When you think about game balance, you probably think about making all possible player options be as equitable as possible; about maintaining a fragile balance between each player’s starting position so everyone has an equal chance of winning every game. But what if I were to tell you that there was a different way to balance your games? What if that way combined a sense of fair play with all the excitement, desffpair, and storytelling opportunities that came with unequal positions? Well, good news! I’m not speaking hypothetically. Welcome to an article about making your game balanced…on average.

Dr. Ro-Galt-Nik’s Mean Bean Machine

When I was a kid, my parents would regularly take me to see the Museum of Science and Industry in Chicago. During one of my visits, I stumbled across a giant version of this thing, which was one of the coolest things I had ever seen:

This Galton Board, also known as a “bean machine”, is a neat visual representation of the natural law of regression toward the mean. Even if you have a function with a wide range of outcomes, if you run that function often enough, it will eventually deliver the distribution of results you expect, with a hill centered on the mathematical mean outcome. To use plainer language, everything will even out as expected, provided you try enough times.

What this means for us as game designers is that there is another option besides trying to make each player’s starting position equal every time: We can also have a wide variety of unequal starting positions and redistribute these starting positions so many times it regresses toward the mean.

I’m Pretty Sure The Genius Did This Once

That last section was pretty abstract, so to make it more practical, I’ll use an example. Let’s look at a game that’s very much in need of redesigning: I’ll call it “Small War”.

Small War is played between two players using part of a standard pack of playing cards: The 2 through 10 of hearts and the 2 through 10 of clubs. These cards are shuffled together and then dealt evenly to both players. Then, each player selects a card and puts it face-down. Once they’ve both chosen a card, they turn them face-up; the player who played the higher card “captures” the other card and forms a pair. Whoever has the most pairs at the end of the game wins.

So obviously, Small War has some problems. The most obvious one is that, because the cards are randomly distributed across both players, it can create a heavily imbalanced scenario where one player might have both 2s, 3s, and 4s and the other has both 8s, 9s, and 10s. How can we fix this so every game of Small War is equitable to both players?

A conventionally balanced version of Small War would simply distribute one copy of each card, 2-10, to each player every game. This turns the game from one based on luck to a tense mindgame where each player tries to figure out when their opponent is going to try to pass their small cards through or try to win the round with a big card. This is cool and everything, but the meta would crystallize quickly after a few rounds and the game would become stale for all but the most hardcore players.

However, there is another way: Keep the gameplay exactly the same but make the game best out of 9 rounds (1 round being what we’d call a “game” in the original). Individual rounds might be extremely unfair, but there’s so many rounds that there’s a good chance of both players’ luck of the draw cancelling out each others’ over time.  Plus, this wider range of opening hand adds more variety, prevents the game from boiling down to set opening and closing strategies, and creates amazing stories where you get dealt an awful hand but manage to overcome your opponent afterwards.

This second case is what Balance On Average (BOA) design is all about.

Defining The BOA

BOA games have a few key features.

• A BOA game is made up of a number of individual rounds, ending after a set number or when a player reaches a particular score.
• Each round begins with players being given a random assortment of components to make do with. The distribution of components is random and each player’s respective strength can be unequal, sometimes brutally so.
• The results of each individual round don’t have anything to do with the rounds after it, except in a “metagame” sense where you might adjust your play based on your score or the amount of time left in the game.

You might be wondering, why even make a game like this? Well, compared to a conventionally balanced game, BOA games have a number of benefits.

• Compared to a regular game, where being put in a bad position early in the game will make you lag behind for 90 minutes, a BOA game can get away with being pointlessly cruel to players because the round will be over in 5 minutes anyway. In fact, cruelty often engenders a desire to play again later and to laugh about it after the fact.
• There’s a wider variety of game states in a BOA game. In a conventionally balanced game, the designer (and developer sometimes) works hard to ensure that every player starts the round at around a 5/10 and maintains that for most of the game. BOA games can deal out gamestates ranging from a 0 to a 12, greatly increasing the number of possibilities.
• BOA games can be deeply emotionally impactful. Getting a strong hand and doing well is more likely to stick in your memory if you’ve dealt with medium-to-weak hands for the last 5 rounds; getting a come-from-behind victory is more meaningful if you were actually behind the other players in a way beyond “number of games played”.

