A combinatorial game is a strategy game with perfect information where players take turns making their moves. These games are pure tests of calculation skills, and must have all of the following properties:
- No hidden information that players could bluff about or use to surprise each other.
- No simultaneous actions, as that requires players to predict each other.
- No real-time actions, as that would give the game a speed element. (Time limits on turns to keep things moving is okay.)
- No dexterity-based challenges.
- No need to memorize in-game information. (Memorization in the form of learning strategy is okay.)
- No randomness. The only exception is that a randomized setup (e.g. Fischer Random Chess) is permissible, since the game is predictable from that point. A first-player advantage or second-player advantage is also acceptable — who goes first is not determined in-game. (In fact, in two-player combinatorial games, one player is guaranteed to have an advantage.)
Note that unlike Abstract Strategy Games, a combinatorial game is allowed to be thematic (Photosynthesis) since its mathematical properties don't care if you're simulating the growth of a forest or just moving tokens around on a featureless board.
These games are usually 2-player only, which eliminates yet another potential unpredictable factor: you only have one opponent, so there's no chance of being screwed over because someone chose to hinder you specifically, or because you weren't able to make the right deals.
The fact that 2-player combinatorial games are deterministic has several interesting consequences. The first is that they're seen as purely skill-based battles of wits, with some of them being among the most long-standing and respected games in the world. This is reflected in media, where Smart People Play Chess. This factor also appeals to the competitive side of the Casual-Competitive Conflict — a well-made combinatorial game has a lot of depth they can dig into, and the more skilled player can't lose by getting screwed by the Random Number God. On the flipside, this means that an expert is guaranteed to wipe the floor with a beginner, so the game probably won't be very fun if there's a large skill discrepancy between the players.
The second is that the deterministic nature of these games makes them solvable. You can, at least in theory, look at every possible sequence of moves and see where it leads. Once every option has been examined, you can see which player is able to force a win, or at least a draw.note This represents a pitfall for games of this genre: if the winning strategy is too easy, the game becomes uninteresting once it has been discovered. With that said, it can still be entertaining to look for that strategy. Some mathematical problems even involve "mathgames" — combinatorial games designed to be solved, not played!
The third ties into the second: the lack of "fuzzy" elements like bluffing or playing the odds makes the genre computer-friendly. If you tell it how the game works, it can simply calculate the possible outcomes of various moves and determine which one is the best. This method has been used to solve games whose strategy trees are too big to be fully explored manually, including checkers and Connect Four. And even if creating a Perfect Play A.I. is not feasible with today's computing power, it's usually possible to make an engine capable of beating even the best human players. Neural networks even enable you to create a strong AI from scratch simply by teaching it the rules and having it play against itself.
Compare Abstract Strategy Game, which has a lot of overlap with this. Contrast Ameritrash Games and Narrative Board Games, which aim for drama and excitement over strategy.
