When you hear “Game Theory,” you might think of complex economics, political negotiations, or scenes from movies like A Beautiful Mind. But at its core, Game Theory is simply the study of strategic decision-making. And what are puzzles like Chess, Sudoku, or even a simple game of Tic-Tac-Toe, if not a series of strategic decisions?
The principles of Game Theory aren’t just for Nobel laureates; they offer a powerful framework for how we can approach and master a huge variety of strategic puzzles. Welcome back to Sequentia, where today we’re thinking one step ahead!
What is Game Theory, Really?
Game Theory analyzes situations where the outcome of your choice depends on the choices made by others (or, in the case of many puzzles, on the constraints of the game itself). It’s all about figuring out the optimal move when the result isn’t entirely in your control.
While it often applies to competitive games, we can adapt its core concepts to single-player logic puzzles. In this case, your “opponent” is the puzzle itself, and the “rules” are its constraints.
Key Game Theory Concepts for Puzzle Solvers:
- Dominant Strategy: The “No-Brainer” Move
- In a game, a dominant strategy is a move that gives you the best outcome, no matter what your opponent does. In a puzzle like Sudoku, this is the equivalent of finding a cell where only one number can possibly go. Placing that “8” because it’s the only option left for that row, column, and 3×3 box is a dominant move. There is no better alternative, and it’s a guaranteed step toward the solution.
- Puzzle Tip:Â Always scan for these “forced” or “dominant” moves first. They are the bedrock of your solution and reduce the puzzle’s complexity without any guesswork.
- Backwards Induction: Thinking from the End
- This is a powerful technique where you analyze a game by starting at the final possible move and working your way backward. Imagine a simple maze puzzle. Instead of starting at the entrance, try starting at the exit and tracing the path backward. Sometimes, this reveals the one true path much more quickly by eliminating dead ends from the finish line.
- Puzzle Tip:Â When you feel stuck, ask yourself: “If I were one step away from solving this, what would the puzzle have to look like?” This can clarify what your immediate goal should be.
- Elimination of Dominated Strategies: Pruning the Possibilities
- This is the heart of puzzles like Logic Grids and Sudoku. If you know a particular choice is always worse than another choice, you can eliminate it from your consideration entirely. In Sudoku, when you pencil in potential candidates for a cell (e.g., “could be a 2 or a 7”), and then prove that it can’t be a 7 because of a rule elsewhere, you have eliminated a “dominated” (losing) strategy.
- Puzzle Tip: Focus not just on what a move can be, but actively prove what it can’t be. Every possibility you eliminate gets you closer to the correct solution.
- Zero-Sum vs. Non-Zero-Sum Thinking
- A “zero-sum” game is one where one player’s gain is exactly another’s loss (like Poker). Many puzzles are “zero-sum” in a way: a correct move is a “win,” and an incorrect move is a “loss.” However, thinking of the process as non-zero-sum can be helpful. Every small bit of information you uncover, every possibility you eliminate, is a gain. It’s not just about the final win; it’s about accumulating small advantages over the puzzle’s complexity.
By consciously applying these concepts, you shift from simply “trying things” to making deliberate, strategic choices. You start to see the puzzle not just as a static object, but as a dynamic game of logic where you can outmaneuver the challenge itself.
What strategies do you find most helpful when you’re deep in a puzzle? Share your go-to techniques in the comments!
