Complexity

Complexity is hard to understand.

Many of the greatest board games have a few rules that make for a "easy to learn, lifetime to master" label. Go, Othello, Chess, and Checkers are just a few examples of completely open-information, deterministic games. I'll focus on the Game of Go, since I'm most familiar with it.

In Go, complexity raises as the game progresses, whereas, in Chess complexity decreases as pieces are taken from the board. Checkers also decreases vastly in complexity as you play it, and as pieces are captured.

So, I've wondered for a while, how to make a very complex game with a few rules. Today, I had to slap myself, as I forgot how important recursion is. The Fibonacci Numbers come from two starting pieces, and one rule. Yet they are infinite, and describe many phenomena found in nature, like sunflower petals.

The Fibonacci numbers, however, are not a game.

Likewise, other infinite mathematical constructs, such as real numbers, can be generated by a simple recursive procedure.

In games, this boils down to a kind of simple explanation. The result of one round has to be important in figuring out what to do the next round.

In counting, as you count, "1,2,3,4..." you're really just saying:

n = 1;

while (true)

{

n = n+1

}

So you need the last "n" to get to the next "n".

In Go, recursion is found as you play.... you always add a piece to the board, so the last number of pieces go up. But there are many complex other ways that recursion subtly comes into play.

As you decide whether a piece is captured, you must look at all of the other pieces it is attached to to see if they are surrounded. This is a recursive question, as my friend Patrick can attest. He decided to program this in Flash and found that it was not as simple as one would think.

Questions of recursion are not evident in Chess' capture rules, which simply state that two pieces cannot occupy the same space at the same time. The status of the king is not important when asking whether a pawn can be captured.

This still does not answer how a game designer can, for instance, find out which 4 or 5 rules produces a fun, and complex system. But for a given set of rules, perhaps we can ask, "how does this lead to recursion."