Part of balancing chance factors is having them come up enough to even out, and another part is weighing them against other factors. Options can present different mixes of risk and reward, different strengths and weakness, different courses of development calling for different strategies.
Such a balance of opportunities has as its object facilitating the emergence of inequality in results among players.
That is obviously a radically different game than one in which the object is equality in results among players.
Trying to play Game B with parts designed to produce Game A, or vice-versa, can be very unsatisfying.
Building on this: it seems fairly obvious to me (but maybe I'm misreading the evidence) that part of what causes the "balance" debate is that different people are trying to use the same set of RPG rules to play very different games.
Related to this is a tendency to limit the notion of "RPG rules" to action resolution mechanics, plus those parts of the character creation mechanics that feed into action resolution. But as Ariosto points out, "balance" questions (Game A vs Game B, for example, or "spotlight sharing" vs "all involved all the time") also connect to other rules aspects like encounter and adventure design, rules for distributing narrative authority, and so on.
Balance issues also turn on the aesthetic point of play. For example, is a game in which the character build and action resolution mechanics mean that some mechanically legal PCs are more likely than others to achieve their desires "unbalanced"? It depends, at least in part, on the relationship between a PC's desires and that player's desires. If part of the point of playing, for the player, is to see his/her PC live out a dramatic life, then the player may be satsified by a system of character building and action resolution that make it likely that her PC will die a failure with her desires unfilled,
provided that the failure is dramatic. For players interested in that sort of play, one "balancing" feature of the rules might be ensuring that it is easier for a PC to be a dramatic failure than a dramatic success - thereby avoiding sacharine storylines - while also making success possible - thereby avoiding bathos.
But for typical D&D play, such character building and action resolution mechanics would be unbalanced, because typical D&D play doesn't involve such a strong metagame player/PC split. Hence the 4e rules make it very hard to create a tragic failure of a PC, whatever the build (provided the GM follows the guidelines for encounter and adventure design). This also connects to the reward mechanics of XP and treasure, which assume that the players will be trying to have their PCs succeed at their encounters (thereby earning the XP and collecting the loot). Those reward mechanics would be
unbalanced in a game meant to support tragic failure, because they would not give resources to the player of the failing PC that would help that player control the development of her PC's (tragic) life.
One interesting feature of the "balance" of 4e is that it does produce encounters where failure for the PCs as a whole looms large in the early part of the encounter, but is then overcome as the conditional resources of the PCs come into play (second wind and other healing, the superior effects of encounter and daily powers, etc). So in 4e, making sure that all PCs are able to participate meaningfully in combat is (in part) about making sure that there is balance across participation in that part of the game where the drama plays out. For players wanting the game to focus on something else - whether drama across some unit of play other than the encounter, or something other than drama - then all 4e's effort dedicated to producing this sort of balance is wasted.
The part of the 4e encounter design and action resolution mechanics which seems to have paid least attention to this sort of dramatic balancing is the skill challenge mechanic. And this seems to be widely regarded by players of the game as one of the aspects of the game most in need of development. But for those who like the sort of play that 4e best supports, developing the skill challenge mechanic would require injecting
more of 4e's encounter/drama balance - including full participatio in all encounters by all PCs - not returning to the "spotlight-sharing" balance of other games and editions.
