What is game balance? At its simplest form game balance is a numbers game. What numbers do we use to make a game balanced or to tip the scales to give advantage to one side. If game balance is about numbers the first question you may ask yourself is "what if a game doesn't have any numbers or math involved?"
Let's look at the playground game of "Tag." Tag has no numbers. Does that mean that the concept of "game balance" is meaningless when applied to Tag? No. Imagine you were going to make Tag The Video Game. To program the game you would find that tag does have numbers. How fast a player can run. How long a player can run. How close the players are to each other. The dimensions of the play area. How long is someone "it." We don't track these numbers on the playground, but if it were a professional sport I'm sure we would have some AWS highlights.
Every game does in fact have numbers (even if they are hidden or implicit), and the purpose of the numbers is to describe the game state.
How do we know if a game is balanced? It can be quite difficult to tell. Chess, for example, is not entirely balanced: it has been observed that there is a slight advantage to going first. However, it hasn’t been definitively proven whether this imbalance is mechanical (that is, there is a bona fide tactical/strategic advantage to the first move) or psychological (players assume there is a first-move advantage, so they trick themselves into playing worse when they go second). Interestingly, this first-move advantage disappears at lower skill levels; it is only observed at championship tournaments. Keep in mind that this is a game that has been played, in some form, for thousands of years. And we still don’t know exactly how unbalanced it is!
In the case of Chess, a greater degree of player skill makes the game unbalanced. In some cases, it works the other way around, where skilled players can correct an inherent imbalance through clever play. For example, in Settlers of Catan, much of the game revolves around trading resources with other players. If a single player has a slight gameplay advantage due to an improved starting position, the other players can agree to simply not trade with that player for a time (or only offer unfair trades at the expense of that player) until such time as the starting positions equalize. This would not happen in casual games, as the players would be unable to recognize a slight early-game advantage; at the tournament level, however, players would be more likely to spot an inherent imbalance in the game, and act accordingly.
In short, game balance is not an easy or obvious task.
Deterministic
A deterministic game is one where if you start with a given game state and perform a particular action, it will always produce the same resulting new game state.
Chess and Go and Checkers are all deterministic. You never have a situation where you move a piece, but due to an unexpected combat die roll the piece gets lost somewhere along the way, or something. (Unless you’re playing a nondeterministic variant, anyway.)
Candyland and Chutes & Ladders are not deterministic. Each has a random mechanism for moving players forward, so you never know quite how far you’ll move next turn.
Poker is not deterministic, either. You might play several hands where you appear to have the same game state (your hand and all face-up cards on the table are the same), but the actual results of the hand may be different because you never know what the opponents’ cards are.
Rock-Paper-Scissors is not deterministic, in the sense that any given throw (like Rock) will sometimes win, sometimes lose, and sometimes draw, depending on what the opponent does.
Note that there are deterministic elements to all of these games. For example, once you have rolled your die in Chutes & Ladders, called the hand in Poker, or made your throw in Rock-Paper-Scissors, resolving the turn is done by the (deterministic) rules of the game. If you throw Rock and your opponent throws Paper, the result is always the same.
Non-deterministic
The opposite of a deterministic game is a non-deterministic game. The easiest way to illustrate the difference is by comparing the arcade classic Pac-Man with its sequel Ms. Pac-Man.
The original Pac-Man is entirely deterministic. The ghosts follow an AI that is purely dependent on the current game state. As a result, following a pre-defined sequence of controller inputs on a given level will always produce the exact same results, every time. Because of this deterministic property, some players were able to figure out patterns of movements; the game changed from one of chasing and being chased to one of memorizing and executing patterns.
This ended up being a problem: arcade games required that players play for 3 minutes or less, on average, in order to remain profitable. Pattern players could play for hours. In Ms. Pac-Man, an element of non-determinism was added: sometimes the ghosts would choose their direction randomly. As a result, Ms. Pac-Man returned the focus of gameplay from pattern execution to quick thinking and reaction, and (at the championship levels, at least) the two games play quite differently.
Deterministic games can theoretically undergo some kind of brute-force analysis, where you look at all the possible moves and determine the best one. The number of moves to consider may be so large (as with the game Go) that a brute-force solve is impossible, but in at least some cases (typically early-game and end-game positions) you can do a bit of number-crunching to figure out optimal moves.
Non-deterministic games don’t work that way. They require you to use probability to figure out the odds of winning for each move, with the understanding that any given playthrough might give a different actual result.
Solvability
This leads to a discussion of whether a game is solvable. When we say a game is solvable, in general, we mean that the game has a single, knowable “best” action to take at any given point in play, and it is possible for players to know what that move is. In general, we find solvability to be an undesirable trait in a game. If the player knows the best move, they aren’t making any interesting decisions; every decision is obvious.
That said, there are lots of kinds of solvability, and some kinds are not as bad as others.
