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Designer's Notebook: A Symmetry Lesson

October 16, 1998

The more observant among you may have noticed that my column didn't come out last month. I was on vacation in Oxford, England, where I was studying the art, architecture, history, and sociology of the English country house. You might wonder why a computer game developer would want to be able to tell the difference between Baroque and Rococo decoration, or why a liberal would want to study the extravagant mansions of a group of people who lived lives of ostentatious dissipation while the downtrodden working classes slaved away in the hot… where was I? Well, anyway, the short answer is that if game developers don't learn something new every once in a while, the whole damn industry is going to end up behind the eight ball again, that's why.

One of the things that the Renaissance brought to English architecture was the classical idea of symmetry, that buildings looked better when the left side was a mirror image of the right side. This was hardly a new idea, but until the Renaissance, people hadn't made much of an effort to apply it to houses. Symmetry applies to all kinds of things besides architecture of course; it applies to art and book design and even music, and it also applies to computer games.

This is a column about symmetry in game design.

I've written before about how the essence of game design is balance. In the case of a multiplayer game, balance means the fundamental condition of fairness, the requirement that all the players have an equal chance of winning at the beginning of the game. In the case of solitaire games (like most computer games), balance means that the game must be neither too easy nor too hard.

The issue is less one of fairness than it is of providing a reasonable challenge and a reasonable chance of winning. One of the best ways of guaranteeing that a multiplayer game is balanced at the beginning is by making it symmetric, that is, by making sure that all the players play by the same rules, and start with the same resources. If you're trying to balance both sides of a beam scale, the easiest way to do it is to put identical objects in either pan, i.e. to pile them up symmetrically.

Chess, checkers, Monopoly, and most other simple games are symmetric: they start with identical resources on all sides. Even in a perfectly symmetric game like chess, there's still one unavoidable element of asymmetry, and that's the fact that someone has to go first. In many games, like tic-tac-toe, going first provides an advantage. There are several ways of reducing the effect of one player going first. One way is to set the game up in such a way that the initial move provides very little strategic advantage.

In chess, for example, the rules of the game are such that you can only move a pawn or a knight on the first turn. These are the two weakest pieces in the game, not counting the king. Thus, the advantage conferred is not significant. In addition, the pieces are four rows apart at the beginning, so no single piece can take or even significantly threaten an enemy piece on the first move. Another way to reduce the effect of going first is to make the game a fairly long one, so that going first makes very little difference over the course of the whole game.
Tic-tac-toe is a very short game, so going first is extremely valuable and whoever goes second is usually on the defensive for the whole game. With a longer game like checkers or chess, it doesn't matter so much.

Finally, a game can incorporate randomness to reduce the effect of going first. Monopoly and backgammon are games in which the players throw dice to move, and since the player going first could very well have a bad throw and the one going second could have a good throw, the moves are much more affected by the die roll than by anything else.

In computer games the issue of who goes first is usually moot, since real-time games far outnumber turn-based games. And the few turn-based games that do exist, like X-Com, usually take much too long for it to make any difference in the end. However, I include it here because I think a computer game designer should also be a competent paper game designer, and for paper games it's an important question.

A variant of the simple symmetry found in chess, checkers, Stratego and the like is the "rotational" symmetry found in Rochambeau (rock-paper-scissors). In Rochambeau, two people choose one of three items at random: rock, paper, or scissors. The winner is determined by the following formula: scissors cuts paper and defeats it; paper wraps rock and defeats it; rock breaks scissors and defeats it. If both choose the same thing they play again.

This mechanism was also found in the old Brøderbund game, The Ancient Art of War. In that game, knights had an advantage over barbarians, barbarians had an advantage over archers, and archers had an advantage over knights. An additional element of this kind of game is hidden information: the fact that one player does not know which of the three options the other player will choose to use. As a result, there's more psychology involved than in a simple game of complete information like chess or checkers.

Asymmetry Caveats

As I said, symmetry is the simplest way of making a game fair, but it tends to emphasize the artificial nature of the contest. Games are often more interesting, and feel more "real," when they contain asymmetries. A very ancient asymmetric game is a board game called Fox and Geese. In Fox and Geese, one player controls one piece (the fox) and the other controls 17 pieces (the geese). The fox can move in any direction and can jump the geese as in checkers, removing them from the board. The geese can only move towards the fox and cannot jump it. The geese win if they pin the fox in so it cannot move. The fox wins if it jumps so many geese that not enough are left to pin it.

