Thursday, December 10, 2009

What is the 'Mathematician Syndrome' ?


Today I’m talking about a design problem that might be a little more personal rather than something more broad ranging.

What is it?

The Mathematician Syndrome is a term I came up with to describe a problem I sometimes have when designing a game. I envision how a player might play the game, and like it so much, that it becomes the only way to play the game. This issue can be very subtle, and I sometimes don’t realize I’m doing it at first. However, the further and further I get into the design and play, the more apparent it is.

A game is the victim of the Mathematician Syndrome when there is a single line of play or a single method of character creation (chargen) that is clearly optimal. So optimal, in fact, than any player who chooses another line of play or character generation is squeezed out or marginalized during actual play. To try to put it more clearly: The Mathematician Syndrome, in essence, is where the designer’s vision of the game unintentionally causes there to be only one possible way to “solve” the game, and once the game is solved, playing it in any other fashion becomes fruitless and uninteresting.

This design flaw (for my own purposes, I call it a flaw) is, I think, more particular to designs intended to support Gamist or Narrativist-oriented decision making during play, rather than any other creative agenda. I say that mainly because those are the types of games I prefer to write and play. I think that since we Gamists love to figure out the optimal settings for various characters, powers, and so on. It’s in our nature to try to “solve” the mathematics of a game to gain the upper hand. At the same time, though, we find any game that allows for a perfect solution, i.e. a single best way to play, lacking enough of a challenge to keep us interested. Narrativist designers can, at times, fall into the trap of creating a game where there is only one way to address the Premise. If the players don’t take certain actions, make specific decisions at specific times, or use a currency in just a precise way, then the entire point of the game is lost. Players are channeled into playing the game like they were the designer.

How is it applied?

The best way to illustrate this is with an example, I think. I once designed a game called: Lichdom. The game begins with players creating a relationship map, goals, and needs for their character. Characters are on a quest to become liches- this is presupposed. To get there, they have to sacrifice the people and things they hold dear to achieve immortality. However, if they sacrifice too much, the character loses his or her sanity, and the player loses the game (note: I think losing in RPGs is perfectly fine, but that is a topic for another time).

There are plenty of currencies and resources for the players to draw upon. However, after playtesting, it became apparent that there is magical number of relationships that you can sacrifice to gain lichdom without going insane. I think it turned out to be 8 exactly. Six or seven with a few bad rolls were often too few to assure undead-ness and nine or ten put the character at too much risk. Especially if the dice turned on their owner. After several attempts to tweak the currencies, character generation, and reward systems, it turned out that the premise of the game made it all too easy to just figure out the optimum number of resources one had to sacrifice and then drive toward that.

The result was a game that lacked any sort of challenge or mystery. Players knew exactly what they had to do, when they had to do it, and how much it would cost them. It undercut any sense of real “sacrifice” and eliminated any emotional attachment to the shared imagined space. The game felt “dead,” which is almost ironic since it’s about liches. But that wasn’t the feeling I was going for. To fix the problem would require an entire redesign. Which I did. But didn’t solve the problem. *sigh*

Instead, I discovered Mathematician Syndrome Lite. Mathematician Syndrome Lite is when there may be two or three lines of play that are clearly optimal but they do not interfere or compete with one another. I decided that there wasn’t enough conflict in the game and since everyone had the same goal (even the GM really) which was to attain lichdom, gaming the numbers was the only challenge left. So I changed the name of the game to “Liches vs. Paladins.” Players could choose to play a warlock attempting to become a lich OR a knight trying to become a paladin by trying to stop such things. I thought this was great! Players will be actively intriguing against one another, and the GM- if I end up needing one- can just be a referee.

I kept most of the rules for making liches and created similar rules for making a paladin. Since there were two, equal and opposite paths to success, I wasn’t concerned about the math so much. I should have been. I had hoped that the players would be devising ways to thwart each other from gaining resources and achieving goals. For instance, if a warlock needed to sacrifice his apprentice upon an altar, the knight could come and resurrect the lad and turn him into a squire. Or the lich could kidnap a paladin’s squire and sacrifice him for essence. I’m not going to bore you with the details of the game, but that’s sort of how play was envisioned.

It didn’t work out that way. The liches had their own relationships and resources that were separate from the Paladins’. The paladins’ paths to advancement were separate entirely from the liches’. As a result, the players hardly interacted at all until a climactic battle at the end when all characters had reached their highest power ratings. It ended up coming down to the results of a single dice roll. Wow. Sheer luck decides the outcome. I’m sure you can guess that no one really enjoyed it.

Why is it bad?

Despite the fact that there were two optimal choices in the second iteration of the game, the net affect was basically the same. The outcome was pretty much known from the beginning. Players’ decisions were almost entirely made for them by the rules. One just had to figure out the math properly. This made it really unfun. Game play and character generation became rote and stale. We could almost predict a player’s next move. This problem was exacerbated by the fact that the two optimum paths never had to cross. They could be played concurrently without balancing each other out. Balance, in this case, meaning “proper support for the type of play you envision for your game.”

Once the proper mathematics of this type of game are discovered, the game is demystified. It’s like, “oh, so that’s how it ends.” This likely limits re-playability, and also runs the risk of de-legitimizing all the player decisions that led up to that point. It wasn’t the role-playing that mattered, it was the calculations in one’s head that made the difference. The interaction among the participants was entirely irrelevant to the game’s outcome. To me, that’s not fun. For a RPG, interaction among the participants is the essence of play- it’s why we do it. A good game will make that the most important feature of play.

Some players find it unfun if a game can be “solved.” In fact, I would venture to say that most do. Mystery, choice, challenge, and significant impact of player decisions are the key to a good roleplaying game, IMHO. The Mathematician Syndrome undercuts all of that.

How can it be avoided?

The best way to avoid the Mathematician Syndrome is playtesting. I know that’s probably the last thing you want to hear. Playtesting is one of the hardest parts of RPG design, but it is also the most necessary. In games with a significant amount of currencies and values, playtesting is the ONLY way to make sure you get the balance right. (see previous definition for balance).
First, I recommend you focus on idealized play, not mechanics. Decide what you want a session of your game to look like. Don’t worry just yet about numbers and equations. Think about actual play. What’s the pacing of your game like? How quickly do you want to move from scene to scene? How quickly should the game reach its climax? Consider those questions before you get really bogged down in the fiddly bits of your game. Once you have an idea of what play would look like around the table, you can go to setting your preliminary numbers. Those numbers- almost certainly- will be revised after your first few sessions of running the game.

Is it Always Bad?

With human beings in the realm of arts and creativity, it’s rare for something to always be bad. So, obviously, the answer is: “No.” If you want to create something, oh, like a one shot game that really packs a punch or makes a statement, then this is not a problem. In fact, it’s probably exactly what you want. There’s nothing wrong with a game that can be “solved” if that’s the exact effect you’re going for. The problem only arises when the Mathematician Syndrome shows up unintentionally in a design. If you want your game to have some longevity or re-playability, then the Mathematician Syndrome most likely is best stamped out if at all possible. Otherwise it can just kill players’ drive to stick with the game.




CountZero said...

Long time now since this post. I truly enjoy your blog, thanks for your work and positive tone. Your game made me think of Dungeon Keeper for some reason, and I was hoping for a happy end of your design. Have you been able to fix your game now?

Troy_Costisick said...


No, unfortunately I have not. I tried, but neer could.

Your post has given me an idea, though. I need to get a website together where I can post my failed designs with a Creative Commons license. That way if someone else wants them, they can have them. Thanks! :)