Trivial Solvability
Normally, when we say a game is solvable in a bad way, we mean that it is trivially solvable: it is a game where the human mind can completely solve the game in real-time. Tic-Tac-Toe is a common example of this; young children who haven’t solved the game yet find it endlessly fascinating, but at some point they figure out all of the permutations, solve the game, and no longer find it interesting.
We can still talk about the balance of trivially solvable games. For example, given optimal play on both sides, we know that Tic-Tac-Toe is a draw, so we could say in this sense that the game is balanced.
However, we could also say that if you look at all possible games of Tic-Tac-Toe that could be played, you’ll find that there are more ways for X to win than O, so you could say it is unbalanced because there is a first-player advantage (although that advantage can be negated through optimal play by both players). These are the kinds of balance considerations for a trivially solvable game.
Theoretical Complete Solvability
There are games like Chess and Go which are theoretically solvable, but in reality there are so many permutations that the human mind (and even computers) can’t realistically solve the entire game. Here is a case where games are solvable but still interesting, because their complexity is beyond our capacity to solve them.
It is hard to tell if games like this are balanced, because we don’t actually know the solution and don’t have the means to actually solve it. We must rely on our game designer intuition, the (sometimes conflicting) opinions of expert players, or tournament stats across many championship-level games, to merely get a good guess as to whether the game is balanced. (Another impractical way to balance these games is to sit around and wait for computers to become powerful enough to solve them within our lifetimes, knowing that this may or may not happen.)
Solving Non-Deterministic Games
You might think that only deterministic games can be solved. After all, non-deterministic games have random or unknown elements, so “optimal” play does not guarantee a win (or even a draw). However, I would say that non-deterministic games can still be “solved,” it’s just that the “solution” looks a lot different: a solution in this case is a set of actions that maximize your probability of winning.
The card game Poker provides an interesting example of this. You have some information about what is in your hand, and what is showing on the table. Given this information, it is possible to compute the exact odds of winning with your hand, and in fact championship players are capable of doing this in real-time. Because of this, all bets you make are either optimal, or they aren’t. For example, if you compute you have a 50/50 chance of winning a $300 pot, and you are being asked to pay $10 to stay in, that is clearly an optimal move for you; if you lost $10 half of the time and won $300 the other half, you would come out ahead. In this case, the “solution” is to make the bet.
You might wonder, if Poker is solvable, what stops it from becoming a boring grind of players computing odds with a calculator and then betting or not based on the numbers? From a game balance perspective, such a situation is dangerous: not only do players know what the best move is (so there are only obvious decisions), but sometimes optimal play will end in a loss, effectively punishing a player for their great skill at odds computation! In games like this, you need some kind of mechanism to get around the problem of solvability-leading-to-player-frustration.
The way Poker does this, and the reason it’s so interesting, is that players may choose to play suboptimally in order to bluff. Your opponents’ behavior may influence your decisions: if the guy sitting across from you is betting aggressively, is it because he has a great hand and knows something you don’t know? Or is he just bad at math? Or is he good at math, and betting high with a hand that can’t really win, but he’s trying to trick you into thinking his hand is better than it really is? This human factor is not solvable, but the solvable aspects of the game are used to inform players, which is why at the highest levels Poker is a game of psychology, not math. It is these psychological elements that prevent Poker from turning into a game of pure luck when played by skilled individuals.
Solving Intransitive Games
Intransitive games are a fancy way of saying “games like Rock-Paper-Scissors.” Since the outcome depends on a simultaneous choice between you and your opponent, there does not appear to be an optimal move, and therefore there is no way to solve it. But in fact, the game is solvable… it’s just that the solution looks a bit different from other kinds of games.
The solution to Rock-Paper-Scissors is a ratio of 1:1:1, meaning that you should throw about as many of each type as any other. If you threw more of one type than the others (say, for example, you favored Paper), your opponent could throw the thing that beats your preferred throw (Scissors) more often, which lets them win slightly more than average. So in general, the “solution” to RPS is to throw each symbol with equal frequency in the long term.
Suppose we made a rules change: every win with Rock counts as two wins instead of one. Then we would have a different solution where the ratios would be uneven. There are mathematical ways to figure out exactly what this new ratio would be. You might find this useful, for example, if you’re making a real-time strategy game with some units that are strong against other unit types (in an intransitive way), but you want certain units to be more rare and special in gameplay than others. So, you might change the relative capabilities to make certain units more cost-efficient or more powerful overall, which in turn would change the relative frequencies of each unit type appearing (given optimal play).
Perfect Information
A related concept to solvability is that of information availability. In a game with perfect or complete information, all players know all elements of the game state at all times. Chess and Go are obvious examples.
You might be able to see, then, that any deterministic game with perfect information is at least theoretically, completely solvable.
Other games have varying degrees of incomplete information, meaning that each player does not know the entire game state. Card games like Hearts or Poker work this way; in these games, each player has privileged information where they know some things the opponents don’t, and in fact part of the game is trying to figure out the information that the other players know. With Hearts in particular, the sum of player information is the game state; if players combined their information, the game would have perfect information.
