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the first turn, every corner mark is strategically equivalent to every other corner mark. The same is true of every edge (side middle) mark. From a strategic point of view, 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. This might suggest that the corner is the best opening move for X, however another study shows that if the players are not perfect, an opening move in the center is best for X.
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412:. The first print reference to a game called "tick-tack-toe" occurred in 1884, but referred to "a children's game played on a slate, consisting of trying with the eyes shut to bring the pencil down on one of the numbers of a set, the number hit being scored". "Tic-tac-toe" may also derive from "tick-tack", the name of an old version of
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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. If all the numbers are used and no one gets three numbers that add
551:
If X plays a corner opening move, O should take center, and then an edge, forcing X to block in the next move. This will stop any forks from happening. When both X and O are perfect players and X chooses to start by marking a corner, O takes the center, and X takes the corner opposite the original.
543:
The second player, who shall be designated "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
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The first player, who shall be designated "X", has three possible strategically distinct positions to mark during the first turn. Superficially, it might seem that there are nine possible positions, corresponding to the nine squares in the grid. However, by rotating the board, we will find that, in
1155:
Another isomorphic game uses a list of nine carefully chosen words, for instance "try", "be", "on", "any", "boat", "by", "ten", "or", and "fear". Each player picks one word in turn and to win, a player must select three words with the same letter. The words may be plotted on a tic-tac-toe grid in
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Blocking an opponent's fork: If there is only one possible fork for the opponent, the player should block it. Otherwise, the player should block all forks in any way that simultaneously allows them to make two in a row. Otherwise, the player should make a two in a row to force the opponent into
491:
Optimal strategy for player X if starting in upper left. In each grid, the shaded red X denotes the optimal move, and the location of O's next move gives the next subgrid to examine. Only two sequences of moves by O (both starting with the center, top-right, left-mid) lead to a draw, with the
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called "Secret X", in which players must guess prices of two small prizes to win Xs (in addition to one free X) to place on a blank board. They must place the Xs in position to guess the location of the titular "secret X" hidden in the center column of the board and form a tic-tac-toe line
567:
If O responds with a center mark (best move for them), a perfect X player will take the corner opposite the original. Then O should play an edge. However, if O plays a corner as its second move, a perfect X player will mark the remaining corner, blocking O's 3-in-a-row and making their own
1342:, the game Ping Tac Toe has one contestant playing the game with nine water-filled glasses and white and orange ping-pong balls, trying to get three in a row of either color. They must alternate colors after each successful landing and must be careful not to block themself.
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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
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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.
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In that case, O is free to choose any edge as its second move. However, if X is not a perfect player and has played a corner and then an edge, O should not play the opposite edge as its second move, because then X is not forced to block in the next move and can fork.
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If X plays edge opening move, O should take center or one of the corners adjacent to X, and then follow the above list of priorities, mainly paying attention to block forks. With perfect play, O can also force a draw by taking the opposite edge from
522:
defending, as long as it does not result in them producing a fork. For example, if "X" has two opposite corners and "O" has the center, "O" must not play a corner move to win. (Playing a corner move in this scenario produces a fork for "X" to win.)
387:) and instead of having any number of pieces, each player had only three; thus, they had to move them around to empty spaces to keep playing. The game's grid markings have been found chalked all over Rome. Another closely related ancient game is
1163:. The numbers 1 to 9 are used in this game. The first player plays with the odd numbers, and the second player plays with the even numbers. All numbers can be used only once. The player who puts down 15 points in a line wins (sum of 3 numbers).
525:
Center: A player marks the center. (If it is the first move of the game, playing a corner move gives the second player more opportunities to make a mistake and may therefore be the better choice; however, it makes no difference between perfect
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If O responds with a corner mark, X is guaranteed to win. By taking any of the other two corners, O can only take the position between the two Xs, then by taking the remaining corner to create a fork, X will win on the next
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allows players to place a quantum superposition of numbers on the board, i.e. the players' moves are "superpositions" of plays in the original classical game. This variation was invented by Allan Goff of
Novatia
1183:
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
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in a row. A 3×3 game is a draw. More generally, the first player can draw or win on any board (of any dimension) whose side length is odd, by playing first in the central cell and then mirroring the opponent's
209:), the game is known as "noughts and crosses", alternatively spelled "naughts and crosses". This name derives from the shape of the marks in the game (i.e the X and O); "nought" is an older name for the number
575:
If O responds with an edge mark, X is guaranteed to win. By taking center, O can only take the corner opposite the corner which X plays first, then by taking a corner to create a fork, X will win on the next
1267:, nine celebrities filled the cells of the tic-tac-toe grid; players put symbols on the board by correctly agreeing or disagreeing with a celebrity's answer to a question. Variations of the show include
508:
of tic-tac-toe (to win or at least draw) if, each time it is their turn to play, they choose the first available move from the following list, as used in Newell and Simon's 1972 tic-tac-toe program.
213:, while "cross" refers to the X shape. While the term "nought" is now less commonly used, the name "noughts and crosses" is still preferred over the American name "tic-tac-toe" in these countries.
1861:
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or 6 (in this situation, O should not take 4 or 7, O should take 2, 3, 8 or 9. In fact, taking 9 is the best move, since a non-perfect player X may take 4, then O can take 7 to win).
360:. Tic-tac-toe's incidence structure consists of nine points, three horizontal lines, three vertical lines, and two diagonal lines, with each line consisting of at least three points.
464:
When considering only the state of the board, and after taking into account board symmetries (i.e. rotations and reflections), there are only 138 terminal board positions. A
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One can play on a board of 4x4 squares, winning in several ways. Winning can include: 4 in a straight line, 4 in a diagonal line, 4 in a diamond, or 4 to make a square.
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There is also a variant of the game with the classic 3×3 field, in which it is necessary to make two rows to win, while the opposing algorithm only needs one.
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When X plays 1 as their opening move, then O should take 5. Then X takes 9 (in this situation, O should not take 3 or 7, O should take 2, 4, 6 or 8):
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is described as similar to tic-tac-toe, in that if all sides engage in full-scale use of their arsenals with the most effective strategies possible,
2016:
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X1 → O5 → X6 → O2 → X8, then O should not take 3, or X can take 7 to win, and O should not take 4, or X can take 9 to win, O should take 7 or 9.
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If X plays the center opening move, O should take a corner, and then follow the above list of priorities, mainly paying attention to block forks.
