Tic-Tac-Toe is a simple game for two players that is well-known to result in a draw if played ‘rationally’. Unlike most board games, pieces cannot be moved or removed once placed, making it an ideal game to play with pen & paper.
The origins of tic-tac-toe are unclear. Many sources claim that it dates from antiquity, but to me it seems like a more recent invention—a degenerate version of Three Men’s Morris. Mentions of it only appear in the 19th century, and the game is very well suited to being played with chalk on slates—such as were used by children in schools during this period. Indeed, A Glossary of Berkshire Words and Phrases (p. 164) describes the game as “the first game taught to children when they can use a slate pencil”.
However, there is an early antecedent of a game which is equivalent in play, if not in presentation. Alfonso X of Castile’s Book of Gamesb, published in 1283, includes the game alquerque de tres which is played on a small merels board with diagonals. Each player has three pawns which they place on the board one at a time, taking turns. If a player can form three in a line then they win; otherwise it is a tie. Later historians (even including H. J. R. Murrayc) have muddied the waters by describing this game as a three-men’s-morris game where the pieces can be moved after being placed, but this is not supported by the original manuscript.d[p. 609]
Some of the earliest known written references to Tic-Tac-Toe in English occur in Charles Babbage’s unpublished manuscript Essays on the Philosophy of Analysis (1812–1820, now held in the British Library as Add. MS 37202), although the game is never mentioned by name.e In 1842, ‘tit-tat-to’ again occurs in his notebooks, when he conceptualizes an automaton that would play the game against a human.ef
One boy who is acquainted with the popular game of checkers, fox and geese, tit-tat-to, hop skip and jump, and a thousand other childish amusements, will communicate all he knows to his school companions with surprising facility.
Just as a fool, who has but seen the diagrams and delineations in the elements of Euclid, will make himself dead sure that all the mathematics in the world could have consisted in nothing more than in making hobscotches [hop-scotch], and catgallowses [a high-jump], and scratchcradles [cat’s cradle], to play at tit-tat-toe with.
In English, tic-tac-toe has gone by many names. It has been variously called ‘tit-tat-to(e)’, ‘tic(k)-tac(k)-to(e)’, ‘(n)oughts & crosses’, ‘crisscross’, ‘tip-tap-toe’,i[p. 136]j[p. 333] ‘Exeter’s Nose’ (a pun on ‘Xs and Os’),e ‘oxen-crosses’k[p. 134], or ‘kit-cat-cannio’.l[p. 200]
Several of these names derive from old counting-out rhymes — think ‘eeny meeny miny mo’ — that begin with ‘tit, tat, toe’. These rhymes date from at least the early 18th century: in 1725, A New Canting Dictionary described ‘Tit-Tat’ as “the aiming of Children to go at first”.
The fullest expression of this rhyme is along the lines of:
Tit, tat, toe,
My first go,
Three jolly butcher boys
All in a row;
Stick one up,
Stick one down,
Stick one in the old man’s crown!Some sources (e.g. Woodson (1871, p. 374)) give this last line as “… in the old man’s (burial-)ground!”; I have no idea what this means.
Aside from its use as a counting-out rhyme, ‘tit-tat-to’ was used to refer to any set of three lined-up objects — in F. W. N. Bayley’s 1842 adaptation of the gruesome Bluebeard fairy-tale, Mrs. Bluebeard discovers that her husband has murdered his six previous wives, and:p[p. 19]
[…] —ah! no more!
She bumps her body down on the floor;
Down on the floor—and, Oh, my eye!
She looks as if she were ready to die!
It isn’t a case of “tit-tat-toe,”
And “three jolly butchers all of a row,”
But Oh . . . Oh . . . Oh . . ! ! !
It’s a double case of tit-tat-toe,
And Six Dead Women all of a Row.Supposedly this is a children’s book.
This usage of referring to neatly-aligned triplets is still current with the Swedish equivalent of tripp, trapp, trull (see more below). The three houses in Kalmar in the following image are nicknamed the “tripp trapp trull houses”:
The same rhyme and name were also used for an unrelated game, using a circular board, in which a player would attempt to locate high-scoring sections of a circle while blindfolded.r[p. 55]
There seems to be a distinction we can draw between languages that have folkish names and those that have more functional names derived from the outward appearance or goal of the game.
Like the English names, one Dutch name (boter, melk, kaas) is derived from a rhyme:v[p. 732]
Boter, melk, kaas,
ik ben de baas.
Butter, milk, cheese,
I am the boss.
Sweden had a similar rhyme:w[p. 163]
Tripp, trapp, trull,
min kvarn är full.
Tripp, trapp, trull,
my mill is full.
In the ‘functional’ group of names are those like the Arabic لعبة إكس-أو ‘the X–O game’; or the Chinese 圈圈叉叉 ‘circles & crosses’, or 井字棋
井 character game’.
