On Apr 8, 5:52 am, Harald Korneliussen wrote:
I still don't get it.

Look, a game is a tree*, right? The root is the initial position,
below it one node for each possible starting move, one below each of
these for the possible replies. At the bottom of the tree (trees grow
downwards in CS and math) are the end nodes, which you can label "win"
and "loss". Or "tie", "draw", "both lose", "both win", "win but your
opponent doesn't lose", if you really want to.

The question of Heraclitian/Calvinball doesn't have to do with
positions that can arise, but the number of rules variants a game can
have. The Heraclitian/Calvinball question asks whether or not the
number of variants a game can have is finite or infinite. Extend this
further, and it would apply to all games, or even all rules for
systems. That is the question.

The thing is, since we are talking _abstract_ games here, what really
matters is the shape of this tree. Whether you describe the game in
terms of moving pieces, connections, capturing, or changing rules, all
that is just flavour. Far from unimportant, but nonetheless it's the
tree that makes the game.

It depends on the flavour. Shape and colors of the pieces is
irrelevant, unless such shape or coloring would have an impact on how
the state of a game changes.

Moreover, observe that from any position in a game tree, there's a
complete game that starts right there. All games are already a vast
collection of subgames. Even for a game with a comparatively modest
tree such as Chess, it is already the case that you never play the
same game twice.

So what exactly are you trying to achieve?

How does one know that there an an infinite number of moves in Chess?
Or, I should phrase that, an infinite number of MEANINGFUL moves. And
people can play the same game twice, as in fool's mate. Checkmate
causes a game to end. The question isn't an attempt to achieve
anything, but a question dealing with the nature of variants.

Are you trying to make chess into a game which has a theoretically
infinite number of moves at one point in the tree? There are many such
games, like Eleusis and Mind Ninja, but it is neither necessary nor
sufficient to save the game from being solved, or even giving humans
the advantage. It won't get it on TV either.

The question looks at the parameters to variants, and whether or not
an infinite number can exist.

When I play abstracts rather than CCGs, it's not because they are more
varied, but because the variation I find there (indeed, the variation
in the ways a single good game can play out) is of a more interesting
kind. I suspect other abstract players feel that way too, especially
those of the traditional abstracts, so I don't see Heraclitan Chess
conquering the world any time soon.

I doubt Heraclitian Chess could ever be played, or even be able to be
defined as to make sure that players would never play the same game
twice. But, if one is working with Chess Variants, then the issue does
arise that if the number of variants is finite, then you can have a
classification system in place that could capture them all, and even
simplify, and perhaps bridge them.

- Rich