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elements. The
Tinkertoy computer, made out of (almost) only Tinkertoys, is able to play tic-tac-toe perfectly. It is currently on display at the
984:
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.
272:. It is straightforward to write a computer program to play tic-tac-toe perfectly or to enumerate the 765 essentially different positions (the
2201:
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Tic-tac-toe is played on a three-by-three grid by two players, who alternately place the marks X and O in one of the nine spaces in the grid.
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3-dimensional tic-tac-toe on a 3×3×3 board. In this game, the first player has an easy win by playing in the centre if 2 people are playing.
1310:, players put symbols up on the board by answering questions in various categories, which shuffle after both players have taken both turns.
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441:, became one of the first known video games. The computer player could play perfect games of tic-tac-toe against a human opponent.
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X1 → O5 → X6 → O9 → X8 → O2 (3, 4, 7) → X4/7 (4/7, 2/3, 2/3) → O7/4 (7/4, 3/2, 3/2) → X3 (2, 7, 4), this game will be a draw.
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162:. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row is the winner. It is a
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There is no universally agreed rule as to who plays first, but in this article the convention that X plays first is used.
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PRICAI 2014: Trends in
Artificial Intelligence: 13th Pacific Rim International Conference on Artificial Intelligence
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1236:, with the moves being chosen by computer and indicated to the chicken with a light invisible to the human player.
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first described in 1558. The US renaming of "noughts and crosses" to "tic-tac-toe" occurred in the 20th century.
2322:
Goff, Allan (November 2006). "Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics".
182:, the game is known as "tic-tac-toe". It may also be spelled "tick-tack-toe", "tick-tat-toe", or "tit-tat-toe".
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1232:. Arcade games with tic-tac-toe-playing chickens were popular in the mid-1970s; the animals were trained using
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If X is not a perfect player, X may take 2 or 3 as a second move. Then this game will be a draw, X cannot win.
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horizontally (across) or diagonally (no vertical lines allowed). There are no Os in this variant of the game.
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284:) on this space. If played optimally by both players, the game always ends in a draw, making tic-tac-toe a
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Although O takes the only good position (5) as the first move, O takes a bad position as the second move:
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Block: If the opponent has two in a row, the player must play the third themselves to block the opponent.
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study of the game shows that when "X" makes the first move every time, the game outcomes are as follows:
253:. Hence, tic-tac-toe is often played by young children who may not have discovered the optimal strategy.
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is an even broader generalization. The game can be generalised even further by playing on an arbitrary
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The different names of the game are more recent. The first print reference to "noughts and crosses" (
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Optimal strategy for player O. Player O can only force a win or draw by playing in the center first.
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220:(where pieces start to move after a certain number have been placed) are confused with each other.
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Although O takes good positions in the first two moves, O takes a bad position in the third move:
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X1 → O5 → X6 → O9, then X should not take 4, or O can take 7 to win, X should take 2, 3, 7 or 8.
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in 1980 (the first player can force a win). Higher dimensional variations are also possible.
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being an alternative word for 'zero'), the
British name, appeared in 1858, in an issue of
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Fork: Cause a scenario where the player has two ways to win (two non-blocked lines of 2).
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Opposite corner: If the opponent is in the corner, the player plays the opposite corner.
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which is also played on a simple grid and requires three pieces in a row to finish, and
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Tic Tac Toe: And Other Three-In-A Row Games from
Ancient Egypt to the Modern Computer
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X1 → O5 → X3 → O2 → X8 → O4 (6) → X6 (4) → O9 (7) → X7 (9), this game will be a draw.
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If X plays 1 opening move, and O is not a perfect player, the following may happen:
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When X plays corner first, and O is not a perfect player, the following may happen:
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is an even broader generalization of tic-tac-toe. It can also be generalized as an
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2158:
Michon, John A. (January 1, 1967). "The Game of JAM: An
Isomorph of Tic-Tac-Toe".
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Win: If the player has two in a row, they can place a third to get three in a row.
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O takes a bad position as first move (except of 5, all other positions are bad):
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for two players who take turns marking the spaces in a three-by-three grid with
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1319:, contestants answer questions to win a turn to influence a tic-tac-toe grid.
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X1 → O5 → X2 → O3 → X7 → O4 → X6 → O8 (9) → X9 (8), this game will be a draw.
735:
X1 → O5 → X6 → O9 → X7 → O4 → X2 (3) → O3 (2) → X8, this game will be a draw.
732:
X1 → O5 → X6 → O9 → X3 → O2 → X8 → O4 (7) → X7 (4), this game will be a draw.
720:
X1 → O5 → X6 → O3 → X7 → O4 → X8 (9) → O9 (8) → X2, this game will be a draw.
715:
X1 → O5 → X6 → O2 → X8 → O9 → X4 (7) → O7 (4) → X3, this game will be a draw.
547:
More detailed, to guarantee a draw, O should adopt the following strategies:
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2330:(11). College Park, MD: American Association of Physics Teachers: 962–973.
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21:"Noughts and Crosses" and "Tic Tac Toe" redirect here. For other uses, see
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In both of these situations (X takes 9 or 6 as the second move), X has a
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Empty side: The player plays in a middle square on any of the four sides.
317:, in which two players alternate placing stones of their own color on an
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2527:– Discussion about the term "cat's game" for a drawn game of tic-tac-toe
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1998:
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Encyclopedia of Video Games: The
Culture, Technology, and Art of Gaming
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a mentally ill murderer by eliciting a tic-tac-toe-playing chicken as
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Players soon discover that the best play from both parties leads to a
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1969:
Patashnik, Oren (September 1, 1980). "Qubic: 4 × 4 × 4 Tic-Tac-Toe".
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729:
X1 → O5 → X6 → O9 → X2 → O3 → X7 → O4 → X8, this game will be a draw.
723:
X1 → O5 → X6 → O8 → X2 → O3 → X7 → O4 → X9, this game will be a draw.
712:
X1 → O5 → X6 → O2 → X8 → O7 → X3 → O9 → X4, this game will be a draw.
701:
X1 → O5 → X9 → O2 → X8 → O7 → X3 → O6 → X4, this game will be a draw.
449:
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269:
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1982:
1720:
entries for "Noughts and
Crosses", "Tick-Tack" and "Tick-Tack-Toe",
1257:
Various game shows have been based on tic-tac-toe and its variants:
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Numerical tic-tac-toe is a variation invented by the mathematician
348:= 2. It can be generalised even further by playing on an arbitrary
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up to 15 then the game is a draw. Plotting these numbers on a 3×3
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2519:"etymology – Why is a tie in Tic-Tac-Toe called a "Cat's Game?""
