In game theory, a game becomes “solved” when someone discovers a strategy for best play that cannot be improved upon. This means that at any point in the game, this “perfect play” solution predicts who will win or lose. There are three levels of solved games: ultra-weak, weak and strong. At the highest level, a solved game actually prescribes the exact moves to make for perfect play, regardless of any prior moves. Tic Tac Toe is firmly in the “strong” category because of its narrow range of options. If both players just avoid obvious losing moves, neither loses and the game results in a draw. It’s no surprise that the game theory term for solved games that permit a tie when played perfectly is ‘futile’ games.
Solved and Futile Games
"A strange game. The only winning move is not to play." --Joshua, from War Games
A famous conversation from the movie WarGames touches on the concepts of solved and futile games, using Tic Tac Toe as an example. When one character mentions how no one plays Tic Tac Toe anymore because it’s always a draw (i.e. it’s a solved and futile game), the heroes realize the opportunity to teach the runaway supercomputer Joshua about no-win situations. After running several such simulations in Tic Tac Toe, Joshua takes the hint and demonstrates that the nuclear war games he’s been programmed with are equally insoluble. In a climactic line, Joshua remarks, "A strange game. The only winning move is not to play."
Not to play indeed. Strategy games should light your brain cells up, not shut them off, but that’s exactly what solved games do once you learn the solution. From that point on, it’s simply a matter of sticking to the solution in a variety of situations, without getting confused or trying to be clever. This prevents a good player from ever learning anything from a better one; the game shuts down at the point where good meets good. Futile games are the worst kinds of solved games, because they leave you exactly where you started, without even the luck of one person going first making a difference. At least flipping a coin would give you an arbitrary winner. Having tested the limits of the game, are we to discard it completely? Should we just teach our children Nine Mens Morris instead, as is commonly done in Germanic regions?
Games are Better Unsolved
With all this going against it, it’s obvious why Tic Tac Toe fades into obscurity with the training wheels and the Elf on the Shelf, but let’s not throw it out quite yet. Chess was once in a similar situation, before the modern rules were introduced. Medieval chess may never have been entirely solved, or entirely futile, but it was far more boring that it is today, with a long tedious opening phase where most of the available moves were equally pointless. When enthusiasts realized the game only really started when someone threatened the middle of the board, they changed the rules to allow pieces to control the board faster. Powerful bishops and queens became the norm, and “mad queen chess” saved chess from the dustbin.
In similar fashion, Tic Tac Toe could be “unsolved” to make it more interesting. Many have tried, either by inserting new rules, or changing the play area. Simply increasing the size of the board helps; the “k-in-a-row game on an m×n” board remains only partially solved. Some variations of this m,n,k-game have their own special names, such as Gomoku, which is normally played on a 15x15 Go board with the same white and black stones. Another common change to the play area is to use three dimensions, either with gravity effects (Connect Four) or without (Qubic).
“Powerful bishops and queens...saved chess from the dustbin.”
By tweaking the rules, things get even more interesting. Consider “misère” Tic Tac Toe, where the winning and losing conditions are reversed, and you have to try and force your opponent to complete a line, or “Wild” Tic Tac Toe where each player chooses whether to place an X or an O on their turn; the first person to complete a line of three is the winner. Combined together and with the O’s removed, these make “Notakto,” usually played on multiple boards at a time. I’ve even seen a “scrolling” version where you draw the crosshatch board around a cylinder such as a toilet paper tube, to remove two edges. This change alone is enough to eliminate draws.
Who Will Win?
Among contenders for the throne of Tic Tac Toe, we have our favorite here at Kubiya games. Our own 3-D version simply called 3D Tic Tac Toe uses both strategies, changing both the board and the rules. The 3D game area has gravity effects like Connect Four, but the objective is slightly different: accumulate as many lines as possible in 14 moves. This scales up the original game’s premise to think defensively and offensively at the same time in a very organic way, so that children can understand the rules and adults can still learn from the challenge.
With time, one of these new versions may rise above the others to rival the original in popularity, to the point where the current version is called “Old-Tac-Toe” or forgotten entirely, like medieval chess. Successfully unsolving Tic Tac Toe could be a greater achievement than inventing a new game, because the foundation game is such a universal part of childhood. Even if none of them becomes wildly popular, the proliferation of these variations could still reinvigorate the old game, turning it into a platform game like pentominoes that can be played multiple ways, where kids grow into one version when they grow out of another. In this coming year, I hope to teach many of these to my kids. My son already beat me at the scrolling version, but I’m ready for a rematch.
What are your favorite variations on Tic Tac Toe? Post them in the comments below!