Categories of games by player numbers

Step-change differences exist between games, based on how many players they have. There are essentially five different categories.

In the following, "players" means either individuals or teams of individuals working together. Whether you want to count AI-controlled opponents as players or merely as part of the game system is up to you.

Zero-Player Games

These are games that have a set-up but no further interaction to them. Conway's Game of Life is the classic example, but games with interactive set-ups (such as Exquisite Corpse) also count. Games that do have interaction but it's either immaterial or preordained are also effectively zero-player: assuming that the players don't believe they can influence luck, Snakes and Ladders (also known as Chutes and Ladders) is a good example of the former; if all players know the solution, Noughts and Crosses (Tic-Tac-Toe) is a good example of the latter. Zero-player games can have multiple players at the set-up stage. For example, in Core War two players write programs independently during set-up; these are then executed simultaneously during play and whichever program is made to crash first by the other loses.

Single-Player Games

These are essentially self-tests. You assert a goal that has a success/failure measure and endeavour to achieve the former. If you have no influence on the result of the test, as with a single coin toss, you're not testing yourself and it's a zero-player game. Otherwise, you're charting a path through a series of contingent states to reach a desired condition. Self-tests can't be won or lost, they can merely be succeeded at, failed at or abandoned. For example, if you were to set yourself the goal of running a marathon, you can't claim to have "won" it if you succeed. Self-tests of an intellectual nature are given a special designation: puzzles. Uncertainty may add jeopardy, but the player is basically just navigating a possibility space with an accompanying end goal. Single-player, large-scale strategy games in the Civilization series really are just very sophisticated games of Patience, and Patience is a puzzle. Players describe puzzles as being finished or not finished, rather than won or lost, succeeded at or failed at. You don't win or succeed at a crossword puzzle or a jigsaw puzzle. However, if the puzzle's possibility space allows for critical decisions that will determine the outcome, the player could count successful completion as victory: it may be argued that you can win at Patience.

Two-Player Games

Two-player games assume an opponent capable of rational thought who in turn assumes you are similarly capable. You can lose a two-player game, which is what happens when the other player wins. All zero-sum, finite two-player games have a solution, though, so there's a strategy that will always lead to a win. If the strategy is known by both players (such as might be the case for Noughts and Crosses), it becomes effectively zero-player; if neither knows the strategy (as is the case for Chess) then it becomes a matter of search, pattern-recognition and bluff; if uncertainty is involved, as in interactive skill-based games such as Snooker and Pool, add luck-testing. If the game is co-operative and not zero-sum then it's a single-player game, according to the definition of "player" I'm using. Otherwise, the game will reduce to each player's making a choice as to whether to co-operate or to defect: basically, you get to decide whether to turn it into a single-player game (co-operate) or a zero-sum two-player game (defect). You can also choose to ignore the other player's autonomy and consider them as part of the environment, in which case you (but not necessarily the other player) are playing a single-player game. If you take no action after setting up, as you could do in, say, a tower defence game, then for you it would amount a zero-player game.

Multi-Player Games

With three or more players, games can add new elements that break the single-strategy approach of two-player games. They don't have to — Monopoly is multi-player but has a dominant strategy: you may as well roll a single die at the start to see who wins. If there is little interaction between players, as in a 100m sprint, the game is effectively single-player. If there is interaction, though, as in a 1,500m middle-distance race, tactics play a part. Multi-player games introduce two mechanics that are not available in two-player games: kingmaking and chip-taking. In a two-player game, kingmaking is simply conceding defeat, but with three or more players it allows the player to decide in their defeat which of their opponents will win. Chip-taking, also known as ganging-up, allows players to form transient alliances to slow down another player's march to victory. While the alliance holds, the co-operating players act as one player at the tactical level while still pursuing separate goals at the strategic level; alliances are therefore shifting, and can change or disintigrate rapidly. Because of this, they may be perceived to exist even when they don't (or vice versa). This ability of a player to choose to help a second player so as to hinder a third is what makes games with three or more players a different beast to games with two players, and is why analyses of two-player games rarely transfer to multi-player games. As with two-player games, it's possible to treat other players as if they were automatons; you (but not necessarily the other players) can therefore play a multi-player game as if it were two-player or single-player; zero-player is also possible, by simply not acting.

Massively-Multiplayer Games

Massively-multiplayer games have so many players that cohesive gameplay breaks down. Individuals can be playing the same game as if it were multi-player, two-player or single-player, all at once; they can even play it as zero-player, which is essentially spectator mode. The reason for this is that the magic circle no longer holds: players are unable to use social norms to regulate the behaviour of others such that they conform to an accepted set of rules. In a multi-player game, if someone is a spoilsport then the other players (often one is enough) can stop playing in protest; the game as a whole is then effectively over. This is not possible in massively-multiplayer games: the game can shed large numbers of players and still continue. The only rules that universally apply in massively-multiplayer games are those enforced by the program code, by customer service representatives and by law enforcement officers from wider society.

The boundaries between zero-, single-, two- and multi-player games are hard. The boundary between multi-player and massively-multiplayer is soft, and depends on the nature of the game itself and the discipline of the players. Nevertheless, there is an experiential difference between all five categories of games.

Whatever the number of players a game has objectively, players are at liberty to play it otherwise. It's entirely possible that one player thinks a game is ongoing when it has long since been abandoned by the other players — or never had any in the first place. Nevertheless, if you design or study a game that fits one of the five categories, be aware that you can't assume that what you learn will apply to games in any of the other categories.