On Apr 10, 12:40 pm, wrote:

I will say this here, that Heraclitian Chess or Calvinball chess are
not meant to be a form of chess that is actually to be played. They
have to do with the boundaries of variants, whether the rules changes
happen at the start (Heraclitian) or also during play (Calvinball), to
the extent of whether they are unlimited or not. And this gets back
to the original question of whether or not it is possible.

I was going to note that one way to implement a Calvinball type of
game would be, for example, to have the Pawns be cubes, which you
would roll (not like dice) in the direction of their moves, which
would be one step in any Rook direction. Then use the face-up symbols
to grant an extra power to one of your pieces.

Are literally infinite variations on the rules possible? No, unless it
is possible for people to play a game where the rules might fill every
volume in every library in a city where all the buildings are
libraries. If there is an upper limit to the complexity of the game,
to the length of its description, then the number of possibilities is
finite.

The good news, though, is that the number of possibilities can still
be quite large.

Also, I'm thinking in terms of digital games like Chess. If one thinks
of an analog game like Billiards, the number of board positions is
infinite.

In terms of games rather than sports, miniatures wargames could be
said to have an infinite number of positions, since pieces can move
arbitrary distances at arbitrary angles.

John Savard