Yet other games have information that is concealed from all of the players. An example of this is the card game Rummy. In this game, all players know what is in the discard pile (common information), each player knows what is in his or her own hand but no one else’s hand (privileged information), and no player knows what cards remain in the draw deck or what order those cards are placed in (hidden information).
Trading-card games like Magic: the Gathering offer additional layers of privileged information, because players have some privileged information about the possibility space of the game. In particular, each player knows the contents of cards in their own deck, but not their opponent’s, although neither player knows the exact order of cards in their own draw pile. Even more interesting, there are some cards that can give you some limited information on all of these things (such as cards that let you peek at your opponent’s hand or deck), and part of the challenge of deck construction is deciding how important it is to gain information versus how important it is to actually attack or defend.
Symmetry
Another concept that impacts game balance is whether a game is symmetric or asymmetric. Symmetric games are those where all players have exactly the same starting position and the same rules. Chess is almost symmetric, except for that pesky little detail about White going first.
Could you make Chess symmetric with a rules change? Yes: for example, if both players wrote down their moves simultaneously, then revealed and resolved the moves at the same time, the game would be completely symmetric (and in fact there are variants along these lines). Note that in this case, symmetry requires added complexity; you need extra rules to handle cases where two pieces move into or through the same square, or when one piece enters a square just as another piece exits the square.
In one respect, you could say that perfectly symmetric games are automatically balanced. At the very least, you know that no player is at an advantage or disadvantage from the beginning, since they have the exact same starting positions. However, symmetry alone does not guarantee that the game objects or strategies within the game are balanced; there may still be certain pieces that are much more powerful than others, or certain strategies that are clearly optimal, and symmetry doesn’t change that. Perfect symmetry is therefore not an “easy way out” for designers to make a balanced game.
The Metagame
The term metagame literally means “the game surrounding the game” and generally refers to the things players do when they’re not actively playing the game, but their actions are still affecting their chances to win their next game. Trading card games like Magic: the Gathering are a clear example of this: in between games, players construct a deck, and the contents of that deck affect their ability to win. Another example would be championship-level Poker or even world-tournament Rock-Paper-Scissors, players analyze the common behaviors and strategies of their opponents. Professional sports have all kinds of things going on in between games: scouting, drafting, trading, training, and so on.
For games that have a strong metagame, balance of the metagame is an important consideration. Even if the game itself is balanced, a metagame imbalance can destroy the balance of the game. Professional sports are a great example. Here is a positive feedback loop that is inherent in any professional sport: teams that win more games, get more money; more money lets them attract better players, which further increases their chance of winning more games. (With apologies to anyone who lives in New York, this is the reason everyone else hates the Yankees.)
Other sports have metagame mechanics in place to control this positive feedback. American Football includes the following:
Drafts. When a bunch of players leave their teams to be picked up by other teams, the weakest team gets to choose first. Thus, the weakest teams pick up the strongest players each year.
Salary caps. If there is a limit to how much players can make, it prevents a single team from being able to throw infinite money at the problem. Even weaker teams are able to match the max salary for a few of their players.
Player limits. There are a finite number of players allowed on any team; a good team can’t just have an infinite supply of talent.
These metagame mechanics are not arbitrary or accidental. They were put in place on purpose, by people who know something about game balance, and it’s part of the reason why any given Sunday, the weakest team in the NFL might be able to beat the strongest team.
From this, you might think that fixing the metagame is a great way to balance the game. Trading card games offer two examples of where this tactic fails.
First, let’s go back to the early days of Magic: the Gathering. Some cards are rarer than others. Thus, some rare cards ended up being flat-out better than their more common counterparts. Richard Garfield clearly thought that rarity itself was a way to balance the game. (In his defense, this was not an unreasonable assumption at the time. He had no way of knowing that some people would spend thousands of dollars on cards just to get a full set of rares.) Today, trading card game designers are more aware of this problem; while one does occasionally see games where “more rare = more powerful,” players are (thankfully) less willing to put up with those kinds of shenanigans.
Second, TCGs have a problem that video games don’t have: once a set of cards is released, it is too late to fix it with a “patch” if some kind of gross imbalance is discovered. In drastic cases they can restrict or outright ban a card, or issue some kind of errata, but in most cases this is not practical; the designers are stuck. Occasionally you might see a designer that tries to balance an overpowered card in a previous set by creating a “counter-card” in the next set. This is a metagame solution: if all the competitive decks use Card X, then a new Card Y that punishes the opponent for playing Card X gives players a new metagame option… but if Card Y does nothing else, it is only useful in the context of the metagame. This essentially turns the metagame into Rock (dominant deck) – Paper (deck with counter-card) – Scissors (everything else). This may be preferable to a metagame with only one dominant strategy, but it’s not much better, and it mostly shifts the focus from the actual play of the game to the metagame: you may as well just show your opponent your deck and determine a winner that way.