On Balance and Personality

It it possible for a game to be perfectly balanced, as all things should be?

I think a good definition of balancing goes something like "Over many rounds, each player has an equal probability of winning under optimal play". The implication is that no one player has a preset advantage before the random setup. The game, then, is in figuring out just what that optimal play actually is—in a balanced game, the win would go to whoever plays the most optimally. One's skill in a game is determined by how closely their decisions converge on the correct ones.

The simple way to ensure a game is balanced is to simulate millions of rounds, and see that the players' win rates approach parity. The problem is that, in any reasonably challenging game, calculating the optimal play in a given position is quite difficult. As an AI major, I briefly considered creating some kind of self-play agent to solve or approximate this for Keeps—but then I realized something.

Keeps is, by construction, self balancing. And it is so for two separate reasons.

The first and most important reason is that the character piles move around. It would not be necessarily problematic if the cards of one pile were somehow expectedly superior to another, because those cards eventually make their way to another player. By virtue of motion, the "strength" of any one pile is spread amongst more than one player. In this way, the pile movement mechanic takes a hop-step towards self-balancing.

The second reason is the Victory Mark system. If you don't yet know, a game of Keeps takes place in a series of rounds. Each round winner gets a Mark, and the first to three Marks wins the game. The system may seem like needless overhead, and often is in times where you just want to play one or two rounds. But when you sit for a session of Keeps, tracking Marks helps guide your decisions toward balanced outcomes. For a very simple example, consider finding yourself in the position to choose between two other players for the victory. The Mark system gives you an actual reason to choose one or the other, instead of just whoever you are less mad at at the moment: the player with less Marks should win. It is selfish and optimal (it means you have more future rounds to get enough Marks to win), and yet it exerts a balancing influence.

During our initial sendout rounds of playtesting, I would often get messages that noted how one character was too strong or weak compared to the others. I am grateful and obviously wanted as much feedback as possible, but what I found interesting was that I got a roughly equal number of these messages for every character being too strong. For example, at the surface, one might be tempted to think "...wait, one of the characters [the Count] has all the money? That is way too overpowered!". In fact, if I had to choose, I would personally consider the Count as the weakest pile to start with. Luckily, Fiat and Acquisition do yield plenty of maneuverability...but you would have to play to understand my reasoning.

My point here is that every Keeps card, regardless of what pile it came from, is highly situational. They all have their moments to shine, and it is the player's goal to hit that timing. There are surely general trends, where a certain card is played more or less often by the winning player, but just like people, a card is not "Good" or "Bad". A card is what it is, and you will learn to love or hate it depending—a card is only as good as the player who wields it.

Just like people, each Keeps card evokes a strong sense of personality. The characters provide an undercurrent for this: the tricksy Fool, the benevolent Count, but over time you start to form an (albeit protean) bond with each card. As you play more and more rounds, the visual cue of the cart art will fire positional recognition for each card, of how it can work into your position.

Offering used to be my least favorite card, until one round it became the only card that would earn me a win. And then I drew it. Trying to make a Keeps hand work is like trying to sit a set of guests at a wedding, thinking through how their personalities unfold and interact. I mean, what other game comes with 36 friends??

-David