On Apr 8, 10:19 pm, "Wlodzimierz Holsztynski (Wlod)"
wrote:
On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"

On Apr 7, 7:55 am, wrote:

So the basic framework for the ultimate chess variant would be: Can
you have a framework for chess and variants that would enable a person
to NEVER play chess the same way twice (by the exact same set of
rules)?

It's only to easy.

I was very conservative. In fact, I have many more
of them, and each sequence consists of astronomically
many variants. (Variants from different sequences
are always different, and so are any two from any
given sequence).

Astronomically large isn't infinite though. You can see one version
laid out by George Duke, in 91 1/2 Trillion Falcon Chess variants, to
see the boundaries he
http://www.chessvariants.org/index/m...ninety-oneanda

The number studied has gotten larger than 91 1/2 Trillion by the way.
However, it still isn't unbound or infinite. Perhaps someone
mathematically can show the number of potential rules governing any
system is finite in nature, then Heraclitian (and its Calvinball
version) wouldn't be possible.

- Rich

In message
wrote:

On Apr 8, 10:19 pm, "Wlodzimierz Holsztynski (Wlod)"
wrote:
On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"

On Apr 7, 7:55 am, wrote:

So the basic framework for the ultimate chess variant would be: Can
you have a framework for chess and variants that would enable a person
to NEVER play chess the same way twice (by the exact same set of
rules)?

It's only to easy.

I was very conservative. In fact, I have many more
of them, and each sequence consists of astronomically
many variants. (Variants from different sequences
are always different, and so are any two from any
given sequence).

Astronomically large isn't infinite though. You can see one version
laid out by George Duke, in 91 1/2 Trillion Falcon Chess variants, to
see the boundaries he
http://www.chessvariants.org/index/m...ninety-oneanda

The number studied has gotten larger than 91 1/2 Trillion by the way.
However, it still isn't unbound or infinite. Perhaps someone
mathematically can show the number of potential rules governing any
system is finite in nature, then Heraclitian (and its Calvinball
version) wouldn't be possible.

- Rich

No, it's trivial to prove that there are infinite possibilities for any rule
system:

Assume a 28 letter alphabet (A-Z plus space and full stop.)

Write down all 28^1 one-character statements A-.
Write down all 28^2 two-character statements AA-..
Write down all 28^3 three-character statements AAA-...
Write down all 28^4 four-character statements AAAA-....

And so on.

This is a countable infinity of 'statements', where each statement consists
of one or more 'sentences'.

Even after you've crossed out all the ungrammatical ones, and all the ones
that do not pertain to Calvinball chess you'll still have a countable
infinity of rules for chess variants remaining. Then there's the infinite
number of different recipes for eggnog, and all the chess/rugby variants
where pawns are allowed to tackle, and so on.


[BTW The number of cross-posted groups for this message is a bit high.
I've removed sci.math and rec.games.design from the followups.

--
Simon Smith

When emailing me, please use my preferred email address, which is on my web
site at http://www.simon-smith.org

On Apr 10, 2:41 pm, Simon Smith wrote:

No, it's trivial to prove that there are infinite possibilities for any rule
system:

Yes, but that assumes that the complexity of any given state of the
rules is unbounded. Which may be a little hard on the people playing
the game.

John Savard

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

On Apr 10, 4:41 pm, Simon Smith wrote:
No, it's trivial to prove that there are infinite possibilities for any rule
system:

Assume a 28 letter alphabet (A-Z plus space and full stop.)

Write down all 28^1 one-character statements A-.
Write down all 28^2 two-character statements AA-..
Write down all 28^3 three-character statements AAA-...
Write down all 28^4 four-character statements AAAA-....

And so on.

This is a countable infinity of 'statements', where each statement consists
of one or more 'sentences'.

Even after you've crossed out all the ungrammatical ones, and all the ones
that do not pertain to Calvinball chess you'll still have a countable
infinity of rules for chess variants remaining. Then there's the infinite
number of different recipes for eggnog, and all the chess/rugby variants
where pawns are allowed to tackle, and so on.

Let's talk about MEANINGFUL rules changes. Changing the colors and
looks of the pieces is irrelevant to the question. While one could
end up having what you state above for letters would show that each
space is a place where a different rule can slide in. While you can
add multiple letters to a statement, this still doesn't show whether
that these amount of spaces are infinite. Of course, in anyone of
those letter spaces, if there can be an infinite range of states
associated with a rule, then that would be infinite. But, outside of
boardsize or time to make a move, what else can have an infinite range
of states for a board? Such as, when it comes to chess, are there an
infinite number of pieces a game of chess, even on an 8x8 board, can
have?

Pretty much, you either have to show that, MEANINGFULLY there are
either an infinite number of MEANINGFUL rules that can be added to a
game, or that one rule can have an infinite number of states, for
Heraclitian/Calvinball to be added.

- Rich

[BTW The number of cross-posted groups for this message is a bit high.
I've removed sci.math and rec.games.design from the followups.

As for this being in sci.math, it does relate to game theory and also
aspects of logic and infinity.