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X1 → O5 → X6 → O2 → X8 → O4 → X9, then X can take 3 or 7 to win.
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X1 → O5 → X6 → O2 → X8 → O3 → X7, then X can take 4 or 9 to win.
256:
Because of the simplicity of tic-tac-toe, it is often used as a
216:
Sometimes, tic-tac-toe (where players keep adding "pieces") and
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Half-Real: Video Games
Between Real Rules and Fictional Worlds
585:
Consider a board with the nine positions numbered as follows:
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1174:, in which the board consisted of eleven holes arranged in a
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3 distinct positions are drawn (often called a "cat's game")
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Games played on three-in-a-row boards can be traced back to
329:
of their own color in a row. Tic-tac-toe is the 3,3,3-game.
1224:
that sought to overturn the state of
Florida's decision to
987:
210:
969:, players can choose to place either X or O on each move.
1615:
She Does Math!: Real-life Problems from Women on the Job
1885:"Flexible Strategy Use in Young Children's Tic-Tac-Toe"
1507:
Pham, Duc-Nghia; Park, Seong-Bae (November 12, 2014).
815:
X1 → O6 → X5 → O9 → X3, then X can take 2 or 7 to win.
812:
X1 → O2 → X5 → O9 → X7, then X can take 3 or 4 to win.
809:
X1 → O9 → X3 → O2 → X7, then X can take 4 or 5 to win.
806:
X1 → O3 → X7 → O4 → X9, then X can take 5 or 8 to win.
787:
X1 → O5 → X6 → O7 → X3, then X can take 2 or 9 to win.
784:
X1 → O5 → X6 → O4 → X3, then X can take 7 or 9 to win.
781:
X1 → O5 → X9 → O3 → X7, then X can take 4 or 8 to win.
1618:. Mathematical Association of America. p. 153.
1285:. Australia had various versions under the names of
375:
An early variation of tic-tac-toe was played in the
1211:
wrote the music for a song "Tit, Tac, Toe" in 1876.
834:share the element of trying to be the first to get
448:students to demonstrate the computational power of
1702:. Series 2. Vol. VI. p. 152 – via
1584:
1166:In the 1970s, there was a two-player game made by
948:tic-tac-toe, the player wins if the opponent gets
532:Empty corner: The player plays in a corner square.
886:, where two players alternate taking turns on an
3873:
2451:"Why did the chicken win the game? Conditioning"
2018:Problem Solving Through Recreational Mathematics
1945:"The best opening move in a game of tic-tac-toe"
1859:
1411:"The History of Tic Tac Toe and Where it is Now"
1919:Hexaflexagons and Other Mathematical Diversions
2813:
2546:
2011:
1539:Golomb, Solomon W.; Hales, Alfred W. (2002).
379:, around the first century BC. It was called
2102:The Theory of Gambling and Statistical Logic
2049:Introducing Game Theory and its Applications
1548:More Games of No Chance (Berkeley, CA, 2000)
1492:: CS1 maint: multiple names: authors list (
231:In the following example, the first player (
2523:English Language & Usage Stack Exchange
1694:
1538:
1156:such a way that a three-in-a-row line wins.
492:remaining sequences leading to wins from X.
429:), developed by British computer scientist
2820:
2806:
2553:
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1640:"Tic tac toe Ancient Roman 1st century BC"
2827:
2265:. John Wiley & Sons. pp. 71–72.
2099:Epstein, Richard A. (December 28, 2012).
2045:
1968:
1942:
1900:
1883:Kevin Crowley, Robert S. Siegler (1993).
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917:Other variations of tic-tac-toe include:
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2258:
2098:
1915:
260:tool for teaching the concepts of good
3874:
2157:
1862:"Searching for the cat in tic tac toe"
1611:
1569:from the original on February 6, 2011.
1534:
1532:
1530:
1328:, several national variants feature a
444:In 1975, tic-tac-toe was also used by
2801:
2534:
2126:
2124:
2122:
1860:Delinski, Bernie (January 21, 2014).
1832:
1764:
1726:
1198:
932:, is played on a 4×4×4 board; it was
18:Paper-and-pencil game for two players
2416:Trillin, Calvin (February 1, 1999).
2321:
2130:
1736:Wolf, Mark J. P. (August 16, 2012).
1735:
882:. Tic-tac-toe is an instance of an
475:44 distinct positions are won by (O)
472:91 distinct positions are won by (X)
23:Noughts and Crosses (disambiguation)
2066:
1527:
13:
2869:First-player and second-player win
2160:The American Journal of Psychology
2119:
2092:
1826:
1554:. Cambridge Univ. Press: 167–182.
1383:
956:
580:
302:The game can be generalized to an
237:
14:
3918:
2473:
1438:"MathRec Solutions (Tic-Tac-Toe)"
1403:
1239:In the 1983 science-fiction film
268:that deals with the searching of
2976:Coalition-proof Nash equilibrium
2689:Harary's generalized tic-tac-toe
2643:
2493:
2479:
1943:Kutschera, Ant (April 7, 2018).
1836:How to never lose at Tic-Tac-Toe
900:Harary's generalized tic-tac-toe
459:
331:Harary's generalized tic-tac-toe
235:) wins the game in seven steps:
40:
2560:
2443:
2409:
2383:
2358:
2315:
2304:
2279:
2252:
2234:"Tic-Tac-Toe as a Magic Square"
2226:
2194:
2151:
2105:. Academic Press. p. 450.
2039:
2005:
1962:
1936:
1922:. University of Chicago Press.
1909:
1876:
1853:
1810:
1784:
1758:
1711:
1687:
1657:
325:board with the goal of getting
280:rotations and reflections (the
276:) or the 26,830 possible games
46:A completed game of tic-tac-toe
2986:Evolutionarily stable strategy
2021:. Dover Publications. p.
1765:Cohen, D.S. (March 12, 2019).
1632:
1605:
1573:
1550:. Math. Sci. Res. Inst. Publ.
