Looking at game design in terms of ways of introducing asymmetry

In many “natural” games, such as sports, and in many traditional board and card games, every participant begins with an equal position and prospects to every other.  This is symmetry.  We can look at game design as devising interesting ways to break up symmetry, to introduce asymmetry.  Some of these are achieved through player choice, some through randomness, some through uncertainty, and some through choice or caveat of the designer.

Asymmetric assets
The most obvious way to break up symmetry is to be asymmetric from the start.  Give each player different assets, or a different position if it’s a spatial/geographical game, or both.  This is a characteristic of most two player wargames but much rarer in wargames for more than two.  It’s rare in Eurostyle games as well.  In fact it’s pretty rare generally because it’s much more work for the game designer.  The designer has to balance at least two different groups in order to make the game fair.  In my experience Britannia-like games are a big pain in the rear because there are four sides that are asymmetric in both assets and locations.  It is much easier to balance a game that’s symmetric.  Diplomacy and Diplomacy variants can be difficult to balance geographically but all sides usually have the same number of units to begin with (in the parent game, Russia is the exception, with four units rather than three).

Asymmetry through game setup
This occurs when players either choose their assets, often according to a point system, or they choose their locations.   In Risk players either choose their locations during the setup or the territory cards are used to randomly distribute them about the board.

Sometimes the board/playing field itself changes from game to game as in Settlers of Catan or computer Civilization.  Or a game may have an exploration component which means that as locations are explored you get a new and non-symmetric board every time.

Asymmetry through roles
Many Eurostyle tabletop games use the idea of roles, such as King’s adviser or merchant, each belonging exclusively to one player in each round.

Vinci/Smallworld uses a kind of role in the Empire characteristics that a player can choose.  The difference is that available roles in typical Eurostyle games are the same every round.  InVinci/Smallworld the pairs of Empire characteristics are rarely repeated within a game, so once selected by one player, they aren’t available to another.

Asymmetry through the roundel
Some tabletop games use a roundel or other means to limit the action choices a player has in his next turn.  As the player “moves” around the roundel, each turn he has a different set of choices in front of him.

Asymmetry through turn order
In some turn-based games there is an advantage to playing first, or last, or some other place in the turn order, and there’s a mechanism to enable players to compete for the most desirable place in the turn order, such as an auction.

Chess is asymmetric with respect to turn order, with white having a much better chance to win than black.  This is accounted for in tournaments by having players play both black and white equally in the course of the tournament.  Another way might be to let black move twice after white’s first move.

(The above three amount to asymmetry through what a player can or cannot do in the sequence of his particular turn.  There are other ways to do this as well.)

Asymmetry through different decks of cards
Collectible card games enable players to make up decks of cards that are different from other players’ decks.  Other games that supply defined decks of cards, such as Fantasy Flight Games’ “Living Card Games”, strictly limit the number of possible decks yet each deck is different from each other deck.

Asymmetry through event cards
Many boardgames include a deck of event cards.  Each player is dealt a hand of cards, so each player has different capabilities.  There are many computer equivalents of this with many names such as beginning skills, perks, etc.

Asymmetry through character classes, feats, skills, perks
In games where the player acts through an avatar, the game often provides alternatives in character class (profession), character ability numbers, skills and feats, and other ways, both functional and cosmetic, to customize the character and make it different from all other characters.

Asymmetry through uncertainty
There are many forms of uncertainty, some of them resulting from randomness, some from the uncertain intentions of other players, and some from hidden information.  Typical games using normal playing cards rely on hidden information, usually combined with the randomization of hands dealt from a shuffled deck to introduce a great deal of asymmetry immediately.

Asymmetry through randomness
I’m sure you knew I would get here sooner or later, because randomness is a straightforward and easily designed way to introduce asymmetry to a game.  That randomness can derive from dice or spinners, shuffled cards, chit draws, and other more esoteric methods.

This can be quite straightforward.  In Britannia, the setup never varies.   But as soon as the game begins, different players attack differently with the Romans; and dice rolls for combat result in even greater variety.  So practically speaking the positions of the Romans, Belgae, and Welsh differ from game to game even though the setup is unvarying.

What may be most important about randomness is whether it occurs as what Geoff Engelstein calls input randomness or output randomness.  Input randomness occurs before a player acts, and may affect all players equally.  An example of this would be drawing a artwork token from a bag that all players will then bid for.  Which painting comes out is random but all players are affected equally even though some may prefer a different painting than the one that came out.  Output randomness occurs after the player acts, and usually affects only that player, as in the combat dice roll in so many wargames.

Output randomness can be accounted for up to a point, but modern hobby gamers tend to feel better about input randomness than output randomness.

Greg Costikyan has written a brilliantly explained discussion of how randomness can be used in games: http://playthisthing.com/randomness-blight-or-bane.