Thursday, May 9, 2024

Zero Sum Game


The friendliness of Tic-tac-toe games makes them ideal 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, 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.

An early variant of Tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had 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. However, according to Claudia Zaslavsky's book Tic Tac Toe: And Other Three-In-A Row Games from Ancient Egypt to the Modern Computer, Tic-tac-toe could originate back to ancient Egypt.[1] 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.[2]
The different names of the game are more recent. The first print reference to "Noughts and crosses", the British name, appeared in 1864. 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 in trying with the eyes shut to bring the pencil down on one of the numbers of a set, the number hit being scored".

Use the Tic Tac Toe handouts at the front of the room to challenge your classmates and then answer these questions:

1) What strategies did you use to win?

2) Why does Tic Tac Toe lose its appeal the more you play?

3) How is Tic Tac Toe an example of a Zero Sum Game?

4) What comparisons can we make between Tic Tac Toe and Global Thermal Nuclear War?

5) What is the only way to win?


Today gamblers can challenge a Tic Tac Toe Playing Chicken.

Can you beat the bird?



1 comment:

  1. Tic Tac Toe loses its appeal because once you know how to play no one wins. There are no winners. The only way to win is not to play.

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