Posts Tagged ‘game theory’

This is the fourth installment of a series by Brian Powers. To catch up, see these:


Math, Art, and Game Design

A Series by Brian Powers

Part 4: The Initial Play Test

Game Design is a bit of a paradoxical form of art. Games are by their very nature social, yet the game design process can be quite a solitary activity. I’d bet most game designers get into this mess because they love playing games, yet they may spend ten times as long (maybe more!) in design mode as they do actually playing the games they design. But we eventually come to the moment: the first time we bring other people into the processand hopefully bring some joy into their otherwise miserable lives.

Well, that’s an exaggeration, but I wouldn’t be lying if I said that play testing is my favorite part of the game development process. Ideally, when creating a new game, you’ll want to test the game yourself before bringing other people into the mix. This is when having dissociative identity disorder comes in really handy, because you have to jump from chair to chair, taking the turn of each player and trying to see things from his/her hypothetical point of view. Unfortunately I couldn’t do this with my game because at its core lie the decisions that players Red and Blue make (without knowledge of each other’s decisions). I needed some actual human beings. Fortunately, I know some of them!

Five of my friends came over this past Sunday afternoon and I showed them what I had been working on. After explaining the rules and the goal of the game, we played six rounds. How did it go?

Let me first go over the rules with you:

We set up the game board with a random assortment of red, blue, and green stones:

We next laid out the Reward Action cards and Modify Action cards, in this way (there are a few more Reward and Modify actions that I haven’t included here, but you should get the idea):

Reward Actions


Make Red XO decision and receive red reward


Make Blue XO decision and receive blue reward


Receive green reward


Take 1 point from each player who chooses “X”


Receive 2 points for O or O, 5 points if both are played


Take 1 point from a player of your choice

Modify Actions

Add 2 stones of any color(s) to the board

Remove any 2 stones from the board

Move 2 stones on the board

Add 1 stone of each color to the board

Remove 1 stone of each color from the board

Swap the positions of 2 stones on the board

To begin, one player is given the “Round Leader” card. This just symbolizes which player gets to choose first during the first round of the game. This card is passed clockwise after each round.

Then, starting with the Round Leader and continuing clockwise twice around the table, each player chooses and takes an action card from the table. Thus, each player gets to take two action cards. Each player must choose one Modify action and one Reward action, and the Red and Blue actions must be taken. So if all but two players have chosen their Reward actions and Red and Blue remain on the table, the last two players are forced to take these two cards.

After each player has two action cards, players exercise their Modify actions, beginning with the Round Leader and following clockwise. You can imagine that, at this point, players each have their own agendas, and they will hopefully be able to modify the board to set things up for themselves to receive a lot of points.

Finally, the two players who chose the Red and Blue actions each get a pair of cards, one with an “X” and one with an “O” (both in their respective color) which allows them each to secretly choose one. They simultaneously reveal their choices and points are awarded. Thus ends a round of the game!

Overall this was a tremendously fun experience for all of us. I was pleasantly surprised how quickly everybody got into the game, how easily they understood the rules – and yet the game was anything but simple. We felt like Fezzini and the Man in Black locked in a battle of wits.

This is exactly what I was going for, and to say I was pleased is putting it lightly.

We played for six rounds, like I said, because it became clear that certain aspects of the game weren’t quite balanced. For example, the “Thief” action allowed a player to take one point from an opponent, but this ended up being pretty weak compared to the other Reward actions. And the “neutral” Green player worked out well too, although I want to balance out the number of green stones on the board so they are more on-par with Red and Blue. Also, I realized that for six players I would want at least eight Modify and Reward actions, so that there are both more options and more opportunities for incentive points.

I would like to mention that, although I have successfully tackled the challenge of making the game fun for more than two players, this has opened up a new problem. Because it was so fun with a group of six, I’m not sure how to capture that same sense of strategy with only two players. We’ll see how this goes.

OK, so, enough about that. My next step is to do more testing! Tweak a few things and play with a new group of people. Test and tweak, test and tweak. This cycle will continue until I get a polished game design that doesn’t need any more changes. Along the way I will, ideally, bring this game to a board game Meetup here in Chicago and have some strangers play while I watch. This is an important step, especially to see how well I’ve written the instructions! I can also give them feedback questionnaires! Ooh, I’m getting all tingly just thinking about it.

I’ll try to get some more testing done soon so that I can come back with my next installment. It may be a few weeks, but I’ll be back as soon as possible, fellow artists! As Chloë would say: “Huzzah!”

(But I would never say that. Not ever.)

P.S. I would also like to mention that I lost pretty miserably. Of the six of us, I came in last with about 9 points.


Brian will be back with another installment later. Until then, cheerio!


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Today’s guest post is the first in a series of posts to come and was written by my pal Brian Powers. He has guest-posted for Real Life Artist before, on topics including surnames that are verbs and getting hit by an egg. is also heavily featured in “This is your Brain on Egg Puns”, the post that is the lifeblood of this blog. Today Brian offers insight into his process as a game developer and designer. (FYI: he’s into card games and board games, not so much video games.)


