tick-tack-toe n : a game in which two players alternately put crosses and circles in one of the compartments of a 3-by-3 board; the object is to get a row of three crosses or three circles before the opponent does [syn: ticktacktoe, ticktacktoo, tic-tac-toe, tit-tat-toe, noughts and crosses]ticktacktoe n : a game in which two players alternately put crosses and circles in one of the compartments of a 3-by-3 board; the object is to get a row of three crosses or three circles before the opponent does [syn: ticktacktoo, tick-tack-toe, tic-tac-toe, tit-tat-toe, noughts and crosses]
Tic-tac-toe, also called noughts and crosses, hugs and kisses, and many other names, is a pencil-and-paper game for two players, O and X, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three respective marks in a horizontal, vertical or diagonal row wins the game. This game is won by the first player, X:
This is a "cat's game", that is, a draw:
Players soon discover that best play from both parties leads to a draw. Hence, tic-tac-toe is most often played by very young children; when they have discovered an unbeatable strategy they move on to more sophisticated games such as dots and boxes. This reputation for ease has led to casinos offering gamblers the chance to play tic-tac-toe against trained chickens.
The simplicity of tic-tac-toe makes it ideal as a pedagogical tool for teaching the concepts of combinatorial game theory and the branch of artificial intelligence that deals with the searching of game trees. It is straightforward to write a computer program to play tic-tac-toe perfectly, to enumerate the 765 essentially different positions (the state space complexity), or the 26,830 possible games up to rotations and reflections (the game tree complexity) on this space.
The first known video game, OXO (or Noughts and Crosses, 1952) for the EDSAC computer played perfect games of tic-tac-toe against a human opponent.
One example of a Tic-Tac-Toe playing computer is the Tinkertoy computer, developed by MIT students, and made out of Tinker Toys. It only plays Tic-Tac-Toe, and has never lost a game. It is currently on display at the Museum of Science, Boston.
Number of possible gamesDespite its apparent simplicity, it requires some complex mathematics to determine the number of possible games. This is further complicated by the definitions used when setting the conditions.
Simplistically, there are 362,880 (ie. 9!) ways of placing Xs and Os on the board, without regard to winning combinations.
When winning combinations are considered, there are 255,168 possible games. Assuming that X makes the first move every time:
- 131,184 finished games are won by (X)
- 1,440 are won by (X) after 5 moves
- 47,952 are won by (X) after 7 moves
- 81,792 are won by (X) after 9 moves
- 77,904 finished games are won by (O)
- 5,328 are won by (O) after 6 moves
- 72,576 are won by (O) after 8 moves
- 46,080 finished games are drawn
Ignoring the sequence of Xs and Os, and after eliminating symmetrical outcomes (ie. rotations and/or reflections of other outcomes), there are only 138 unique outcomes. Assuming once again that X makes the first move every time:
- 91 unique outcomes are won by (X)
- 21 won by (X) after 5 moves
- 58 won by (X) after 7 moves
- 12 won by (X) after 9 moves
- 44 unique outcomes are won by (O)
- 21 won by (O) after 6 moves
- 23 won by (O) after 8 moves
- 3 unique outcomes are drawn
A player can play perfect tic-tac-toe if they choose the move with the highest priority in the following table.
- Win: complete three in a row.
- Block: block their opponent from completing three in a row
- Fork: threaten a win with two possible completions in two ways
- Block Fork:
- Option 1: create two in a row to force a block (Note:
Sometimes, if one forces a block in this manner, the other player's
block will result in a fork and a winning position, so care must be
taken when there is more than one way to create two in a row. For
example, if X has played the center and a corner, and o is in the
opposite corner, o must play a corner and not an edge or else x
- Option 2: if there is a configuration where the opponent can fork, block that fork
- Option 1: create two in a row to force a block (Note: Sometimes, if one forces a block in this manner, the other player's block will result in a fork and a winning position, so care must be taken when there is more than one way to create two in a row. For example, if X has played the center and a corner, and o is in the opposite corner, o must play a corner and not an edge or else x will win).
- Centre: play the centre
- Opposite Corner: if the opponent is in the corner, play the opposite corner
- Empty Corner: play an empty corner
- Empty Side: play on an empty side
The first player, whom we shall designate "X," has 3 possible positions to mark during the first turn. Superficially, it might seem that there are 9 possible positions, corresponding to the 9 squares in the grid. However, by rotating the board, we will find that in the first turn, every corner mark is strategically equivalent to every other corner mark. The same is true of every edge mark. For strategy purposes, there are therefore only three possible first marks: corner, edge, or center. 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.
