What makes a game balanced?
Not that every option is equally good — that is neither achievable nor desirable — but that no option dominates so completely that the others become pointless, and that skilled play is rewarded more than choosing correctly at the start.
What balance is not:
Not mathematical equality. If every character, faction or strategy performed identically, variety would be cosmetic and choice meaningless. Differences are the point.
Not equal win rates across all players. A better player should win more often. Balance concerns the options, not the outcomes.
What designers actually aim for:
No dominant strategy. If one approach beats all others in all circumstances, every other option is decoration, and the game collapses into a single line of play.
Rock-paper-scissors relationships, where strong options have counters, so the correct choice depends on context and on what opponents are doing.
Comparable power at comparable difficulty. An option may be stronger if it is harder to execute, which rewards skill without unbalancing the game. High-skill-ceiling options with modest win rates but high performance in expert hands are generally considered well designed.
No runaway leader problem. If being ahead makes it easier to get further ahead, games are decided early and the remainder is a formality. Many designs include catch-up mechanics, which must be subtle enough not to punish good play.
No kingmaking, where a player who cannot win decides who does.
Meaningful decisions throughout, rather than a game determined by the first few moves.
How balance is actually achieved: extensive playtesting, statistical analysis of outcomes at different skill levels, and — for digital games — ongoing patching informed by real player data, which physical games cannot do.
The tension designers live with. Perfectly balanced games can feel sterile, while asymmetry and imbalance can produce memorable, dramatic play. Some celebrated games are not well balanced at all and are loved anyway, because they are interesting. Balance is a means to sustained engagement, not an end in itself — which is the point most balance arguments miss.