The Chess Variant Pages

Mutators

The existing chess variants (CVs) use an enormous wide of different concepts in their rules. Some of those new rules have a special feature, they can be used in other variants, creating new games. A simple and good example is the pass rule: A player may pass his turn. If you apply this rule to FIDE chess, you get a different game, Passing Chess (or whatever...). I will call to this kind of rules, mutators.

What I want is to start a discussion about this concept, namely:

What makes a certain rule a Mutator?

Definition: A mutator M is a well-defined and reasonable concept that applied at least to one game G, produces a new game, denoted G[M].

Remark: A game G with mutator M, that is G[M] is, by definition, a new game. So we can apply other mutator M' on it to produce another new game denoted by G[M][M'].

I inserted the reasonable word in the mutator definition, to avoid questionable mutators like rule 8th-yellow: "The game must be played on the 8th floor of a yellow building". I trust your common sense :-)

Even so, this is a not a strict definition, since I didn't define what a game is (a rather complex issue). To avoid this problem (since we will deal just with CVs), I use the next definition:

Definition: Let's denote "FIDE Chess" as game FIDE. A chess variant C is the result of applying N mutators, M1, M2, ..., Mn to FIDE, that is, C = FIDE[M1][M2]...[Mn].

Remark: A consequence is that every CV can be defined in terms of Mutators.

Example: Assume the Pass rule as a mutator. So, Passing Chess is defined by FIDE[Pass].

How Mutators interact with each other?

What if we use more than one mutator in a game? Can we use the same mutator twice? It depends, of course...

Some initial notation:

Now for some concepts:

Assume the following mutators:

Examples:

More Mutators...

Here are some other mutators (only a few of them are mine, the others were taken from various sources). Some mutators would need more explanations to remove ambiguities, but the main idea is there.

Fell free to send me more!

Mutator Prefixes

Let's imagine the following CV: The game is equal to FIDE chess until turn 40, then it behaves like Misere Chess. How to do it? This could be done only with mutators parameterized with other mutators (see next section). Other way is to insert a new notation called prefixes. A Prefix is a condition that is attached to one or more mutators. A mutator only works if its prefix condition is true, otherwise it behaves like mutator NIL, i.e., it changes nothing. A prefix P of mutator M in game G is denoted by G::P[M]::

List of Prefixes:

It is also possible to combine prefixes using the logical operators, like and, or, not, ...

Examples:

High-Order Mutators

High-order mutators are mutators that receive one or more mutators as parameters.

Instead of using prefixes, the job can be done using high order mutator Apply, which syntax is [Apply(mutators, condition)] where the mutators are only applied if condition is true. The example FIDE::turn>40[Misere]:: becomes FIDE[Apply([Misere],turn>40)].

Other high-order mutators:

Examples:

Of course, if there are some problems defining what makes a mutator reasonable, there is an extra problem with high-order mutators and that is an interpretation one (e.g., what is the inverse of mutator X?)

 

Contributions

Claude Chaunier, Torben Mogensen, Bill Taylor

written by Joćo Pedro Neto


Written by Joćo Pedro Neto.
WWW page created: February 8, 2000.