is further complicated by the definitions used when setting the conditions, like board symmetries. Consider a board with the nine positions named as follows:

a	b	c
d	e	f
g	h	i

Possible symmetry are

1. Identity (a)(b)(c)(d)(e)(f)(g)(h)(i) 3⁹
2. 90 deg Rotation Clockwise(acig)(bfhd)(e) 3⁹
3. 180 deg Rotation Clockwise (ai)(bh)(ig)(fd)(e) 3⁵
4. 270 deg Rotation Clockwise(acig)(bdhf)(e) 3⁹
5. Reflection respect the vertical axe (ac)(df)(gi)(b)(e)(h) 3⁶
6. Reflection respect the horizontal axe (ac)(df)(gi)(b)(e)(h) 3⁶
7. Reflection respect 45 deg the one trough (gec) (ai)(bf)(dh)(e)(c)(g) 3⁶
8. Reflection respect 135 deg the one trough (aei) (cg)(db)(hf)(a)(e)(1) 3⁶

Because those symmetries plus the identity acting on the positions of the TIC-TAC-TOE are a permutation Group we can use the Polya method to enumerate the equivalent states, by the Orbit formula we have than that the number of orbits (the different 3-coloring pattern of our Tic-Tac-Toe board) is 2862 non symmetrical equivalents states. But many of them are not possible boards, according to the rules of the game. In the early 1960s Donald Michie proved that his M.e.n.a.c.e.,a Machine Educable Noughts And Crosses Engine, coud learn play tic tac toe with only 304 MatchBoxes so we need some euristic to reduce useful states. Since the X start first, we will have always a number of O in ours boards equals to the numbers of X or to X-1 (when is time to play for O), different numbers of symbols reefers to ILLEGALS boards. We also check for boards with 2 tris because of course the match will stop early, or we are at the end of the game if the X realize 2 tris.

Without symmetric reductions	With reduction by symmetry	furter info
19683	Overall Primary 2862	Example
Valid Boards 5868	Primary Valid 820	Symmetric 16821
MIDDLEGAME 4520	Primary middlegame 627	Box for player X 338, Box for Player O 289
WINNING 1332	Primary Winning "X" 129 "O" 61
DRAW 16	Primary Draw 3
ILLEGAL 13815	Primary illegal 2042	Simmetrical Illigal 11773

In a computer simultaion of the MENACE the final states (winnings & draws) doesn’t need any board-allocation because only the previous state should contain the beads to lead the move, we have to allocate boxes only for the 627 Middle game states and because X will choose only when it’s up to him to move we will need 338 Box for the player X and 289 for the player O. Analyzing the following table we can improve little further because we can easily found some illegal states and some unnecessary ones.

Level	Board	X wins	O wins	Draw
0 X	1	0	0	0
1 O	3	0	0	0
2 X	12	0	0	0
3 O	38	0	0	0
4 X	108	0	0	0
5 O	153	21	0	0
6 X	183	21*	21	0
7 O	95	58	15**	0
8 X	34	23*	23	0
9 --	0	6	2**	3

No winnings games for player X at level 6 and 8 *

No winnings games for player O at level 7 and 9 **

But already included into the winning set so no boards to eliminate,

We coud eliminate the 34 boards of the level 8 because in that case X have no choose but has only one possible move.

We have now the 304 MatchBoxes of the original M.E.N.A.C.E.

--Nø (talk) 15:19, 30 May 2017 (UTC)

Best opening move is misleading / wrong

The article currently says:

"Player X can win or force a draw from any of these starting marks; however, playing the corner gives the opponent the smallest choice of squares which must be played to avoid losing[16]. This makes the corner the best opening move for X, when the opponent is not a perfect player."

This is based on a reference to Gardner (16) but his work does not exactly show why this is so, and either way, I have published an article which tends to disagree. Furthermore, Gardners work refers to "rational" players, which I understand to be the opposite of "not a perfect player", and I am unsure why it says "not a perfect player" rather than "is a perfect player", or indeed why that phrase at the end of the paragraph is necessary or what it adds. Why is this even so?

As such I shall edit the article. My article is here: http://blog.maxant.co.uk/pebble/2018/04/07/1523086680000.html

Akayet (talk) 19:55, 7 April 2018 (UTC)

Simplest strategy for X?

