Disclaimer: Boring stuff ahead. Read at your own risk.
Dun worry. This post is not on math. My math isn't qualified enough to post on. Its on an interesting observation i made while playing the LOTR risk game with some of the guys at Minds cafe on Friday. Given the normal rules of Risk, where the objective is to garner as much army and land as possbile, and also to kill peanut of course, LOTR Risk is rather different. I'll try to explain the rules a little more concisely for those who have not played before.
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Rule 1: There are 4 players, 2 good and 2 evil.
Rule 2: Standard engagement rules of Risk are applied.
Rule 3: The One Ring moves from the Shire to Mount Doom on a definite path.
Rule 4: Good wins when the ring reaches Mount Doom. Evil wins when the ring is discovered in the land they control.
Subrule 4a: When the ring is in a land controlled by the evil side, they get to roll 2 dice. If the point of the roll is 12 or more (double sixes), the ring is discovered.
Subrule 4b: Certain conditions allow additional points to be included in the die roll, so a die roll of 12 or more is more possbile to achieve.
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Alright then, the purpose of my boring you with these details was to show the huge number of variables present in the game, which makes it highly complex. Indeed, in addition to human variables as well, it is hugely complex. However, what i observed was that although the game was so complex, it was resolved in an extremely simplistic way due to time constraint. Good and evil rolled dice, and the larger number would win.
The interesting thing was not exactly the observation that a complex problem like that could be reduced to such a simple resolution, but the fact that this resolution would actually hold, no matter how many of such games were played. The winning or losing of the game is very simply based on your die roll being larger or smaller than your opponents. The many variables introduced in the game simply provide additional dimensions, not full dimensions, but fractal dimensions to the fundamental rolling of dice. The game is still won or lost by the score of the dice roll, but certain conditions allow additional points to be added to the roll.
I found this observation to be hugely similar to the idea (and observation) of recursive patterns and fractal theory. The occurence of these observations in nature are now reflected in a normal board game. This is not to say that scientific observations have not been garnered from board games, contrarily there has been a lot of research on board games. However, based on my very rudimentary knowledge of game theory, so far probabilty theory seems to be the driving component of game theory. I think the incorporation of fractal theory in the study of board games would prove to be in order for a better understanding of complex systems.
