I should like balls infinitely better... if they were carried on in a different manner... It would surely be much more rational if conversation instead of dancing were made the order of the day.
Much more rational, my dear Caroline, I dare say, but it would not be near so much like a ball.
Jane Austen, Pride and Prejudice
Often an abstract game is introduced to the world with the claim that it requires "a minute to learn, a lifetime to master." How the marketers could know that the latter half of this is true for a game that was invented less than a lifetime ago would be worth inquiry, but here I mean to write on the first half of the slogan. The simplicity of a game's rules is related to the quality of elegance.
Mathematicians use the same word about their work. For example, compare the following proofs of a theorem of geometry, that the base angles of an isosceles triangle are congruent:
Note that the second proof is a step shorter than the first. Also, the second proof involves only the given figure, without introducing a new point. The point D has nothing to do with what we wish to prove; its use detracts from the first proof's elegance.
One more example, from computer programming. It often happens that a programmer wishes to assign a value to a boolean variable (one whose value can be either "true" or "false"). Perhaps a programmer writing code to play a game of dominos has created a variable called GameOver that will be used to indicate the end of the game, when a player has no dominos left. If the number of a player's dominos is stored in a variable called Dominos, here are two ways the programmer might assign the value to GameOver in Pascal:
if (Dominos = 0) then GameOver := true else GameOver := false;
GameOver := (Dominos = 0);
Again, the second way is shorter and simpler; it represents the idea intended (that the game is over when the player has no dominos left) without introducing an extraneous idea (the syntax of the if/then command). It is more elegant.
Applying the word elegance to games comes naturally. In many abstract games such as Go, Hex, and Othello, a single idea leads to an endlessly fascinating game. Elegance is an aesthetically pleasing quality in a good game; there is a sense of wonder that a few simple rules can yield a game so well suited for play. One can readily imagine that at this moment there could be aliens playing Go or Hex by the light of a distant sun. The game seems like an inevitability, as if it were never invented but only discovered; the universe seems to have smiled upon us and given us a really swell toy.
Games please us in two ways: as objects of play and as objects of contemplation. The pleasure afforded by a game's elegance arises when we contemplate, not when we play (although we may contemplate while we play). A game's elegance only deserves praise if the game itself is good to play—if it is deep but clear, dramatic yet decisive, and so on. A game can be elegant without being fun. As David Smith, inventor of the excellent (and highly elegant) game of Trax, has remarked, "It would be hard to find a game more elegant and less useful than Tic Tac Toe."
Elegance, in games as elsewhere, is only a conditional merit; a mistaken mathematical proof may be exquisitely simple, but does not earn the epithet of elegant. Woody Allen's movie Sleeper, in which Allen's character awakens in the far future, includes a delightful sight-gag illustrating the point: Allen approaches an ultramodern and supremely elegant "chair" consisting of an S-shaped strip of metal projecting from the floor, and spends most of a minute attempting to sit on the thing without falling off. Beautiful form only counts if the required functions have been fulfilled.
Furthermore, a game can be good to play without being elegant. In the mathematical sense, my single-speed bicycle is more elegant than a Rolls-Royce: look at all the unnecessary machinery it dispenses with! But the limousine is superior in many other ways. The rules for entering, moving, and capturing in Jim Albea's fine game of Plateau might require half an hour to learn; but the players who have taken the time find the game well worth it.
Consider the rules of Chess: the basic Rook and King moves are simple and elegant; but then the rules for castling intrude like extraneous points and lines in a geometry proof. Defining the pawn's powers requires no fewer than five distinct rules; en passant capture pops up out of nowhere like a rabbit out of a magician's hat. Peace to all Chess-lovers, but Chess is not an elegant game.
Nor need it be. Every inelegant accretion in the rules of chess has a good reason based on improving the game's play. The en passant capture has nothing of inevitability about it, but it increases the reward for developing pawn attacks and thereby adds to the game's drama. The often-criticized rule that stalemate is a draw also increases Chess's drama, by giving a player hope of salvaging something even after he can no longer win. In Othello and Pente, the rules governing the opening play detract slightly from those games' elegance, but they also reduce the first-player advantage. Rules that enhance play should not be deleted in the name of elegance. Kevin Maroney's game of Ur-Chess (Varying Chess) is rather like Caroline Bingley's suggestion in the quote I used for my introduction: it would make Chess much more rational, but not near so much like Chess.
Where then does one draw the line? In the words of Will Strunk Jr., in The Elements of Style:
A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subjects only in outline, but that every word tell.
Rules should not be multiplied unnecessarily, but a game that plays well with complex rules should not be faulted for them.
Good games can be elegant or inelegant, elegant games can be good or bad. Elegance in a good game is an especially endearing feature, but it can never impress us on its own. As a lover of mathematics, and having particular fondness for contemplating beautiful games, the elegant games will always be my favorites. But the most important thing about a game is not whether it can be learned in a minute, but whether it goes on rewarding play for a lifetime.
- J. Mark Thompson