In case it deserves mention in the article, and assuming I didn't overlook it there, probably the simplest strategy for X is to start in the center (5 with the numbering in the article) and then answer each of O's moves "almost-opposite". So if O starts in 1, X replies with 6, if in 2 then 9, and so on. This strategy gradually rotates the play counterclockwise, thereby forcing O's every subsequent move; if O doesn't move where forced the game immediately ends with a win for X, otherwise after all 9 moves it ends with a draw.

I believe this strategy was used in the 1950s for a toy computer playing the game. As a freshman at Sydney University in 1962 I designed and built a machine out of some multipole relays and two telephone exchange stepping switches that implemented this strategy. This was the first computer of any kind that I ever had anything to do with, obviously not a stored-program computer of course. My first encounter with a stored program computer was two years later. Vaughan Pratt (talk) 01:54, 12 June 2018 (UTC)

Can’t this article just fit into another one &/ be renamed

Should this article be renamed to Xs & Os and or merged with 3 men merellus since it is only slightly different, XO just places stuff in a box while 3 men merellus allows moving about. Xs & Os (or Exes & Ohs) can just simply be a section of 3 Men Morris.

These are good solutions to the differing terms problem with the American term dominance currently on the article. Chocolateediter (talk) 21:04, 18 November 2020 (UTC)

or SOS (game) Chocolateediter (talk) 21:06, 18 November 2020 (UTC)

Tic tac toe

So we will be doing tic tac tor 86.9.134.224 (talk) 18:05, 3 May 2022 (UTC)

can i add unofficial versions of tic tac toe

just asking Some random editor from nowhere (talk) 19:24, 29 October 2022 (UTC)

Only with in-depth publications in journals or books as references about them. See our prohibition on original research. —David Eppstein (talk) 20:13, 29 October 2022 (UTC)

Tic-Oat-Two

Add it 2A0B:F100:22:21B7:CDCA:F310:25E9:46F5 (talk) 14:44, 29 November 2022 (UTC)

Page WAY too long

The only useful sentence in this article:

"Players soon discover that the best play from both parties leads to a draw. Hence, tic-tac-toe is often played by young children who may not have discovered the optimal strategy."

All the other stuff is fluff and can never happen since only infants would fail to know how to get a draw.

Tic-Tac-Toe is basically a non game, or no better than a shell game. If a game is bound to end in a draw, is it a "game", nah. Tallard (talk) 20:22, 1 April 2023 (UTC)

Semi-protected edit request on 16 April 2023

Remove hyphens after “universally” and “mentally”. These are adverbs and are not hyphenated before the words they modify. Misemefein (talk) 18:29, 16 April 2023 (UTC)

 Done M.Bitton (talk) 20:21, 16 April 2023 (UTC)

Semi-protected edit request on 9 June 2023

I need to add something on tic tac toe a variant of the game has been left off the list 11111s (talk) 21:04, 9 June 2023 (UTC)

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. JTP ^{(talk • contribs)} 21:15, 9 June 2023 (UTC)

An anecdote about nursing homes which may not belong in the article.

In nursing homes, if staff suspect dementia, a quick informal test is to play a game of Tic-Tac-Toe with the patient going 1st. If it ends in a draw, the staff figure that the resident is reasonable cognitively intact. If the resident looses, the staff arrange for proper cognitive tests, which always show dementia (cognitively intact adults playing Knots-And-Crosses always end in draws, without exceptions). The staff accompany this test with asking the patient to draw an analogue clock showing a specific time. If the resident fails either informal test, the formal test is just a formality because the staff know that the formal test will show dementia. — Preceding unsigned comment added by 73.189.192.219 (talk) 10:58, 9 March 2024 (UTC)

Noughts and crosses, by the way. —Tamfang (talk) 19:13, 17 April 2024 (UTC)

How many games of Tic-tac-toe are there?

There are 9 possible squares on the first move. 8 on the second move, 7 on the third, and so on. That means there are 9! (362,880) games of tic-tac-toe. but are there really? Some games are over before every square is filled in. So, if you stop playing after someone win, you get rid of 107,712 games and end up with 255,168 games. But we can still keep going! A game that starts like this: X5-> O1-> X3-> O7 is the same as: X5-> O9-> X7-> O3. There are only 3 opening moves: 1. The center 2. The edge 3. The corner. If you choose 2 or 3, the symmetry of the board means that it doesn't matter which edge or corner you choose. So that rules out 223,272 games and end up with 31,896 games.

history section

reference for terni lapilli is broken 5.151.181.34 (talk) 09:59, 25 October 2024 (UTC)