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Tic-Tac-Toe VariantsIn standard tic-tac-toe, the second player can force a draw, but the three-by-three grid is a somewhat artificial restriction, and in fact, given enough room, the first player could always achieve a three-in-a-row. This page is about tic-tac-toe-like games in which there is some pattern to achieve other than the three-in-a-row. Most of what appears here is from Martin Gardner's article, "Harary's Generalized Ticktacktoe", in The Colossal Book of Mathematics.The idea of changing the goal of tic-tac-toe is almost as old as tic-tac-toe itself. In Japan, a five-in-a-row game called ninuki renju (which is, I believe, Japanese for the computer kicks my butt) is so popular that it has seen endless tinkering to reduce the inherent first-player advantage and bring the game into greater balance. The 20th-century combinatorist Frank Harary looked at games in which the goal was not necessarily n-in-a-row, but the achievement of some "animal". These animals are patterns of cells more commonly known as polyominoes; for example: (how these come out depends on how your browser displays tables. no promises.)
I haven't played with Snakey enough to have a sense of whether he is a first- or second-player win, although Ava, having never played at all, thinks she would rather play defense. (Since in theory Player 2 should never win outright, we will declare her the winner if Player 1 is unable to make a Snakey on a reasonable-sized grid, say 12-by-12.) It probably makes sense to play games in pairs, switching roles, to even things out. Many more variations seem worth investigating -- give each player a different animal to try to make; play on different grids, etc. |
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