- Rich

On Apr 10, 8:00 pm, Quadibloc wrote:
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.

As I see it here, the only way Heraclitian/Calvinball is going to be
infinite, is if you either have one rule with infinite states, or an
infinite number of game rules that can be added, of distinct types.
If they are of the same type, then that is merely another state of a
given rule. And my question comes back to a LITERAL infinite number
of rules existing. That is the original question Heraclitian/
Calvinball poses.

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

It gets astronomical, as George Duke's 91 1/2 Trillion Falcon Chess
Variants rule show.

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.

Yes, when it comes to analog, you can have an infinite number of
states, assuming that the universe is infinitely small. The digital
equivalent for Chess is the infinitely big chess board. In that, you
can have an infinite number of start positions, so thus Chess on an
infinite chess board is infinite. Of course, one may then argue
despite infinite states, there are universal strategies that can be
applied over all the board configurations.

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.

Yes, in analog, presuming there is an infinite number of different
spot between two points in the universe that are perceived to be
different to the human eye, then it is possible to have an infinite
number of set ups. And I believe this is one of the aspects of the
physical world that Heraclitus touched on with his never the same
river twice. Of course, you bring Zeno in with the paradox, then an
infinite number of spaces between two points sounds absurd, because
one if his is true, then one can always travel half the distance
between two points. And if this is so, then you end up where nothing
should end up reaching is destination.

- Rich

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Quadibloc wrote:

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.

Unless, of course, the Planck Length (1.61609735×10^-35 meters) is
the quantum of distance and the Planck Time (5.3907205×10^-44 Seconds)
is the quantum of time. If they are, then the number of positions in
Billiards is finite. The smallest difference in starting billiard ball
position that can lead to a difference in ending billiard ball position
that is larger than the resolution of the human eye is far larger than
the Planck Length.

As for a game with infinite variations, the human brain has a large
but finite number of possible states, and thus such a game would
have to map multiple variations to one brain state, and thus the
brain would see those multiple variations as being the same variation.


--
Guy Macon
http://www.guymacon.com/

On Apr 11, 4:36 am, Guy Macon http://www.guymacon.com/ wrote:
Content-Transfer-Encoding: 8Bit

Quadibloc wrote:
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.

Unless, of course, the Planck Length (1.61609735×10^-35 meters) is
the quantum of distance and the Planck Time (5.3907205×10^-44 Seconds)
is the quantum of time. If they are, then the number of positions in
Billiards is finite. The smallest difference in starting billiard ball
position that can lead to a difference in ending billiard ball position
that is larger than the resolution of the human eye is far larger than
the Planck Length.

As for a game with infinite variations, the human brain has a large
but finite number of possible states, and thus such a game would
have to map multiple variations to one brain state, and thus the
brain would see those multiple variations as being the same variation.

Yes, I am oversimplifying. After all, a game like PONG by Atari,
although it mapped a game played with idealized physical objects to a
digital system with a finite number of states, was adequate.

A game that is finite, but not in a well-defined way, whose boundaries
are not obvious like those of my Random Variant Chess, that has,
instead of 10^5 sets of rules, 10^1000 sets of rules, of which
somewhere around 10^100 are distinguishable but one can't really put a
finger on the exact number... would be perhaps as close to Heraclitean
Chess as one might get in the real world, but it might be close
enough.

John Savard

On Apr 11, 8:54 am, Quadibloc wrote:
On Apr 11, 4:36 am, Guy Macon http://www.guymacon.com/ wrote:



Content-Transfer-Encoding: 8Bit

Quadibloc wrote:
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.

Unless, of course, the Planck Length (1.61609735×10^-35 meters) is
the quantum of distance and the Planck Time (5.3907205×10^-44 Seconds)
is the quantum of time. If they are, then the number of positions in
Billiards is finite. The smallest difference in starting billiard ball
position that can lead to a difference in ending billiard ball position
that is larger than the resolution of the human eye is far larger than
the Planck Length.

As for a game with infinite variations, the human brain has a large
but finite number of possible states, and thus such a game would
have to map multiple variations to one brain state, and thus the
brain would see those multiple variations as being the same variation.

Yes, I am oversimplifying. After all, a game like PONG by Atari,
although it mapped a game played with idealized physical objects to a
digital system with a finite number of states, was adequate.

A game that is finite, but not in a well-defined way, whose boundaries
are not obvious like those of my Random Variant Chess, that has,
instead of 10^5 sets of rules, 10^1000 sets of rules, of which
somewhere around 10^100 are distinguishable but one can't really put a
finger on the exact number... would be perhaps as close to Heraclitean
Chess as one might get in the real world, but it might be close
enough.

John Savard

I believe to get at the answer to this question, there either has to
be an infinite number of specific rule categories with a set number of
states, or a single rule category that has an infinite number of
rules. Outside of an infinite sized board, or varying the amount of
time people have to play (or make their turns), the question then
becomes, whether or not there is either an infinite number of rules
categories, or a given category (such as pieces) that is infinite.

- Rich

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