1500:
1466:
1460:
1429:
1377:
166:, with a forced draw assuming
1:
2914:Simultaneous action selection
2484:The dictionary definition of
1767:"OXO aka Noughts and Crosses"
1370:
1220:recounts the true story of a
894:board until one of them gets
819:
242:Game of Tic-tac-toe, won by X
3846:List of games in game theory
3026:Quantal response equilibrium
3016:Perfect Bayesian equilibrium
2951:Bayes correlated equilibrium
1792:"Tinkertoys and tic-tac-toe"
1386:"GamesCrafters: Tic-Tac-Toe"
340:, specifically one in which
27:Tic Tac Toe (disambiguation)
7:
3315:Optional prisoner's dilemma
3046:Self-confirming equilibrium
2324:American Journal of Physics
2046:Mendelson, Elliott (2016).
1819:Original Tinkertoy Computer
1346:
482:
223:
10:
3923:
3780:Principal variation search
3496:Aumann's agreement theorem
3159:Strategy-stealing argument
3071:Trembling hand equilibrium
3001:Markov perfect equilibrium
2996:Mertens-stable equilibrium
2699:Strategy-stealing argument
2259:Schumer, Peter D. (2004).
1902:10.1207/s15516709cog1704_3
1839:. BookCountry. p. 7.
1742:Greenwood Publishing Group
1390:gamescrafters.berkeley.edu
1279:. The British version was
823:
363:
20:
3816:Combinatorial game theory
3803:
3762:
3544:
3488:
3475:Princess and monster game
3270:
3172:
3079:
3031:Quasi-perfect equilibrium
2956:Bayesian Nash equilibrium
2937:
2836:
2717:
2652:
2641:
2568:
2238:Oh Boy! I Get to do Math!
2137:. MIT Press. p. 51.
2052:. CRC Press. p. 19.
1718:Oxford English Dictionary
1513:. Springer. p. 735.
1251:no side will actually win
990:
110:
102:
94:
86:
78:
68:
51:
39:
3831:Evolutionary game theory
3564:Antoine Augustin Cournot
3450:Guess 2/3 of the average
3247:Strictly determined game
3041:Satisfaction equilibrium
2859:Escalation of commitment
2391:"452: Poultry Slam 2011"
1916:Gardner, Martin (1988).
1644:Sweetooth Design Company
1442:Mathematical Recreations
1436:Schaefer, Steve (2002).
1247:global thermonuclear war
1170:Toys & Games called
173:
3887:Abstract strategy games
3836:Glossary of game theory
3435:Stackelberg competition
3061:Strong Nash equilibrium
2370:The Library of Congress
1541:"Hypercube tic-tac-toe"
454:Computer History Museum
439:University of Cambridge
385:three pebbles at a time
266:artificial intelligence
3902:Paper-and-pencil games
3861:Tragedy of the commons
3841:List of game theorists
3821:Confrontation analysis
3531:Sprague–Grundy theorem
3051:Sequential equilibrium
2971:Correlated equilibrium
2418:"The Chicken Vanishes"
2015:; Chein, Orin (2000).
1949:The Kitchen in the Zoo
1833:Bolon, Thomas (2013).
1612:Parker, Marla (1995).
961:
501:
493:
299:
274:state space complexity
243:
117:, tactics, observation
3634:Jean-François Mertens
2709:Paper-and-pencil game
2311:Twice crosses-circles
2262:Mathematical Journeys
2131:Juul, Jesper (2011).
1473:mathworld.wolfram.com
1467:W., Weisstein, Eric.
960:
838:-in-a-row, including
499:
490:
294:
241:
152:paper-and-pencil game
73:Paper-and-pencil game
3763:Search optimizations
3639:Jennifer Tour Chayes
3526:Revelation principle
3521:Purification theorem
3460:Nash bargaining game
3425:Bertrand competition
3410:El Farol Bar problem
3375:Electronic mail game
3340:Lewis signaling game
2884:Hierarchy of beliefs
2694:Hales–Jewett theorem
2630:Ultimate tic-tac-toe
2502:at Wikimedia Commons
2214:on December 20, 2016
2078:Puzzles in Education
1971:Mathematics Magazine
1353:Hales–Jewett theorem
1234:operant conditioning
1207:wrote the words and
826:Tic-tac-toe variants
504:A player can play a
282:game tree complexity
187:Commonwealth English
136:Commonwealth English
3811:Bounded rationality
3430:Cournot competition
3380:Rock paper scissors
3355:Battle of the sexes
3345:Volunteer's dilemma
3217:Perfect information
3144:Dominant strategies
2981:Epsilon-equilibrium
2864:Extensive-form game
2615:Quantum tic-tac-toe
2336:2006AmJPh..74..962G
2080:. December 11, 2007
1669:www-cs.canisius.edu
1292:Personality Squares
1191:Quantum tic-tac-toe
427:Noughts and Crosses
350:incidence structure
296:Incidence structure
207:New Zealand English
170:from both players.
132:noughts and crosses
58:Noughts and Crosses
36:
3790:Paranoid algorithm
3770:Alpha–beta pruning
3649:John Maynard Smith
3480:Rendezvous problem
3320:Traveler's dilemma
3310:Gift-exchange game
3305:Prisoner's dilemma
3222:Large Poisson game
3189:Bargaining problem
3094:Backward induction
3066:Subgame perfection
3021:Proper equilibrium
2752:Three men's morris
2397:. December 2, 2011
2395:This American Life
2074:"Wild Tic-Tac-Toe"
1822:. January 5, 1978.
1798:on August 24, 2007
1722:dictionary.oed.com
1581:Zaslavsky, Claudia
1325:The Price Is Right
1222:legal defense team
1217:This American Life
1209:John Rogers Thomas
1199:In popular culture
967:"wild" tic-tac-toe
962:
840:three men's morris
502:
494:
389:three men's morris
300:
264:and the branch of
244:
218:three men's morris
34:
3892:Discrete geometry
3869:
3868:
3775:Aspiration window
3744:Suzanne Scotchmer
3699:Oskar Morgenstern
3594:Donald B. Gillies
3536:Zermelo's theorem
3465:Induction puzzles
3420:Fair cake-cutting
3395:Public goods game
3325:Coordination game
3199:Intransitive game
3129:Forward induction
3011:Pareto efficiency
2991:Gibbs equilibrium
2961:Berge equilibrium
2909:Simultaneous game
2795:
2794:
2725:Nine men's morris
2513:. March 11, 2002.
