I suspect many people who read my blog don't follow the comments when those comments go on at great length and over several days so I want to summarize a bit what came of the last balance post I made on tuesday. lebkc came up with a definition for a balanced game that read like thus:
"equally successful for all players under perfect play"?
I think I would rewrite it slightly to be like thus:
"A balanced choice is one where any of the options will produce a similar average result in terms of performance when chosen by a player that otherwise plays perfectly."
Thing is, lebkc's argument doesn't work for game balance on a whole game level at all but I think it works great for a single choice. I don't know which way he intended it. It isn't doing anything particularly innovative there but it certainly sums up the idea that if a set of choices all have similar performance results when played perfectly they are all balanced against one another. However, I was talking about defining what makes a game balanced or not rather than what makes a choice balanced or not. I don't think I was particularly clear on that point which is probably why the discussion has been so vigorous and we have been so much talking past each other.
Any choice within a game can be put into the set of choices that is balanced (as per definition above) or unbalanced. The trick to defining a balanced game in my mind is to figure out how we derive overall game balance from looking at the individual choices. Clearly all games of any complexity have many choices that are widely unbalanced but this does not prevent us from thinking of the game as unbalanced at all. In chess you can spend every move moving a knight in and out of his starting position - this is not balanced as a strategy against "play well" but it doesn't make chess unbalanced. In WOW you can refuse to put on gear and this is not balanced against putting on gear but yet that isn't going to change our minds about whether or not we call the entire game balanced. It is clear that there are some specific choices that will trigger us to think that a game is imbalanced but that the size of balanced/unbalanced sets is not the trigger and I can't see any other clearly identifiable pattern.
As such I don't think we can derive a definition for a balanced game that can be arrived at without looking at the preferences and beliefs of the players. Clearly humans have tendencies and we can make good educated guesses about what they will think and reasonably call things balanced or not based on those guesses and I don't think there is any other way to resolve whether a game is, as a whole, balanced or not. Individual choices can be mathed and played out to arrive at a defensible, logical conclusion as to their balance or lack thereof. I don't think a whole game can be approached in this fashion.