## Friday, September 4, 2009

### Games and Difficulty to Just Play

I got the chance to play a handful of games of Equations yesterday with my department chair. This is a game I was introduced to in the eighth grade in a half-semester math games course. I finally tracked it down on the Internet last year and got a set at Christmas. Woohoo!

Until yesterday I had only played two or three games with my set.

It's hard to convince people to play Equations, mostly because you have to find someone willing to spend time playing a game and also who isn't bored by elementary math. The intersection of these sets isn't tiny, but it also isn't prevalent. Add to this that the rules are pretty complex and it's very hard to get random people to make it all the way to one game.

There is a reason I'm more interested in games with simple rules: it's easier for people to learn to play right off the bat. Whether or not it is easy to determine who can win is often second-hand to making the game accessible for many players. I love the game Equations---and I don't think it could exist without all the complicated rules---but it takes a few games to really understand what all the possible moves are. It's possible that you can make a winning, game-ending move this turn, but never see it (and no one else at the table might see it). Games are often like this. You can fully listen to or read the rules, but unless you see some of the moves acted out by people, you may not comprehend how the rules can be used. It often takes a few plays of any game before people have an understanding of all the moves they can make.

The above difficulty of seeing immediate-winning moves could be taken a step farther, though.

Question: is there a game where it is hard to get the set of all possible moves?

In the project my students are working on, one of the methods for their game class is: getChildren() which gives them all the potential moves from the current state. Are there games for which this is an unreasonable request?

I can see the following potential clarifications/things-I-am-interested-in/etc

Yes: there might be games that have an exponential number of children, relative to their size. I would rather, however, say that we should consider the complexity in terms of (size of game + number of children) since otherwise Nim already has this property.

Maybe: I'm kinda interested in games engineered around this question. I suspect they exist, mostly because I don't think it would be hard to throw in solving a 3-SAT question as part of each turn.

Totally: I want to know if there are already any games like this, either games that are played or games that are studied (or both!).

Today's post is a bit brief, as I will be driving this afternoon. This is not a long weekend for me, however; there will be the usual post on Monday! :) Have a great weekend!