Game Balance in general means that the game provides each player with either the same opportunities, chances and options, or with equivalent ones. Chess provides the players with many of the same options (the pieces) and theoretically equivalent opportunities (going first or second), although IIRC at the extreme high level, going first is more valuable. Risk provides each player with the same chances each time he sits down to the table, but those chances won't result in the same options and often won't result in the same opportunities (randomly ending up with no way to control a continent, for example).
Balance in traditional RPGs is somewhat complicated by two factors: first, most of the players are on the same side, and second, the 'game' doesn't usually end with the 'session.'
I. THE PLAYERS ARE MOSTLY ON THE SAME SIDE
This is where the concept of 'spotlight balance' comes in. Basically, it means that each player should be able to contribute meaningfully in any situation that takes more than a few minutes real time to resolve.
(Caveat: This assumes all the players WANT to contribute meaningfully in any situation, which is not always the case. Too often I see people assume that a player who sits back and doesn't do much in certain situations (usually either combat or in-character dialogue) is 'dragging the game down' or 'not having fun.' I fail to see how this is the case; if they aren't involved, then they're intentionally relinquishing the spotlight to the other players in that circumstance, and what's wrong with that?)
Since combat in D&D takes a great deal more time than other activities, 'spotlight balance' is usually achieved by the same thing 'tactical balance' is: making characters combat options roughly equivalently useful. This is one of two reasons I refer to D&D as a 'Tactics/RPG,' the other being that by default it places combat on a 2D grid to allow the players to visually grasp the tactical situation.
In a cooperative game in which combat was resolved with a single roll but, say, cooking took an hour real-time to resolve, rough equivalence in cooking options would then become the priority. Spycraft gives us a good example of non-combat activities that can take a lot of in-game time to resolve, in its Dramatic Conflicts. I'm not entirely sure it allows all the players to involve themselves sufficiently for my tastes, but it is an example of a relatively traditional RPG with a set of in-depth non-combat rules.
Of course, being equally ABLE to contribute and contributing equally are two very different things - this is where involvement and play skill come into play (equality of outcome rather than equality of opportunity).
II. THE GAME DOESN'T END WITH THE SESSION
My rule when it comes to randomization is this: if it has an impact for the entire campaign, it is inappropriate for it to be random. If it has an impact for only the current session, it is appropriate for it to be random. That means, basically, max hit points, ability scores and character death are things I don't want the dice determining. Everything else is fair game.
(Caveat: My personal preference, just in terms of the kind of games I like, is for considerably less randomness even in play; it has nothing to do with the ease or complexity of the system - chess is as difficult as your opponent can make it and has all of one random element, for example - it's just my preference. However, I don't think this is a design principle.)
I would not be opposed to random hit points if they were 'done wrong' as I've seen several people say they did the first time they played: rolled anew each session. This puts starting randomness on a per-session rather than per-campaign basis.
Rolling ability scores each session would be a huge pain, so I'm *always* opposed to rolling for those.
Gameplay-dictated character death, or more specifically randomization-dictated character death, has a huge impact in my games, because the settings I use don't have Rez-marts like core D&D. Worse, however, is the effect randomization-dictated death has on the style of play and what the game's simulation elements are simulating.
III. WHAT, IF ANYTHING, IS BEING SIMULATED
Any argument that begins with "but in the real world" or the equivalent automatically fails to move me; D&D is not the real world. It is a game. "In the real world," a lone footman in a lucky position is not going to "kill" a fortress, yet in chess a pawn can take a rook. "In the real world," coherent nation states do not crop up with provinces in random locations all over the world and then wage war in large part to achieve geographic unity, yet in Risk this is what they do.
D&D is also a heroic fantasy game. What makes "sense" for a player character is what makes "sense" for an action hero in a movie, or the protagonist of a Sword and Sorcery yarn - not what would make sense for even a highly skilled person in real life. If doing what would make sense for the latter is rewarded (with life, wealth and XP) and doing what makes sense for the former is penalized (with death, negative modifiers and failed missions), then the game is not simulating what it should be: its source material.