2511:Wolfram MathWorld
2498:Media related to
2457:. August 28, 2018
2344:10.1119/1.2213635
2272:978-0-471-22066-4
2202:"TicTacToe Magic"
2144:978-0-262-51651-8
2112:978-0-12-397870-7
2059:978-1-4822-8587-1
2032:978-0-486-40917-7
1929:978-0-226-28254-1
1889:Cognitive Science
1846:978-1-4630-0192-6
1751:978-0-313-37936-9
1697:Notes and Queries
1675:on March 13, 2013
1625:978-0-88385-702-1
1520:978-3-319-13560-1
1287:Celebrity Squares
1282:Celebrity Squares
1270:Storybook Squares
1264:Hollywood Squares
1152:
1151:
928:Another variant,
906:, where rows are
844:nine men's morris
760:property to win.
695:
694:
409:Notes and Queries
352:, where rows are
121:
120:
3914:
3897:Positional games
3856:Topological game
3851:No-win situation
3749:Thomas Schelling
3729:Robert B. Wilson
3689:Merrill M. Flood
3659:John von Neumann
3569:Ariel Rubinstein
3554:Albert W. Tucker
3405:War of attrition
3365:Matching pennies
3006:Nash equilibrium
2929:Mechanism design
2894:Normal-form game
2849:Cooperative game
2822:
2815:
2808:
2799:
2798:
2684:Kaplansky's game
2653:Related concepts
2647:
2635:Wild tic-tac-toe
2555:
2548:
2541:
2532:
2531:
2526:
2525:. March 5, 2014.
2514:
2497:
2483:
2467:
2466:
2464:
2462:
2447:
2441:
2440:
2438:
2436:
2413:
2407:
2406:
2404:
2402:
2387:
2381:
2380:
2378:
2376:
2362:
2356:
2355:
2319:
2313:
2308:
2302:
2301:
2299:
2297:
2283:
2277:
2276:
2256:
2250:
2249:
2247:
2245:
2230:
2224:
2223:
2221:
2219:
2213:
2207:. Archived from
2206:
2198:
2192:
2191:
2155:
2149:
2148:
2128:
2117:
2116:
2096:
2090:
2089:
2087:
2085:
2070:
2064:
2063:
2043:
2037:
2036:
2013:Averbach, Bonnie
2009:
2003:
2002:
1966:
1960:
1959:
1957:
1955:
1940:
1934:
1933:
1913:
1907:
1906:
1904:
1880:
1874:
1873:
1857:
1851:
1850:
1830:
1824:
1823:
1814:
1808:
1807:
1805:
1803:
1794:. Archived from
1788:
1782:
1781:
1779:
1777:
1762:
1756:
1755:
1744:. pp. 3–7.
1733:
1724:
1715:
1709:
1707:
1701:
1691:
1685:
1684:
1682:
1680:
1671:. Archived from
1661:
1655:
1654:
1652:
1650:
1636:
1630:
1629:
1609:
1603:
1602:
1590:
1577:
1571:
1570:
1568:
1545:
1536:
1525:
1524:
1504:
1498:
1497:
1491:
1483:
1481:
1479:
1464:
1458:
1457:
1455:
1453:
1448:on June 28, 2013
1444:. Archived from
1433:
1427:
1426:
1424:
1422:
1407:
1401:
1400:
1398:
1396:
1381:
1339:Minute to Win It
1316:Beat the Teacher
1298:All Star Squares
1147:
1138:
1130:
1122:
1114:
1105:
1099:
1096:
1093:
1088:
1085:
1080:
1077:
1074:
1067:
1061:
1058:
1053:
1050:
1047:
1044:
1039:
1036:
1029:
1023:
1020:
1017:
1012:
1009:
1004:
1001:
998:
995:
988:
759:
757:
756:
753:
750:
690:
686:
679:
675:
668:
664:
655:
651:
644:
640:
633:
629:
620:
616:
609:
605:
598:
594:
588:
587:
437:computer at the
395:, a game of the
180:American English
128:American English
44:
37:
33:
3922:
3921:
3917:
3916:
3915:
3913:
3912:
3911:
3872:
3871:
3870:
3865:
3799:
3785:max^n algorithm
3758:
3754:William Vickrey
3714:Reinhard Selten
3669:Kenneth Binmore
3584:David K. Levine
3579:Daniel Kahneman
3546:
3540:
3516:Negamax theorem
3506:Minimax theorem
3484:
3445:Diner's dilemma
3300:All-pay auction
3266:
3252:Stochastic game
3204:Mean-field game
3175:
3168:
3139:Markov strategy
3075:
2941:
2933:
2904:Sequential game
2889:Information set
2874:Game complexity
2844:Congestion game
2832:
2826:
2796:
2791:
2713:
2648:
2639:
2605:Order and Chaos
2600:Number Scrabble
2564:
2559:
2517:
2505:
2476:
2471:
2470:
2460:
2458:
2449:
2448:
2444:
2434:
2432:
2414:
2410:
2400:
2398:
2389:
2388:
2384:
2374:
2372:
2366:"Tit, tat, toe"
2364:
2363:
2359:
2320:
2316:
2309:
2305:
2295:
2293:
2285:
2284:
2280:
2273:
2257:
2253:
2243:
2241:
2232:
2231:
2227:
2217:
2215:
2211:
2204:
2200:
2199:
2195:
2172:10.2307/1420555
2156:
2152:
2145:
2129:
2120:
2113:
2097:
2093:
2083:
2081:
2072:
2071:
2067:
2060:
2044:
2040:
2033:
2010:
2006:
1983:10.2307/2689613
1967:
1963:
1953:
1951:
1941:
1937:
1930:
1914:
1910:
1881:
1877:
1858:
1854:
1847:
1831:
1827:
1816:
1815:
1811:
1801:
1799:
1790:
1789:
1785:
1775:
1773:
1763:
1759:
1752:
1734:
1727:
1716:
1712:
1693:
1692:
1688:
1678:
1676:
1663:
1662:
1658:
1648:
1646:
1638:
1637:
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1610:
1606:
1599:
1578:
1574:
1566:
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1537:
1528:
1521:
1505:
1501:
1485:
1484:
1477:
1475:
1465:
1461:
1451:
1449:
1434:
1430:
1420:
1418:
1409:
1408:
1404:
1394:
1392:
1382:
1378:
1373:
1365:Number Scrabble
1349:
1276:Hip Hop Squares
1214:Episode 452 of
1201:
1145:
1136:
1128:
1120:
1112:
1103:
1097:
1094:
1091:
1086:
