Friday, September 11, 2009

Channeling Strength and Game Theory

OK, hold onto your hats for a minute while I discuss some mathematics before getting to the game portion of this post.

There is an area of mathematics called game theory that attempts to formalize what it means to play a game in an intelligent manner. When you apply this area to the study of competitive behavior you get some interesting things. For instance, it deals with solutions of games (how to win, no mater what the opponent does), optimal strategies in general, etc.

Where might you have seen this area of mathematics before?  Well, if you've ever seen the movie A Beautiful Mind, about the life of John Nash, then you've seen a movie about one of the most famous game theorists of all time. It is an area that is heavily applied in economics, which is how Nash won a nobel prize in economics...for doing some mathematics. (He developed the concept of a Nash Equilibrium, which is pretty nifty when looking for solutions in a lot of different cases. Even if, as John von Neumann said, it's "just a fixed-point theorem" after all.)

So, what area of game theory are we interested in here? It's one of the first things that a new student of the field will learn, the idea of domination where it applies to different strategies. Essentially, if one strategy is better than another in every situation, it dominates that other strategy, and no sane player would ever use that weaker strategy. Domination isn't necessarily the best concept to apply in all cases, but it will serve the purpose for this discussion.

How does this apply to the MUD? Well I've heard a few players (and Imms) wondering "Why would I ever choose medium or strong channeling strengths in creation when I now have gifted available to me?" Well, on the surface, these people are trying to make an argument that the strategy of choosing gifted dominates the strategy of choosing strong. I.e., that there aren't any drawbacks to choosing gifted instead of one of the other strength levels. Well, this was something that I thought about a little bit when folks were saying "the aLGORITHM is ready to go!  Let's implement this mother!" It's worth thinking about, and it's something I put my head together with Vandread about. So, the code already was in place to do what we needed, which is break this domination that gifted has to some extent.

How is it broken? Well, think about this. There has to be no drawbacks for one strategy to dominate the others, but let me present you with a drawback. Namely, how can you ensure that you'll actually reach your full channeling potential if you choose gifted as your strength in creation? It may seem like a funny thing, but it's pretty crucial. Jeshin has recently posted a comment from Kimadi about our search for realism (at least, as real as you can get in the Wheel of Time setting) in the MUD. Essentially, when we decided to enforce a wider spread of flow strengths, we were trying to get people to set up characters that were closer to the experience that can be found in the WoT books since most channelers there are at least a little bit proficient with all the flows. So what's the other piece of realism that I'm trying to hint at here? Well, in the books RJ made it very clear that the process of going from random shlub to uber-channeler wasn't an easy one. Life as a wilder was extremely dangerous, and not something that a lot of people survived. Certainly, more didn't make it than did. Combine this with the high number of people that choose to create channelers because it is "cool" or whatever, and the result is that it is necessary for people to fail when trying to become totally powerhouse channelers.

I claimed above that the code to ensure this was already installed, but why haven't we seen it? I mean, there are very very very few people around now who remember when gifted and strong were removed from creation, so folks haven't really ever known anything different than the land where medium was king. Thus, people haven't noticed that a medium strength channeler has a much lower chance to burn out before becoming a real force than one with a higher channeling strength.... Well, I assure you, folks are about to notice. All I have to say for folks who choose gifted and then try to work their way up in ability level...good luck, because you will definitely need it. There are ways to make it easier, which of course I won't share, but in general it's something that will require more thought and work than medium ever did.

So, there's a moderately compelling reason why one should at least think twice before choosing gifted in creation for their channeling strength as opposed to medium. The gifted strategy doesn't entirely dominate the others in this sense, as you are definitely taking a risk of putting a bunch of time in only to fall victim to some tough random number generation in the end.


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