The second player, whom we shall designate "O," must respond to X's opening mark in such a way as to avoid the forced win. Player O must always respond to a corner opening with a center mark, and to a center opening with a corner mark. An edge opening must be answered either with a center mark, a corner mark next to the X, or an edge mark opposite the X. Any other responses will allow X to force the win. Once the opening is completed, O's task is to follow the above list of priorities in order to force the draw, or else to gain a win if X makes a weak play.
VariationsMany board games share the element of trying to be the first to get n-in-a-row: three men's morris, nine men's morris, pente, gomoku, Qubic, Connect Four, Quarto, Gobblet. The m,n,k-games are a family of generalized games based on tic-tac-toe.
- 3-dimensional tic-tac-toe on a 3×3×3 board, though the first player has an easy win by playing in the centre. Another variant is played on a 4×4×4 board though it was solved by Victor Allis in 1994 (the first player can force a win). 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.
- 4 player 3-dimensional tic-tac-toe: Not as easy to win by the first player, the symbols are O's X's triangles and squares, otherwise the rules to 3-D tic-tac-toe apply.
- In misère tic-tac-toe you win if the other player gets n in a row. The 3×3 game is a draw.
- 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 can't 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.
- 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 X's or O's in a row wins the game. This makes for a much more defensive game of chess.
- There is a game that is isomorphic to tic-tac-toe, but on the surface appears completely different. Two players in turn say a number between one and nine. A particular number may not be repeated. The game is won by the player who has said three numbers whose sum is 15. Plotting these numbers on a 3×3 magic square shows that the game exactly corresponds with tic-tac-toe, since three numbers will be arranged in a straight line if and only if they total 15.
- 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.
- Various game shows have
been based around the game:
- On Hollywood Squares nine celebrities filled the cells of the tic-tac-toe grid.
- In Secret "X", a pricing game on The Price is Right, contestants must get three Xs in a row by correctly pricing items, and then find the one X in the middle column to complete a line.
- In Tic-Tac-Dough players put symbols up on the board by answering questions in various categories.
- In Beat the Teacher contestants answer questions to win a turn to influence a tic-tac-toe grid.
- 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.
- Quantum tic tac toe allows players to place a quantum superposition of numbers on the board
- Another variation on tic-tac-toe is played on a larger grid (say 10x10) where the object is to get 5 in a row. The increased amount of space creates a greater complexity.
- Another variation on tic-tac-toe that is popular in Vietnam that the player has to get 5 in a row to win the game. It's called CroaZero (not sure if this is the correct spelling - could be CrossZero. Each player takes turn to mark "x" and "o" on the board. The stategy is to not only blocking the opponent, but creating chances for yourself to form 5 in a row in any direction. The board is unlimited and has no boundary until one wins.
Alternative namesAround the world, the game has a number of alternative names.
- Tic-tac-toe, tick-tat-toe, or tit-tat-toe (USA , Canada)
- Noughts and crosses or naughts and crosses (United
Kingdom, Ireland, Australia,
- "Noughts and crosses" is a sensibly descriptive name for the game, except in the United States, where "nought" is regarded as an archaism and where a lone "x" is not generally referred to as a "cross".
