Free Download Tic-tac-toe App
Candy Belmont
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.[3] If played optimally by both players, the game always ends in a draw, making tic-tac-toe a futile game.[4]
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.[5] 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.[6] 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.[9] 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,[10] 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.[11] 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.[12]
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.[13][14] The computer player could play perfect games of tic-tac-toe against a human opponent.[13]
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.[15] It is currently on display at the Computer History Museum.[16]
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.[19]
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.
Grae and I love playing tic-tac-toe. We play it down in the courtyard with sidewalk chalk, we play it at the beach in the sand, and we play it at restaurants with napkins and pens. So why not play with LEGO too?!
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_X
The 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.
My sister-in-law, Susan, was the brains behind this project. She and her dad made all the tic-tac-toe boards by sawing a tree trunk into disks. I love that some of them cracked and looked weathered. You can make the boards out of anything you'd like. I've seen them on mini chalkboards, but you could even just draw chalk lines on the sidewalk.
The arrangement of lines in this image might look like an oceanic game of tic-tac-toe, but in fact, the grid can be explained by a relatively common atmospheric feature. Ship tracks are long, narrow clouds that form in the sky over the ocean when water vapor condenses around tiny particles in ship exhaust.
In the latest work, published in Nature Communications, Qian, Philip Petersen and Grigory Tikhomirov first mixed up a solution of nine blank DNA origami tiles in a test tube. Those DNA tiles assembled themselves into a tic-tac-toe grid. Next, two players took turns adding one of nine X or O DNA tiles into the solution. Each of the game pieces was programmed precisely to swap out only one of the tile positions on the original, blank grid, based on the DNA sequences positioned along its edges.
I first thought about upcycling it into a tooth fairy tote, but since my oldest son, Rowan, has become obsessed with playing tic-tac-toe (thanks, Papa), I decided an on-the-go game would be of more use to us.
My goal was to find out who wins when both players play optimally. For instance, in normal tic-tac-toe, it is well-known that the first X should go in the middle of the board, and if player O counters successfully, the game should end in a tie. Is the outcome of Quantum TiqTaqToe, too, predetermined to end in a tie if both players play optimally? And, if not, what is the best first move for player X? I sought to answer these questions through the power of computation.
In order to solve the unsolved, one must first solve the solved. As such, my first attempt was to create an algorithm that would figure out the best move to play in regular tic-tac-toe. This first attempt was rather straightforward, and I will explain it here:
Here, player O has two options: they can win the game by putting their O on the bottom center square, or lose the game by putting it on the right center square. Any seasoned tic-tac-toe player would make the right move in this scenario, and win the game. However, since the model trains on random moves, it thinks that player O will win half the time and lose half the time. Thus, to the model, this game state is not favorable to either player, when in reality it is absolutely favored towards O.
During my first meeting with Spiros and Evert, they pointed out this flaw in my model. Evert suggested that I study up on something called a minimax algorithm, which circumvents this flaw, and apply it to tic-tac-toe. This set me on the next step of my journey.
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