Why do we play games where each player wins or loses?
I don't mean this is the whiny, why-can't-we-all-just-get-along manner of most people who ask that question. I mean it as a serious enquiry; we do, after all, play such games, and it is likely that there is a reason.
The activities in which we engage differ in difficulty. At the easy end are things which are boring, or things like sleep. At the difficult end are things that most people find unpleasant, and prefer to do as little of as possible. In the middle are some things which are complex enough to be interesting, but not so difficult as to be strenuous or unpleasant.
Games, almost universally, fall (for the people who play them) in the range of things which are difficult enough to be interesting but easy enough to be enjoyable.
Successful games, in light of the above, almost always have several features in common:
The reason for these features is that, generally, the smaller in scope a problem, the easier and more tractable it is. "Fun" problems are usually just a little bit beyond the complexity for which an optimal solution can be found. (tic-tac-toe is an example of a game which is too easy for most adults - all games will result in a draw.) The features above exist to limit the scope of the games to a size which is fun instead of being overwhelming and frustrating.
After all, a game must have some restrictions or rules. There's a game which has none at all, and it's called "real life." Anything we call a game is simplified through the introduction of constraints.
The nature of the constraints, however, is quite telling. The constraints remove the requirement for two abilities which are rare - creativity and initiative. Creativity is the ability to have new ideas which are fundamentally different from ideas which have been had before; to find new solutions to a situation which are orthogonal to standard practice. The requirement that "moves" be selected from a predetermined set makes creativity irrelevant. This is quite necessary, because creativity is a rather rare ability, and certainly not one which is involved in any activity easy enough to be "fun" for most people.
The second ability, initiative, is even rarer than creativity. This is the ability to select goals for oneself, decide what is good and worth doing, and do it, instead of simply reacting to one's environment. Games, happily for their players, provide a set of objectives and an initial state to which one can react.
So, then, why do we play games where one side wins and the other loses?
We play such games because we are incapable of anything better.
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