The languages with ‘folkish’ names also tend to have ‘functional’ names as well; an alternate Swedish name is ‘tre-i-rad’ (‘three in a row’), and Dutch has the straightforward ‘kruisje rondje’ (‘cross circle’).
On the other hand, the English poet Wordsworth didn’t think the game was worthy of a name at all. In The Prelude, he describes playing the game as a child:x[ll. 538–544]
Eager and never weary we pursued
Our home-amusements by the warm peat-fire
At evening, when with pencil and smooth slate,
In square divisions parcelled out, and all
With crosses and with cyphers“cyphers” here means “zeroes” scribbled o’er
We schemed and puzzled, head opposed to head
In strife too humble to be named in verse
In Greek it is called τρίλιζα (triliza), or πατητό (patito) in Thessaloniki.This is given in [y] as “butito”, played in Larnaca on Cyprus. Patito (‘stepping’) is also used for hopscotch.
You know this, right?
See, e.g. Hexaflexagons and other mathematical diversions (pp. 37–46).
#The 15 Game
This game is also known as “Number Scrabble”aa or “Pick15”.
To play: Write down the numbers from 1–9 on a piece of paper. Each turn, a player claims a number for themselves by marking it, and a number can only be claimed by one player. The first player to claim 3 numbers that add to 15 is the winner.
This game is isomorphic to the game of tic-tac-toe. Astonishingly, this form was invented by Babbage in his initial analysis of the game.ab[p. 127]
To show the equivalence, write down the numbers in the form of the (unique) 3×3 magic square:
From this it can be seen that the game is the same as tic-tac-toe. Each row, column, and long diagonal sums to 15.
This is another isomorphic variant invented by John Michon.aa It is the projective geometry dual of the standard game, where each cell is replaced by a line and each winning line by a point, in such a way that each cell-line intersects the appropriate winning-line points.
If this is confusing, muse upon the following diagram: the red solid vertical line represents the middle cell of the Tic-Tac-Toe board; it crosses four points (winning lines). The four blue dashed lines are the corner cells, which cross three points (winning lines) each, and the four green dotted lines are the side-centre cells, which cross two points (winning lines) each.
To play, players take turns claiming an entire line, which crosses several points. Once a player has claimed a line it may not be claimed by the other player. The first player that claims all three lines that pass through any single point wins the game.
Yet another isomorphic variant is played as follows:v[p. 732]
Write down the nine words ‘Spit’, ‘Not’, ‘So’, ‘Fat’, ‘Fop’, ‘As’, ‘If’, ‘In’, and ‘Pan’ on separate pieces of paper. The players take turns taking a single card. A player wins if they collect all the cards with a given letter (e.g. ‘In’, ‘If’, and ‘Spit’ would win since these are all the words containing ‘i’).
This can be shown to be the same game in the following way (note that the number of letters in each word is the same as the number of lines that can be formed through that square):
Being a simple game, Tic-Tac-Toe is easily programmed, and so was one of the first automated games. As noted above, Charles Babbage studied the problem but never built an actual machine.
The earliest fully automated player was constructed by a Frank T. Freeland of Philadelphia, who described its implementation in an 1879 journal article.ac According to the article, the machine was built and exhibited in 1878 before being moved to the University of Pennsylvania. Its whereabouts (if it still exists) are currently unknown.For more about Freeland, see [ad]. This machine predates any other implementations by some 70 years!
Later (but still early, in the computing world) implementations of the game include:
- Bertie the Brain (analog, 1950)
- OXO (for the EDSAC, 1952)
- Relay Moeae (relay-based, 1956), the first to be programmed with a variable strategy and with a chance of making a mistake
Chickens have also been trained to ‘play’ the game.af agah The first of these games, “Bird Brain”, was developed in the late 1970s by Animal Behavior Enterprises, a company founded by Marian & Keller Breland, who were students of B. F. Skinner, the behavioural psychologist.ai[p. 73] In reality, the game is rigged—the chicken only ever pushes a single button, and the move to be played is chosen by a computer.aj
Some general references for the game are The Oxford History of Board Games (112–3), Board and Table Games from Many Civilizations (p. 91), and A History of Board-Games Other Than Chess (§3.2.1, p. 40).
Lowsley, Barzillai (). A Glossary of Berkshire Words and Phrases. English Dialect Society: London, UK.
Alfonso X (). ‘Libro de açedrex, dados e tablas’. Alfonso X: Toledo, Spain.
Murray, H. J. R. (). A History of Board-Games Other Than Chess. Oxford University Press: Oxford, England, UK. ISBN: 0-19-827401-7.
