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.

Gamasutra – News – GDC Austin: Raph Koster’s Deceptively Simple Coin Toss. It’s got a couple of images.

He offered several examples of complex games broken down into abstract graphs. For instance, he took the strategy board game Blokus, in which four players use tiles of various shapes to try to block other players’ ability to place a piece. Only corner-to-corner contact is allowed between pieces of the same color. No edges can touch, and the object is to use as many of your allotted tiles as possible.

Xemu’s Long-Winded Game Industry Ramblings :: AGDC ‘09: Raph Koster on Games and Math is a liveblog of the talk I gave a couple of hours ago here at GDCAustin.

The talk was first a very brief intro to game grammar approaches, followed by digging into the math behind very common game mechanics that have stood the test of time, and then lastly a look at some of the “bugs” in human cognition that games tend to exploit. It was supposed to be an intermediate talk, not superadvanced, so I hope I hit the right levelof complexity for everyone!

The room was pretty packed — 300 people, I am told! There’s also commentary on Twitter if you go looking.

I will try to get the slides up soon.

Mint.com is a personal finance site that won the judges’ award at TechCrunch40 the same year that Metaplace won the audience award. It helps you do budgeting and other such dull tasks, all in slick interface.

Despite the zillions of products out there to do this, we still managed to wheel, deal, and borrow ourselves into a financial crisis (that is still ongoing, though swine flu may be eclipsing it just now). Clearly, something was lacking in the appeal here, for if said product category were truly successful, we wouldn’t be in this fix.

Now, Mint is in closed beta on a feature that turns personal finance into a game, complete with points earned for doing things like socking away some cash into the savings account each month, or switching to a credit card with annual rewards. Get enough points in a sustained way, and you too can be a Financial Guru.

This seems like a fairly straightforward harnessing of game-style incentive systems towards a laudable goal (though I should note that said credit card with rewards is likely from one of Mint’s partners). But honestly — money is points anyway, isn’t it? Why is it that we value the cash less than the flat-screen TV?

Read the rest of this entry »

A Model of Play is a fascinating poster (available as a PDF or as images) that takes what seems like a very game-grammar point of view on the concept of play — even freeform play.

In play, one of the primary goals is to have fun — to continue engaging in the conversation that creates fun. Individuals choose the means for achieving that goal; they choose the topic of conversation, for example, which game to play. Within a topic, they choose different strategies and pursue a series of sub-goals, adjusting means according to their effectiveness. Goals and sub-goals and associated means form a tree (or web) of possibilities for action.

Among the grammar principles that are mentioned is the notion that play always requires two, even if the second person is a “virtual person.” The notion that interactivity is inherently a conversation can be traced back to at least Chris Crawford, of course.

Also cool is the “step by step” logic version found here, which builds the poster argument by argument.

Project Horseshoe, 2008, report, section 5 specifically is the game grammar take on multiplayer games. Wish I could have been there!

Developing behaviors via genetic algorithms of various sorts has been around a long time now. You come up with a basic environment and ruleset, then you let loose millions of generations of simple AIs to keep trying to surivive. You then have the AIs tweak themselves based on what survived well, attempting to evolve the best survivor.

This can be used for lots of purposes — and now it’s being applied to game design. Starting with a simple Pac-Man like environment, researchers are generating zillions of procedural games, and then testing to see which is most fun. But how to measure the fun?

It should be pretty straightforward to see how game rules can be represented to be evolved: just encode them as e.g. an array of integers, and define some sensible mutation and possibly recombination operators. (In this particular case, we use a simple generational EA without crossover.) For other rule spaces, some rules might be more like parameters, and could be represented as real numbers.

What’s the much trickier question is the fitness function. How do you evaluate the fitness of a particular set of game rules? …

Our solution is to use learnability as a predictor of fun. A good game is one that is not winnable by a novice player, but which the player can learn to play better and better over time, and eventually win; it has a smooth learning curve.

via Togelius: Automatic Game Design.

Read the rest of this entry »

Here’s a cool, very game-grammary approach to board game design that is inspired, as my initial game notation work was to some degree, by music.

What I arrived at was a series of “discoveries” or “conclusions” about specific models of game design that I assert can help one in the process of identifying not only problems in a game design but also what may be lacking or not present yet that could help a game reach the next level. As I arrived at these conclusions, I found that they felt very much like many of the typical principles of composition that I encountered while studying music.

via Reflections Across the Board: The “Music” of Game Design: Part 1.

The bulk of the article ends up examining a particular “atom” called the “Tri-Level Resource Exchange Model.” Atoms like these are usually termed “design patterns” in software. The article lands at identifying the number 5 as apparently very important in this model; I don’t think it is coincidence that it fits nicely in the famous 7 +/2 range.

The “Theory of Fun” website is down, caught between two webhosts, and has been for a while (with the book out of print, it hasn’t been a priority to sort out). But I keep getting requests for the materials that were hosted there and not here, so here they are.

• The PDF of the original AGC 2003 keynote and Serious Games Summit 2004 keynote, “A Theory of Fun.” This is the black and white cartoon one with the low-res, that turned into A Theory of Fun for Game Design, the book.
• The PDF of the GDC 2005 advanced design lecture “A Grammar of Gameplay,” which sort of kicked off the current wave of “game grammar” stuff. As you can see, Dan Cook’s diagrams are much prettier than mine. Just picture one of his atoms fitting inside one of the boxes I drew though.
• The PPT of the Training Fall 2005 keynote “Why Games Matter,” which is sort of rehashing ATOF for a non-game-developer audience.

If you weren’t sick of this debate already, here’s more.

So this, really, is the problem with World of Warcraft’s torture sequence. It does not model any consequences. You torture the sorcerer, but nothing particularly comes of it. You just move on to the next quest.

This would be lame in a TV show, but is arguably even lamer in a videogame, because it’s not too hard to imagine all sorts of repercussions that would have been dramatically fascinating while actually enhancing the gameplay.

For example, Lich King maker Blizzard Entertainment could have made the Art of Persuasion quest optional — but endowed it with some unusually lucrative loot or experience. That would have made it a genuine moral quandary: Should you do a superbad thing for a really desirable result?

– “Why We Need More Torture in Videogames“, Clive Thompson in Wired