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Adrian King wrote on Tue, Dec 9, 2008 12:55 AM UTC:
1. I think Jonathan Weissman's analysis shows that your concern is
well-founded; the flaw he found sounds like an example of what you're
thinking of. 

2. You'd surely have to put some constraints on the rule sets you could
create. Otherwise, if I were White, on my first move I'd just create a
rule that says 'White always wins'.

To be in the spirit of the original game, you'd want to have rule space
where each rule change was a small increment, more analogous to the move
of a single piece than to a wholesale shuffling of the pieces on a board.
I've never seen any such rulemaking system; do you know of one?

2a. Strictly speaking, in a game with a finite number n of possible
states, the number of possible rule sets is also finite. To see this:

. Define the rules of a game as a function f(s) => ss that maps each game
state s to a set ss of legal successor states.

. The number of possible state sets, nss, is finite. In fact, it is 2 to
the power n (because each state is either in or not in a given set).

. Therefore, the number of possible functions f(s) => ss is also finite,
and equal to nss to the power n (because f maps from each of n values of s
to one of the nss values of ss).

So, literally speaking, there is not an infinite number of rule sets that
can materialize, at least not if you disallow rules that make the game
state larger (e.g., by enlarging the board or dropping new pieces on it).
However, the maximum number of rule sets is really big -- (2 to the n) to
the n, where n is the already very big number of possible of states of an
FIDE chessboard.

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