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X-Only Tic Tac Toe

Traditional Tic Tac Toe is pretty boring when both players know how to play. The strategy of the game is extremely simple, to the point a game between two reasonably good players always ends in a draw. In this video by Numberphile, Thane Plambeck explains a Tic Tac Toe variant that alleviates this problem, and game theory can be used to analyze why.

In Plambeck’s variant, both players play X. That is to say that either player can use the other player’s pieces to complete three in a row. Without too much analysis, a significant problem can be found with this approach. It is a dominant strategy for Player 1 to play the center, since Player 2 will then have no choice but to put two in a row, allowing Player 1 to win on the next turn. The solution that Plambeck proposes is to modify the game in one more way: to play the Misère, or losing, form of the game.

In the Misère version, each player is instead trying to lose (ie. to force the other player to complete three in a row). In this game, Plambeck describes strategies that are much more nuanced than those in the regular version of the game. There are still dominant strategies (for instance, the first player should still play the center) but the game is not quite as trivial. Most importantly, there will always be a winner.

This video does a good job discussing an interesting variant of a well-known game. It ties into this Networks course because Tic Tac Toe is a game, and it can be readily analysed with the tools of game theory. While Tic Tac Toe may never be a difficult game, it is certainly a fun one to analyze.


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