The BOA In Action

The majority of BOA games are traditional games hailing from long before the advent of the modern “designer game”. The one Americans are probably the most familiar with is poker. You might have a terrible hand in one round and a godly hand in the next, but besides the metagame of playing more or less aggressively depending on how many chips you have compared to your opponents, the outcome of one round doesn’t affect the performance of your hand in the next.

Other card or card-equivalent games that make use of BOA include bridge, rummy, and mahjong. Much of the strategy of any of these games involves not only capitalizing on good rounds, but knowing when your starting hand is good compared to the other player or team’s and throwing away your hand as safely as possible if you you can’t catch up. For games with an easier learning curve, Uno is the textbook definition of BOA (as the distribution of wilds and special cards like draw 2s unevenly weighs starting hands), though presumably many groups only play one game at a time.

The majority of designer games that use BOA balancing are trick-taking games, likely because trick-taking card games have more fidelity to the classics of the genre than most other kinds of game. Some, like The Bottle Imp, adhere strictly to keeping rounds separate and tallying up scores on a piece of paper; others allow you to mitigate a bad hand (Nyet!) or give players a way to catch up after a nasty round (Tournament at Camelot). You could also charitably describe impress-the-judge games like Stand Back, Citizen! as BOA, since the suitability of your hand to the prompt will change each round.

Some games that look like BOA games but aren’t include “dude smasher” games like Magic, Hearthstone, and Netrunner (as you usually play three rounds max against a single opponent); drafting games like Bunny Kingdom or 7 Wonders (as your actions in earlier rounds dictate what you do in later ones); and fast social deduction games like One Night Ultimate Werewolf (as you’re not playing multiple rounds in one game – you’re playing multiple very short games).

One of the most interesting interpretations of BOA design is Condottiere. Condottiere is a sort of hybrid between BOA and conventional design because “getting a new hand” and “starting a new round” isn’t a 1:1 ratio: Players draw new hands once all but one player are out of cards. This means that players with bad hands can force balance on average by increasing the number of hands per game, while a player with a great hand might be tempted to string their hand across multiple rounds while flirting with the disaster of throwing away most of their good cards. I still haven’t seen this mechanic anywhere else meaningful, and it remains a great source of inspiration for me.

BOA Constrictions

Despite the several advantages of BOA design, games of that nature have a tiny foothold in the tabletop game industry as a whole, for reasons both meaningful and coincidental.

Part of the reason for the modern unpopularity of BOA design might be due to the meteoric rise of video games right around when the properties of a “well-designed” board game were starting to become mainstream around designers. It stood to reason that a balanced board game should resemble a balanced video game, with players selecting an asymmetric faction, strategy, or character near the beginning of the game and having a roughly even chance of winning with it at equal player skills. 

Another, perhaps more legitimate reason is that it’s hard to build a sense of momentum in a BOA game because each round is specifically detached from the next. You can have excitement and progress within a round, but compared to an Agricola or Dominion where a player’s engine and strategy slowly builds up to a splashy finish, BOA games frequently feel more “even”, with emotional impact primarily arising from unusual situations that may not always occur every game.

BOA games also have many more restrictions than conventional games. As discussed, BOA games have to have a long series of short rounds, each of which randomly redistributes starting positions. There’s only so many ways you can achieve this, and many of the good ones have been covered by conventional games. There are additional UX concerns with this system, as you need the redistribution itself to be relatively quick and painless (like shuffling and dealing out a deck of cards, as is common) and the scorekeeping to be something more modern than someone having to grab a pencil and sheet of paper. That said, I believe that BOA games are so overlooked by modern tabletop designers that their true potential remains unexplored – maybe there’s some mechanic hiding in the BOA space waiting to revolutionize the industry.

Conclusion

All game designers can fall victim to a kind of design myopia, where we grow so used to the evaluations and demands of our particular slice of the community that we forget that there are many ways to make a fun, dynamic game, some less mainstream than others. Looking at BOA games has been extremely helpful for me in this regard, and I hope to one day find even more interesting methods of balancing a game and keeping its players happy.