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1059:
1056:
1051:
1048:
1045:
1042:
1037:
1034:
1027:
1021:
1018:
1015:
1010:
1007:
1002:
999:
996:
993:
973:Number Scrabble
872:Order and Chaos
828:
822:
754:
751:
748:
747:
745:
691:
688:
684:
680:
677:
673:
669:
666:
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656:
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638:
634:
631:
627:
621:
618:
614:
610:
607:
603:
599:
596:
592:
583:
581:Further details
485:
462:
366:
298:for tic-tac-toe
226:
176:
64:
47:
30:
19:
12:
11:
5:
3920:
3910:
3909:
3904:
3899:
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3843:
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3813:
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3801:
3800:
3798:
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3764:
3760:
3759:
3757:
3756:
3751:
3746:
3741:
3736:
3731:
3726:
3721:
3719:Robert Axelrod
3716:
3711:
3706:
3701:
3696:
3694:Olga Bondareva
3691:
3686:
3684:Melvin Dresher
3681:
3676:
3674:Leonid Hurwicz
3671:
3666:
3661:
3656:
3651:
3646:
3641:
3636:
3631:
3626:
3621:
3616:
3611:
3609:Harold W. Kuhn
3606:
3601:
3599:Drew Fudenberg
3596:
3591:
3589:David M. Kreps
3586:
3581:
3576:
3574:Claude Shannon
3571:
3566:
3561:
3556:
3550:
3548:
3542:
3541:
3539:
3538:
3533:
3528:
3523:
3518:
3513:
3511:Nash's theorem
3508:
3503:
3498:
3492:
3490:
3486:
3485:
3483:
3482:
3477:
3472:
3467:
3462:
3457:
3452:
3447:
3442:
3437:
3432:
3427:
3422:
3417:
3412:
3407:
3402:
3397:
3392:
3387:
3382:
3377:
3372:
3370:Ultimatum game
3367:
3362:
3357:
3352:
3350:Dollar auction
3347:
3342:
3337:
3335:Centipede game
3332:
3327:
3322:
3317:
3312:
3307:
3302:
3297:
3292:
3290:Infinite chess
3287:
3282:
3276:
3274:
3268:
3267:
3265:
3264:
3259:
3257:Symmetric game
3254:
3249:
3244:
3242:Signaling game
3239:
3237:Screening game
3234:
3229:
3227:Potential game
3224:
3219:
3214:
3206:
3201:
3196:
3191:
3186:
3180:
3178:
3170:
3169:
3167:
3166:
3161:
3156:
3154:Mixed strategy
3151:
3146:
3141:
3136:
3131:
3126:
3121:
3116:
3111:
3106:
3101:
3096:
3091:
3085:
3083:
3077:
3076:
3074:
3073:
3068:
3063:
3058:
3053:
3048:
3043:
3038:
3036:Risk dominance
3033:
3028:
3023:
3018:
3013:
3008:
3003:
2998:
2993:
2988:
2983:
2978:
2973:
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2958:
2953:
2947:
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2935:
2934:
2932:
2931:
2926:
2921:
2916:
2911:
2906:
2901:
2896:
2891:
2886:
2881:
2879:Graphical game
2876:
2871:
2866:
2861:
2856:
2851:
2846:
2840:
2838:
2834:
2833:
2825:
2824:
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2793:
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2749:
2742:
2737:
2736:
2735:
2727:
2721:
2719:
2715:
2714:
2712:
2711:
2706:
2701:
2696:
2691:
2686:
2681:
2673:
2656:
2654:
2650:
2649:
2642:
2640:
2638:
2637:
2632:
2627:
2622:
2617:
2612:
2607:
2602:
2597:
2596:
2595:
2585:
2580:
2578:3D tic-tac-toe
2574:
2572:
2566:
2565:
2558:
2557:
2550:
2543:
2535:
2529:
2528:
2515:
2503:
2491:
2475:
2474:External links
2472:
2469:
2468:
2442:
2422:The New Yorker
2408:
2382:
2357:
2314:
2303:
2278:
2271:
2251:
2240:. May 30, 2015
2225:
2193:
2166:(1): 137–140.
2150:
2143:
2118:
2111:
2091:
2065:
2058:
2038:
2031:
2004:
1977:(4): 202–216.
1961:
1935:
1928:
1908:
1895:(4): 531–561.
1875:
1866:timesdaily.com
1852:
1845:
1825:
1809:
1783:
1757:
1750:
1725:
1710:
1686:
1665:"Morris Games"
1656:
1631:
1624:
1604:
1597:
1572:
1526:
1519:
1499:
1459:
1428:
1417:. July 1, 2019
1402:
1375:
1374:
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1255:
1254:
1237:
1212:
1200:
1197:
1196:
1195:
1188:
1185:
1164:
1157:
1150:
1149:
1142:↘
1140:
1132:
1124:
1116:
1110: ↙
1107:
1106:
1100:
1089:
1081:
1069:
1068:
1062:
1054:
1040:
1031:
1030:
1024:
1013:
1005:
991:
986:
985:
970:
955:
954:
938:Oren Patashnik
923:
922:
910:and cells are
824:Main article:
821:
818:
817:
816:
813:
810:
807:
800:
799:
796:
789:
788:
785:
782:
772:
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742:
741:
740:
739:
736:
733:
730:
724:
721:
718:
717:
716:
713:
703:
702:
693:
692:
683:
681:
672:
670:
661:
658:
657:
648:
646:
637:
635:
626:
623:
622:
613:
611:
602:
600:
591:
582:
579:
578:
577:
573:
569:
561:
560:
557:
553:
537:
536:
533:
530:
527:
523:
519:
516:
513:
484:
481:
480:
479:
476:
473:
461:
458:
365:
362:
356:and cells are
225:
222:
189:(particularly
175:
172:
119:
118:
112:
108:
107:
104:
100:
99:
96:
92:
91:
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84:
83:
80:
76:
75:
70:
66:
65:
63:
62:
59:
55:
53:
49:
48:
45:
17:
