Google Tic-Tac-Toe: A Fun and Easy Way to Challenge Your Brain
A writer and a software engineer engage in an extended conversation as they take a hands-on approach to exploring how machine learning systems get made and the human choices that shape them. Along the way they build competing tic-tac-toe agents and pit them against each other in a dramatic showdown!
See the original version: -tic-tac-toe-original-post/This is also a fun variant, but is sadly solved, as explained here: -breitner.de/blog/604-Ultimate_Tic_Tac_Toe_is_always_won_by_XThe rule that if you get sent to a board which is already won, you get to choose a board was introduced to break this strategy.
In Commonwealth English (particularly British, South African, Australian and New Zealand English), the game is known as "noughts 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 zero, 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.
Because of the simplicity of tic-tac-toe, it is often used as a pedagogical tool for teaching the concepts of good sportsmanship 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 or 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. If played optimally by both players, the game always ends in a draw, making tic-tac-toe a futile game.
The game can be generalized to an m,n,k-game, in which two players alternate placing stones of their own color on an m-by-n board with the goal of getting k of their own color in a row. Tic-tac-toe is the 3,3,3-game. Harary's generalized tic-tac-toe is an even broader generalization of tic-tac-toe. It can also be generalized as an nd game, specifically one in which n equals 3 and d equals 2. It can be generalised even further by playing on an arbitrary incidence structure, where rows are lines and cells are points. 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.
An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called terni lapilli (three pebbles at a time) 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 three men's morris which is also played on a simple grid and requires three pieces in a row to finish, and Picaria, a game of the Puebloans.
The different names of the game are more recent. The first print reference to "noughts and crosses" (nought being an alternative word for 'zero'), the British name, appeared in 1858, in an issue of Notes and Queries. 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".[This quote needs a citation] "Tic-tac-toe" may also derive from "tick-tack", the name of an old version of backgammon first described in 1558. The US renaming of "noughts and crosses" to "tic-tac-toe" occurred in the 20th century.
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In 1952, OXO (or Noughts and Crosses), developed by British computer scientist Sandy Douglas for the EDSAC computer at the University of Cambridge, became one of the first known video games. The computer player could play perfect games of tic-tac-toe against a human opponent.
In 1975, tic-tac-toe was also used by MIT students to demonstrate the computational power of Tinkertoy 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 Museum of Science, Boston.
A player can play a perfect game 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.
Many board games share the element of trying to be the first to get n-in-a-row, including three men's morris, nine men's morris, pente, gomoku, Qubic, Connect Four, Quarto, Gobblet, Order and Chaos, Toss Across, and Mojo. Tic-tac-toe is an instance of an m,n,k-game, where two players alternate taking turns on an mn board until one of them gets k in a row. Harary's generalized tic-tac-toe is an even broader generalization. The game can be generalised even further by playing on an arbitrary hypergraph, where rows are hyperedges and cells are vertices.
This tutorial will guide you through the building of a new environment: making your Reachy play autonomously a real game of tic-tac-toe against a human player. You can see what it will look like once finished in the video below:
If you're looking for something more sociable, tic-tac-toe is available as a one- or two-player title; play against the computer in easy and medium mode, or "impossible" (but, as its name suggests, it's a bit of an uphill battle). Or challenge a friend to a game of naughts and crosses.
Quantum tic-tac-toe is a "quantum generalization" of tic-tac-toe in which the players' moves are "superpositions" of plays in the classical game. The game was invented by Allan Goff of Novatia Labs, who describes it as "a way of introducing quantum physics without mathematics", and offering "a conceptual foundation for understanding the meaning of quantum mechanics". How-to-play
I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet. However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.If you are a teacher who is using these puzzles in your classroom, please send me an email at email@example.com with information about what you teach and where you teach. I will be happy to forward an answer key to you.