Math, Art and Game Design

A Series by Brian Powers

Part 1: The Game Concept

When Chloë asked if I’d be interested in writing a guest post on Real Life Artist about game design, I FIGURATIVELY jumped at the chance! Although I’m a mathematician by training, a banker by experience, and a teacher by occupation, I consider myself an amateur game designer.

As with many forms of media production, game publishing has become more and more feasible for the individual with a small budget in recent years and we’ve seen a burgeoning burgeon of amateur game designers coming onto the scene. In 2008 there were essentially no options for an affordable small run of a card game (one or two copies), but now websites like Superior POD and the Game Crafter make it not only possible but relatively simple to publish your own game. This does NOT, however, mean you will make money from the game or become famous! Haha! We don’t do this for money! We are artists! We do it for Zeus!

But let’s not get ahead of ourselves—before we publish a game, we have to design it, and before we design it, we need some sort of concept. The concept can come from anywhere—the most boring place is a flash of inspiration, but as Ze Frank nicely explains, we shouldn’t wait for inspiration before we make something. We can look for ideas everywhere.

I’ve had many ideas for games: some I’ve acted upon, and some are on the back burner.

  • Pensacola: A strategy game where players run competing retirement homes and try to make money before their residents “move on”.
  • Crazy Celebrities: A card game where players are celebrities trying to become crazy (like Tom Cruise, Lindsay Lohan or Charlie Sheen) without destroying their careers.
  • Get Sick: A card game where you try to fake diseases to fool your boss into letting you take sick days.
  • Cult Classic: A card game where players compete to found cults and lure the most followers they can.
  • Pathways: An abstract tile-placing game where you build a connected path between points A and B.
  • Element Tower Defense: A novel tower defense computer game I made a number of years ago, to be played in Warcraft III.

And the list goes on.

The game that I want to discuss here is a concept that I’ve been playing with in my head for a while now. I’m not really sure what to call it but we’ll hopefully see it evolve as this series of blog posts develops. The game involves players manipulating the rewards they receive from various actions and then strategically taking these actions. That’s the simplest way I can describe it, but I want to talk a little bit about Game Theory in order to delve further into it.

Game theory is a branch of mathematics with heavy applications to economics, political science, international relations, sociology, biology … any situation that involves one or more individuals or collectives making strategic decisions in order to maximize some sort of positive result for themselves. These situations are abstracted into a ‘game‘ and represented using mathematical tools such as matrices for analysis, and often we can find the ‘solution’ or ideal set of strategies for the game. The name “game theory” is a bit of a misnomer because the theory really isn’t so much focused on the games we play for fun, but that’s the name it’s stuck with.

This may all seem pretty dense, so let me present a classic example (in fact, the inspiration for this latest of my game concepts):

Consider two individuals. Each person has two options: be nice or be mean. If they are both nice then they are rewarded with 3 points each. If they are both mean then they are given 1 point each. If one is nice and the other is mean, then the meany gets 5 and the goody-two-shoes gets nothing (out of whatever deal they make – the meanie takes advantage). We can depict this situation as a matrix, with each box showing the points for player 1 and player 2 as an ordered pair:

Player 2



Player 1 Nice

(3, 3)

(0, 5)


(5, 0)

(1, 1)

This situation has come to be known as the prisoner’s dilemma. It is a dilemma because although you can see that collectively the greatest benefit for the pair is when both are nice to each other, both players have a tasty incentive for meanness. If both players are mean, however, they are stuck with each getting a low reward, a third as much as they would have got if they had been nice in the first place.

The prisoner’s dilemma has been studied and written about A LOT. Although I think it’s completely fascinating—and I can’t recommend enough the book The Evolution of Cooperation by Robert Axelrod—I don’t want to dwell on it. What I’m interested in is how this could be turned into a board game.

The game becomes a lot more interesting if the rewards could be adjusted through repeated plays of the game. As you begin to recognize your opponent’s strategies, perhaps you can re-balance the rewards to favor yourself, or choose actions that will give you the upper hand.

The challenges I’m facing are:

  • make the game fun for 2 or more players,
  • make the game interesting strategically,
  • make the game aesthetically pleasing (in other words: fly!),
  • design it in such a way that it doesn’t rely on extraneous game pieces.

Calling these “challenges” may be too dramatic – they are just steps that need to be taken, and that I haven’t taken yet. I feel good about this game idea, and I’m eager to see it through. Hopefully the process will be interesting enough for you to want to read about.

So we have a concept. The next step is to figure out the game mechanics! What are game mechanics? Obviously they are little grease monkeys who play checkers all day. (If you have an infinite number of grease monkeys with an infinite number of checkers boards, would they design Monopoly? Maybe they need an infinite number of typewriters too.)

In our next installment we’ll get all into game mechanics and some of the nuts and bolts of game play design!

(You can go on to Part 2: The Game Mechanics now if you like!)

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