9:
6:
4:
3:
2:
3919:
3908:
3905:
3903:
3900:
3898:
3895:
3893:
3890:
3888:
3885:
3883:
3880:
3879:
3877:
3862:
3859:
3857:
3854:
3852:
3849:
3847:
3844:
3842:
3839:
3837:
3834:
3832:
3829:
3827:
3824:
3822:
3819:
3817:
3814:
3812:
3809:
3808:
3806:
3804:Miscellaneous
3802:
3796:
3793:
3791:
3788:
3786:
3783:
3781:
3778:
3776:
3773:
3771:
3768:
3767:
3765:
3761:
3755:
3752:
3750:
3747:
3745:
3742:
3740:
3739:Samuel Bowles
3737:
3735:
3734:Roger Myerson
3732:
3730:
3727:
3725:
3724:Robert Aumann
3722:
3720:
3717:
3715:
3712:
3710:
3707:
3705:
3702:
3700:
3697:
3695:
3692:
3690:
3687:
3685:
3682:
3680:
3679:Lloyd Shapley
3677:
3675:
3672:
3670:
3667:
3665:
3664:Kenneth Arrow
3662:
3660:
3657:
3655:
3652:
3650:
3647:
3645:
3644:John Harsanyi
3642:
3640:
3637:
3635:
3632:
3630:
3627:
3625:
3622:
3620:
3617:
3615:
3614:Herbert Simon
3612:
3610:
3607:
3605:
3602:
3600:
3597:
3595:
3592:
3590:
3587:
3585:
3582:
3580:
3577:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3551:
3549:
3543:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3517:
3514:
3512:
3509:
3507:
3504:
3502:
3499:
3497:
3494:
3493:
3491:
3487:
3481:
3478:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3431:
3428:
3426:
3423:
3421:
3418:
3416:
3415:Fair division
3413:
3411:
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3391:
3390:Dictator game
3388:
3386:
3383:
3381:
3378:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
3353:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3303:
3301:
3298:
3296:
3293:
3291:
3288:
3286:
3283:
3281:
3278:
3277:
3275:
3273:
3269:
3263:
3262:Zero-sum game
3260:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3235:
3233:
3232:Repeated game
3230:
3228:
3225:
3223:
3220:
3218:
3215:
3213:
3211:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3181:
3179:
3177:
3171:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3149:Pure strategy
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3114:De-escalation
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3086:
3084:
3082:
3078:
3072:
3069:
3067:
3064:
3062:
3059:
3057:
3056:Shapley value
3054:
3052:
3049:
3047:
3044:
3042:
3039:
3037:
3034:
3032:
3029:
3027:
3024:
3022:
3019:
3017:
3014:
3012:
3009:
3007:
3004:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2969:
2967:
2964:
2962:
2959:
2957:
2954:
2952:
2949:
2948:
2946:
2944:
2940:
2936:
2930:
2927:
2925:
2924:Succinct game
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2890:
2887:
2885:
2882:
2880:
2877:
2875:
2872:
2870:
2867:
2865:
2862:
2860:
2857:
2855:
2852:
2850:
2847:
2845:
2842:
2841:
2839:
2835:
2831:
2823:
2818:
2816:
2811:
2809:
2804:
2803:
2800:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2747:
2743:
2741:
2738:
2733:
2732:
2731:
2728:
2726:
2723:
2722:
2720:
2718:Similar games
2716:
2710:
2707:
2705:
2702:
2700:
2697:
2695:
2692:
2690:
2687:
2685:
2682:
2680:
2678:
2674:
2672:
2670:
2666:
2662:
2658:
2657:
2655:
2651:
2646:
2636:
2633:
2631:
2628:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2594:
2591:
2590:
2589:
2586:
2584:
2581:
2579:
2576:
2575:
2573:
2571:
2567:
2563:
2556:
2551:
2549:
2544:
2542:
2537:
2536:
2533:
2524:
2520:
2516:
2512:
2508:
2507:"Tic-Tac-Toe"
2504:
2501:
2496:
2492:
2490:at Wiktionary
2489:
2488:
2482:
2478:
2477:
2461:September 15,
2456:
2452:
2446:
2431:
2427:
2423:
2419:
2412:
2396:
2392:
2386:
2371:
2367:
2361:
2353:
2349:
2345:
2341:
2337:
2333:
2329:
2325:
2318:
2312:
2307:
2292:
2291:BoardGameGeek
2288:
2287:"Check Lines"
2282:
2274:
2268:
2264:
2263:
2255:
2239:
2235:
2229:
2210:
2203:
2197:
2189:
2185:
2181:
2177:
2173:
2169:
2165:
2161:
2154:
2146:
2140:
2136:
2135:
2127:
2125:
2123:
2114:
2108:
2104:
2103:
2095:
2079:
2075:
2069:
2061:
2055:
2051:
2050:
2042:
2034:
2028:
2024:
2020:
2019:
2014:
2008:
2000:
1996:
1992:
1988:
1984:
1980:
1976:
1972:
1965:
1950:
1946:
1939:
1931:
1925:
1921:
1920:
1912:
1903:
1898:
1894:
1890:
1886:
1879:
1871:
1867:
1863:
1856:
1848:
1842:
1838:
1837:
1829:
1821:
1820:
1813:
1802:September 27,
1797:
1793:
1787:
1772:
1768:
1761:
1753:
1747:
1743:
1739:
1732:
1730:
1723:
1719:
1714:
1705:
1700:
1698:
1690:
1674:
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1666:
1660:
1645:
1641:
1635:
1627:
1621:
1617:
1616:
1608:
1600:
1598:0-690-04316-3
1594:
1589:
1588:
1582:
1576:
1565:
1561:
1557:
1553:
1549:
1542:
1535:
1533:
1531:
1522:
1516:
1512:
1511:
1503:
1495:
1489:
1474:
1470:
1469:"Tic-Tac-Toe"
1463:
1452:September 18,
1447:
1443:
1439:
1432:
1416:
1412:
1406:
1391:
1387:
1384:Garcia, Dan.
