GDCA: Games Are Math slides posted
Using isomorphic graphs to analyze MMORPG combat
I have posted up the slide deck (PPT) and a page of images of slides for my GDC Austin talk, “Games Are Math: 10 Core Mechanics That Drive Compelling Gameplay.”
This talk starts out with some game grammar stuff that may be familiar, then moves into looking at a definition of NP-complete problems, then provides ten examples of how they can be used to look at games, then finishes by examining cognitive bugs in the brain that many games exploit. Please note, I am not a mathematician nor even claim to be very good at math. 🙂
As usual, this along with all my other talks can be found on the Gaming Presentations page, reached by clicking “Games” on the top bar of the site, then choosing Presentations from the sidebar. For those of you who never click the top bar and think all that is here is the blog — there’s a wealth of stuff available there. 🙂 I’ve recently updated it to include a few presentations that were buried and hard to find, such as the audio for my Games For Change closing address, the videos for Living Game Worlds IV and Siggraph Sandbox, and more.
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Great notes! I don’t understand a thing about “NP-complete”, but there’s still enough to make me think.
One minor math-geeky issue, though… you have a picture where you ask about the minimum number of colors needed to fill it with no color touching itself. It’s filled with five colors, but you only need four.
It’s an example off the web, actually.
Here’s the 2007 Sandbox panel video: http://video.google.com/videoplay?docid=8626636079511778490
And here’s the UCSD panel video: http://www.youtube.com/watch?v=lXliVs0JCR4
The Churchill Club panel video is floating around somewhere. GameSpot has the video, oddly, in the Halo Xbox 360 category.
That was a great talk Raph…thanks for that.
Why wasn’t that a keynote again? 😉
Ilsoap:
“P” is the name for the class of problems that can be solved by a computer in an amount of time that is a polynomial function of the number of inputs. (“polynomial time”) e.g. if you have a list of numbers, and your problem is to find the largest number, you can solve the problem in time = seconds to check each number * length of list.
“NP” is the name for the class of problems whose solutions can be verified by a computer in polynomial time. This includes everything in P. It also includes the problems Raph discussed in the presentation. e.g. Pentominoes: given a board where the pentominoes have been placed, you can check each pentomino to make sure it’s not overlapping anything, and that all of them are on the board. You can do that in polynomial time, so the pentomino problem is NP.
“NP Complete” is the name for the class of problems that are in NP, where each problem also has the property that you can “convert” any NP problem to it. That is, for any instance of an NP problem, there’s a way to make an instance of the NP Complete problem such that solving the NP Complete problem provides a solution to the NP problem. (An example of such a conversion is the number-picking game -> Tic Tac Toe example in the presentation.)
Wikipedia has a decent introduction to this stuff. For more about running times and polynomial time, Plain English explanation of Big O has a pretty good overview.
Personally, I never much liked mathematical games and I think they’re pretty much the antipathy of fun.
I always felt it ironic when designers would brag about their rock-paper-scissors class system designs as-if a game meant for children actually showed some sort of sophistication.
For instance, one of the first games I ever wrote was just a few lines of Basic code. It asked the player to solve some square roots, timed how long it took them to answer, and after 10 or so questions computed a score.
Does a game get more mathematical then that?
Well, one of the first players to try it was a guy who was destined to score 1600 on the SAT. He carefully considered each question and produced (in his head) an answer out to multiple decimal places. Alas, he didn’t score very well, because as we soon discovered the game rewarded those who could quickly enter a rough answer better. Turned out it was more of an action, fast response game then a math game; but the best part was watching how frustrated the math whiz became as he continued to try to win with accuracy rather then to just succumbing to punching in something close quickly.
Or to summarize… illiciting an emotion from the player should be the highest goal of any game, or art for that matter. Make games that are fun, not work.
The big mean monster doesn’t have to just keep beating on the tank while the support characters do their thing. Let unpredictable events happen.
Leave room for chaos.
Well done. As a mathematics student (at berkeley no less!), it is always refreshing to see pure mathematics presented artfully to any audience in whatever context. Mathematics is really a celebration of beautiful structure – appreciating innate relationships and understanding the implications of these connections. I have always believed it could contribute much more to game design.
Alas I don’t see myself finding work in the game industry anytime soon – apart from the annual lecture I don’t know if there is any demand for such an abstract skillset =[
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