Aug 27, 2009

Vampire Games Require Zombie Math

The Freakonomics blog highlighted a mathematical analysis of a zombie attack. This is pretty nice timing for me.

It is no secret that (good) game design generally involves a strong grasp of mathematics. Messrs. Knizia and Garfield each have a PhD in Mathematics that predates their design careers.

This is not a coincidence, as they are not alone among game designers in being mathematically inclined. Designing a complex, interactive system that doesn't spin out of control requires an ability to intuitively understand the math of that system.

Some weeks ago, I had the following back-and-forth with a gaming friend of mine:

vampire themed board game based on resource (humans) management. start working on it
Brilliant! Oh, man I actually think that is a pretty cool idea.
i figure you all play as a vampire house...and when yu eat people, they join you, but then you have to support your house and there are less people to feed on...etc
I was also thinking a house, but you would have two choices for each human captured: convert to vampire or turn into food. There would also have to be a mechanic about human population control. Take too many humans, and the population disappears.
your point about population is my thought exactly, and that will be one of the key strategic impacts - balancing the population while at the same time feeding...maybe even protecting your "herd" from opposing houses?
I'm still trying to figure out how the interactive component would work.

I have other projects I'm currently working on, so I haven't done much with the idea since then. But I did turn it over in my mind for a few hours here and there, and one of the problems with a vampire resource management game is that the system seems perfectly designed to spiral out of control and collapse in on itself at the end.

Now I have a formal proof of what I had intuited. The paper I linked to at the start of this post mathematically models a zombie attack. Though the game idea concerned vampires, the paper was still relevant.

Zombies and vampires, while obviously different in the real world (ahem), are mechanically quite similar in games. They both attack humans for food (be it brains or blood). They both reproduce by converting humans. Thus they both run into the problem of their population growing as their food supply shrinks.

When I do get around to designing around this idea, I'll need to find a balance between vampire population growth and human population preservation. If you have any suggestions on how to do this, let me know in the comments.


  1. Ideas:
    -The vampires are more wrapped up in internal politics and infighting once their numbers increase?
    -Bloodline dilution - the newer vampires are less awesome than the master vampires and more vulnerable...
    -The human population begins responding more effectively as the threat is known. Perhaps vampire hunters arise spontaneously and make certain areas more difficult to hunt? This would be more interactive as each vampire player now has choices of where to hunt, and whether to eat the easy humans or fight vampire hunters.

  2. Thanks, Todd! These definitely deserve some consideration.

  3. Is the fact that your food supply dwindles not itself a limiter and interesting variable that a player would have to contend with?

    Maybe it's a game end timer - when the humans become extinct, the game is over.

    I don't know if you're modeling Human Population Growth as well in your game, but it stands to reason that over time the humans that survive will reproduce. Though the time scale on that might not jive with the rest of the game.

    Todd's ideas are good, all decent reasons players might not want to go too crazy converting people into Vampires.