- Kringetjies en Kruisies (South Africa)
- Kaat koot or Zero-kata (Hinglish - India)
- Katam kataa (Hindi - India)
- Ix Igul (X Circle) (Israel)
- Kata kuti (Bangladesh and West Bengal)
- Phulli Gola (Marathi)
- Exy-Ozys, Xsie-Osies (verbal name only) (Northern Ireland)
- Boxin' OXen (Republic of Ireland)
- X's and O's (Republic of Ireland) , Canada, (Dundee,Scotland)
- Tee-taa-toe (Jamaica)
- X si O (Romania)
- Amőba (Hungary)
- Luffarschack (Sweden)
- Jogo do Galo (meaning "Rooster's Game") (Portugal)
- Jogo da Velha (meaning "Old Lady's Game") (Brazil)
- Tris, filetto, crocetta e pallino, cerchi e croci, or tria (Italy)
- Kółko i krzyżyk (a circle and a cross) (Poland)
- Boter, kaas en eieren (Butter, cheese, and eggs) (Netherlands)
- Morpion (France)
- Tres en raya (Spain and Ecuador)
- Gato (Chile, México and Costa Rica)
- Iks-Oks (Serbia and Mongolia)
- Križić-kružić (a circle and a cross) (Croatia)
- Kaat kar ya Zero Pa (UPunjabi - Pakistan)
- Michi (Perú)
- Križci in krožci (crosses and circles) (Slovenia)
- Крестики-нолики (crosses and zeroes) (Russia)
- Морски шах (sea chess) (Bulgaria)
- Ta-Te-Ti (Argentina)
- Τρίλιζα (Triliza) (Greece)
- X ṣi Zero (Romania)
- X O (Iran, Egypt, Arabic Speaking Countries)
- Cüz (Turkey)
- Bondesjakk (farmer's chess) (Norway)
- La Vieja (Venezuela)
- Piškvorky (Czech Republic and Slovakia)
- Triqui (Colombia)
- Bicho Chocha (XO)(Mexico)
- دووز (Iran)
- Ristinolla(cross-zero) or Jätkänshakki((Finland)
- Equis Cero (XO) (Dominican Republic)
- Trips-traps-trull (Estonia)
- X Mix Drix (Israel)
- Kryds og Bolle (Cross and buns) (Denmark)
- Deppenschach (Austria)
- Croa-Zero (Vietnam)
- Cross-Zero (Vietnam)
- 圓圈交叉 (circle-cross), 井字過三關 (Hong Kong)
- Mylla (mill) (Iceland)
- Desas (Sausages) (Latvia)
Sometimes, the names of the games Tic-tac-toe (where players keep adding "pieces") and Three Men's Morris (where pieces start to move after a certain number have been placed) are confused.
In the film, teenage computer hacker David Lightman (Matthew Broderick) unknowingly breaks into the United States' defense computer, WOPR, where he innocently starts a game of "Global Thermonuclear War". This triggers a sequence of events that eventually leads to the computer preparing to launch actual nuclear missiles. Lightman eventually influences the computer to play tic-tac-toe against itself, whereby the computer determines that neither side can win-–an analogy to full scale nuclear war, which is made explicit when the computer then fails to find a winning stratagem for a nuclear strike. The computer then concludes that "[t]he only winning move is not to play" and indicates a desire for a game of chess instead.
- Wolfram's MathWorld
- Ostermiller.org Tic-Tac-Toe strategy guide
- How many Tic-Tac-Toe games are possible?
- Tic Tac Toe Extreme (Multiplayer Tic Tac Toe)
- A free Tic-Tac-Toe game online
- Multi Tic-Tac-Toe Games 3x3, 4x4, 6x6
- ChessandPoker.com step-by-step strategy guide for both players
- PDF of "How to Win at Tic-Tac-Toe"
- Demonstration of isomorphism between Tic-Tac-Toe and 'Game of 15'
- iPod Tic-Tac-Toe.
- Where does tic tac toe come from?
- New 5x5x5 3D TTT PC Game!
- Wicked Tic-Tac-Toe
ticktacktoe in Belarusian (Tarashkevitsa): Крыжыкі-нулікі
ticktacktoe in Catalan: Tres en ratlla
ticktacktoe in Czech: Piškvorky
ticktacktoe in Danish: Kryds og bolle
ticktacktoe in German: Tic Tac Toe
ticktacktoe in Spanish: Tres en raya
ticktacktoe in French: Morpion (jeu)
ticktacktoe in Galician: Pai fillo nai
ticktacktoe in Korean: 틱택토
ticktacktoe in Croatian: Kružić i križić
ticktacktoe in Italian: Tris (gioco)
ticktacktoe in Hebrew: איקס עיגול
ticktacktoe in Latin: Cruces et circuli
ticktacktoe in Lithuanian: Kryžiukai-nuliukai
ticktacktoe in Dutch: Boter, kaas en eieren
ticktacktoe in Japanese: 三目並べ
ticktacktoe in Polish: Kółko i krzyżyk
ticktacktoe in Portuguese: Jogo da velha
ticktacktoe in Russian: Крестики-нолики
ticktacktoe in Serbian: Икс-окс
ticktacktoe in Finnish: Ristinolla
ticktacktoe in Swedish: Tic Tac Toe
ticktacktoe in Thai: โอเอกซ์
ticktacktoe in Vietnamese: Tictactoe
ticktacktoe in Chinese: 井字過三關