1380:
1376:
1366:
1363:
1361:
1360:
1356:
1354:
1351:
1350:
1341:
1340:
1335:
1331:
1327:
1326:
1321:
1318:
1317:
1312:
1309:
1308:
1307:Tic-Tac-Dough
1303:
1300:
1299:
1294:
1293:
1288:
1284:
1283:
1278:
1277:
1272:
1271:
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1244:
1243:
1238:
1235:
1231:
1227:
1223:
1219:
1218:
1213:
1210:
1206:
1205:George Cooper
1203:
1202:
1192:
1189:
1186:
1182:
1177:
1173:
1169:
1165:
1162:
1161:Ronald Graham
1158:
1154:
1153:
1148:
1141:
1139:
1133:
1131:
1125:
1123:
1117:
1115:
1109:
1108:
1101:
1090:
1082:
1071:
1070:
1063:
1055:
1041:
1033:
1032:
1025:
1014:
1006:
992:
989:
983:
978:
975:or Pick15 is
974:
971:
968:
964:
963:
959:
951:
947:
943:
942:
941:
939:
935:
931:
926:
920:
919:
918:
915:
913:
909:
905:
901:
897:
893:
889:
885:
881:
877:
873:
869:
865:
861:
857:
853:
849:
845:
841:
837:
833:
827:
814:
811:
808:
805:
804:
803:
797:
794:
793:
792:
786:
783:
780:
779:
778:
775:
769:
766:
765:
764:
761:
737:
734:
731:
728:
727:
725:
722:
719:
714:
711:
710:
708:
707:
706:
700:
699:
698:
682:
671:
660:
659:
647:
636:
625:
624:
612:
601:
590:
589:
586:
574:
570:
566:
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564:
558:
554:
550:
549:
548:
545:
541:
534:
531:
528:
524:
520:
517:
514:
511:
510:
509:
507:
498:
489:
477:
474:
471:
470:
469:
467:
466:combinatorics
460:Combinatorics
457:
455:
451:
447:
442:
440:
436:
432:
431:Sandy Douglas
428:
424:
423:
417:
415:
411:
410:
405:
400:
398:
394:
390:
386:
382:
381:terni lapilli
378:
373:
371:
370:ancient Egypt
361:
359:
355:
351:
347:
343:
339:
337:
332:
328:
324:
320:
316:
314:
310:
306:
297:
293:
289:
287:
283:
279:
275:
271:
267:
263:
262:sportsmanship
259:
254:
252:
247:
240:
236:
234:
229:
221:
219:
214:
212:
208:
204:
200:
196:
195:South African
192:
188:
183:
181:
171:
169:
165:
161:
157:
153:
149:
148:Irish English
145:
141:
137:
133:
129:
125:
116:
113:
109:
105:
101:
97:
93:
89:
85:
81:
77:
74:
71:
67:
60:
57:
56:
54:
50:
43:
38:
32:
28:
24:
16:
3907:Solved games
3709:Peyton Young
3704:Paul Milgrom
3619:Hervé Moulin
3559:Amos Tversky
3501:Folk theorem
3212:-player game
3209:
3134:Grim trigger
2767:Connect Four
2744:
2734:Tic-Stac-Toe
2676:
2668:
2664:
2660:
2561:
2522:
2510:
2486:
2459:. Retrieved
2455:Star Tribune
2454:
2445:
2433:. Retrieved
2421:
2411:
2399:. Retrieved
2394:
2385:
2373:. Retrieved
2369:
2360:
2327:
2323:
2317:
2306:
2294:. Retrieved
2290:
2281:
2261:
2254:
2242:. Retrieved
2237:
2228:
2218:December 17,
2216:. Retrieved
2209:the original
2196:
2163:
2159:
2153:
2133:
2101:
2094:
2082:. Retrieved
2077:
2068:
2048:
2041:
2017:
2007:
1974:
1970:
1964:
1952:. Retrieved
1948:
1938:
1918:
1911:
1892:
1888:
1878:
1865:
1855:
1835:
1828:
1818:
1812:
1800:. Retrieved
1796:the original
1786:
1774:. Retrieved
1770:
1760:
1737:
1713:
1696:
1689:
1679:September 5,
1677:. Retrieved
1673:the original
1668:
1659:
1647:. Retrieved
1643:
1634:
1614:
1607:
1586:
1575:
1551:
1547:
1509:
1502:
1476:. Retrieved
1472:
1462:
1450:. Retrieved
1446:the original
1441:
1431:
1419:. Retrieved
1414:
1405:
1393:. Retrieved
1389:
1379:
1357:
1337:
1330:pricing game
1323:
1314:
1305:
1296:
1290:
1286:
1280:
1274:
1268:
1262:
1256:
1240:
1215:
1181:intersecting
1171:
1143:
1135:
1127:
1119:
1111:
982:magic square
949:
927:
924:
916:
895:
891:
887:
860:Connect Four
835:
829:
801:
790:
776:
773:
762:
743:
704:
696:
584:
562:
546:
542:
538:
506:perfect game
503:
463:
443:
426:
420:
418:
407:
401:
384:
380:
377:Roman Empire
374:
367:
345:
341:
335:
326:
322:
318:
312:
308:
304:
301:
255:
248:
245:
232:
230:
227:
215:
184:
177:
159:
155:
139:
131:
123:
122:
95:Playing time
31:
15:
3882:Tic-tac-toe
3826:Coopetition
3629:Jean Tirole
3624:John Conway
3604:Eric Maskin
3400:Blotto game
3385:Pirate game
3194:Global game
3164:Tit for tat
3099:Bid shading
3089:Appeasement
2939:Equilibrium
2919:Solved game
2854:Determinacy
2837:Definitions
2830:game theory
2782:Toss Across
2704:Futile game
2593:Treblecross
2562:Tic-tac-toe
2500:Tic Tac Toe
2487:tic-tac-toe
1870:Times Daily
1649:December 4,
1591:. Crowell.
1176:geometrical
1172:Check Lines
876:Toss Across
832:board games
286:futile game
258:pedagogical
164:solved game
124:Tic-tac-toe
52:Other names
35:Tic-tac-toe
3876:Categories
3470:Trust game
3455:Kuhn poker
3124:Escalation
3119:Deterrence
3109:Cheap talk
3081:Strategies
2899:Preference
2828:Topics of
2757:Nine Holes
2730:Score Four
2435:August 29,
2375:August 29,
2296:August 29,
2244:August 29,
2084:August 29,
1954:August 29,
1776:August 29,
1704:Wikisource
1371:References
1359:m,n,k-game
977:isomorphic
908:hyperedges
904:hypergraph
898:in a row.
884:m,n,k-game
820:Variations
414:backgammon
270:game trees
203:Australian
87:Setup time
3654:John Nash
3360:Stag hunt
3104:Collusion
2430:0028-792X
2352:0002-9505
1991:0025-570X
526:players.)
450:Tinkertoy
419:In 1952,
397:Puebloans
168:best play
140:Xs and Os
98:~1 minute
61:Xs and Os
3795:Lazy SMP
3489:Theorems
3440:Deadlock
3295:Checkers
3176:of games
2943:concepts
2772:Connect6
2570:Variants
1771:Lifewire
1583:(1982).
1564:Archived
1488:cite web
1347:See also
1242:WarGames
1230:evidence
912:vertices
483:Strategy
433:for the
344:= 3 and
224:Gameplay
144:Canadian
115:Strategy
3547:figures
3330:Chicken
3184:Auction
3174:Classes
2787:Pentago
2740:Gobblet
2588:Notakto
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