Wargames, which often purport to be simulations of historical events, are often asymmetric because the manpower, equipment, and field positions of the opposing forces were asymmetric in the first place. As a result, balancing a wargame so that each player has a similar chance of winning is a considerable challenge. Often this is done by giving different victory conditions for each side (which we also saw in Fox and Geese). In the case of a massive army besieging a small garrison force, the victory condition for the garrison is not the defeat of the massive army, which is clearly impossible, but to hold out for a given length of time or number of turns. If the army overruns the garrison in the time allowed, it wins; if not, it loses.

One of the most popular asymmetric computer games right now is Starcraft. Starcraft is a game that requires constructing a series of buildings as you build an army; this is also found in Command & Conquer and Dungeon Keeper. In Starcraft, armies belong to one of three races: Terrans, Protoss, and Zerg. The functions of the buildings are relatively similar between the races, but the weaponry of the units (particularly the high-level ones), their production costs, their production mechanisms, and their durability are all quite different.

In general Protoss units are very tough but also very expensive, while Zerg units are cheaper and weaker, and Terran units are somewhere in between. Zerg units heal themselves over time; Terran units can be quickly repaired, but only by a special repair unit; Protoss units cannot be healed or repaired, but can use rechargeable shields to defend themselves. This asymmetry has, of course, given rise to a great deal of debate about which race it is better to play with. If you read the addendum to the manual, it's clear that some last minute tuning took place to improve the odds for some of the races, because a few features to which the manual refers are not in the game

In computer games it's easier to balance asymmetric elements because the die rolling is kept out of sight, and you can fudge the probabilities without the player(s) knowing about it. I don't know that this was done in Starcraft, but it seems likely.

There's another kind of symmetry, or at least balance, to consider, and that's the balance among the types of tactics required by a single player to win the game. Games often contain design flaws that allow players to exploit loopholes in the rules to win the game by repeated use of a single tactic.

This is particularly true of on-line multiplayer simulations with an economic element. The designer wants, and expects, the players to use a variety of tactics, but because of a design flaw, one tactic works so much better than the others that the players abandon all but it, making the game rather dull. In general you want to force players to adopt a variety of tactics to make the game more interesting. The simulation of a professional football game that I work on naturally duplicates the rules of real football. Football used to be a fairly symmetric game, especially when players played both offense and defense.

With the advent of specialized offensive and defensive tactics, the game has become quite asymmetric, at least during any one series of downs. (Of course, it's not asymmetric in the sense that the two teams play by different rules or have different victory conditions.) As a result, the rules are constantly being revised to try to keep the game balanced between offense and defense. Similarly, there's the balance between running with the ball and passing it. In American professional football, passing is slightly more important than running, but teams really must be able to do both well to succeed. Canadian football rules aim for a different balance, significantly emphasizing the passing game and the offense generally overall.

Going back to the English country house for a minute, another interesting development was the invention of "landscape gardening." Instead of laying out a formal (and often highly symmetric) flower garden, gardeners like Lancelot "Capability" Brown designed an entire landscape of lawns, sculptures, waterfalls, copses of trees, and little buildings - usually imitations of Roman shrines. One of the principles of his designs was surprise. Following a path would lead to an unexpected vista or a statue that was hidden from the main house. The landscape garden encourages - and rewards - the visitor's inclination to explore.

This is another worthwhile principle to consider in game design. The obvious parallel is to adventure games, where exploration is the point, but it can apply to other kinds of games as well. A game need not be exactly the same from beginning to end. An unexpected surprise or an unusual twist that emerges partway through can please, encourage, and reward the player. In a way, they represent an asymmetry in time: the game's beginning is not symmetrical with its end. This is a double-edged sword, however. It's best not to change your style of game too dramatically.

For example, Heart of China started as a more-or-less conventional adventure game, but at one point jumped to a rather crudely implemented 3D tank simulation. If you didn't succeed at that, you couldn't go on. It was frustrating; if I had wanted a tank simulator, I would have bought a tank simulator. Above all the surprise, whatever it is, should fit smoothly and naturally into the game, to seem as if it belongs there. Symmetry in game design is simple, easy, and intuitive, but it often leads to an artificiality, a "game-like" feel that nowadays we're usually trying to avoid. Asymmetry is a very powerful tool for generating interest and realism, but it complicates the design and tuning of a game substantially. Use it with care.

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