Golladay, Sonja Musser (). Los Libros de Acedrex Dados e Tablas: Historical, Artistic, and Metaphysical Dimensions of Alfonso X’s Book of Games. PhD thesis, University of Arizona: Arizona, USA.
Singmaster, David (). ‘Sources in recreational mathematics’.
Monnens, Devin (). ‘“I commenced an examination of a game called ‘Tit-Tat-To’”: Charles Babbage and the “First” Computer Game’. Proceedings of the 2013 DiGRA international conference: DeFragging Game Studies vol. 7.
Pickett, John (). ‘The New School; or Lancasterian System’. The Academician (1): page 91. John C. Francis: London, England, UK.
Taylor, Robert (). The Devil’s Pulpit: or Astro-Theological Sermons. Calvin Blanchard: New York.
Frederick, Dinsdale (). A glossary of provincial words used in Teesdale, in the county of Durham. J. R. Smith: London, England, UK.
John C. Francis (). Notes and Queries (volume 12 (Series 8)). John C. Francis: London, England, UK.
Norman, Douglas (). London Street Games. The St. Catherine Press: London.
Moor, Edward (). Suffolk Words. J. Loder: London, UK.
Anonymous (). A New Canting Dictionary. London, UK.
Opie, Iona and Peter Opie (). The Lore and Language of Schoolchildren. Oxford University Press: United Kingdom.
Woodson, W. W. (). ‘The Nursery Witch’. Our Monthly vol. 3: pages 371–375. The Presbytarian Magazine Company: Cincinnati.
Bayley, F. W. N. (). Comic Nursery Tales (3rd edition). WM. S. Orr & Co.: London.
Monkhouse, Cosmo (). ‘Some pictures of Children’. The Magazine of Art vol. 7: pages 133–137. Cassel and Company: London, Paris, and New York.
Ernest Nister (). The Games Book for Boys and Girls. Ernest Nister: London, UK.
Skeat, Walter W. (). ‘“Tit-Tat-To”’. Notes and Queries vol. 9 (Series II) (28): page 26.
Doornkaat Koolman, Jan ten (). Wörterbuch der Ostfriesischen Sprache (Dritter Band, Q–Z). Norden: Herm. Braams.
Fiske, Willard (). Chess in Iceland and in Icelandic literature, with historical notes on other table-games. The Florentine Typographical Society: Florence.
Berlekamp, Elwyn, John Conway, and Richard Guy (). Winning Ways (2nd edition) (volume 3). A K Peters: Natick, MA, USA. ISBN: 978-1-56881-143-7.
Pennick, Nigel (). Games of the Gods: The origin of board games in magic and divination. Samuel Weiser: York Beach, ME, USA. ISBN: 0-87728-696-5.
Wordsworth, William (). The Prelude. Edward Moxon: London, UK.
Anonymous (). ‘Butito’. The Australian Children’s Folklore Newsletter (11): pages 12–13.
Gardner, Martin (, originally published 1959). Hexaflexagons and other mathematical diversions. The University of Chicago Press: Chicago, USA.
Michon, John (). ‘The Game of JAM: An Isomorph of Tic-Tac-Toe’. The American Journal of Psychology vol. 80 (1): pages 137–140. University of Illinois Press: IL, USA.
Dubbey, John (). The Mathematical Work of Charles Babbage. Cambridge University Press: Cambridge, UK.
Freeland, Frank T. (). ‘An Automatic Tit-Tat-To Machine’. Journal of the Franklin Institute of the State of Pennsylvania vol. 102 (1): pages 1–9.
Fine, Thomas A. (). ‘The Mystery of the Victorian Tic-Tac-Toe Computer’. Sentence Spacing.
Berkeley, Edmund C. (). ‘“Relay Moe” Plays Tick-Tack-Toe’. Radio-Electronics, December, 1956: pages 50–52.
Kaufman, Michael (). ‘Cross Out a Landmark On the Chinatown Tour’. The New York Times, August 14, 1993.
Trillin, Calvin (). ‘The Chicken Vanishes’. The New Yorker, February 8, 1999: pages 38–41.
Gregory, Kia (). ‘Chinatown Fair Is Back, Without Chickens Playing Tick-Tack-Toe’. The New York Times, June 10, 2012.
Marr, John N. (). ‘Marian Breland Bailey: The Mouse Who Reinforced’. The Arkansas Historical Quarterly vol. 61 (1): pages 59–79.
Animal Behavior Enterprises n.d. ‘Bird Brain Manual’. Animal Behavior Enterprises.
Parlett, David (). The Oxford History of Board Games. Oxford University Press: Oxford, England, UK. ISBN: 978-0-19-212998-7.
Bell, R. C. (, originally published 1960). Board and Table Games from Many Civilizations. Dover Publications: New York, NY, USA. ISBN: 978-0-486-23855-5.