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Date: 07 Apr 2008 07:55:10
From:
Subject: Is Heraclitian (aka Calvinball) Chess possible?
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I want to thank George Macon in he future of Chess thread for bringing
up Calvinball, and bringing attention one website that offered one
spin on it, that is the basis of the this question.
This is a theoretical question, meant to test whether or not, even
through boundaries, if the ruleset to chess is finite or infinite.
This does NOT mean playing chess this way is the best way to play
chess, but it does as the question of whether or not chess itself
could remain unsolved if you introduce variant rules. A separate
question would be whether or not doing this would produce games that
aren't even chess. I will leave that as a subset question to this
question, to be asked another time, regarding what is the minimum set
of fix rules needed to still qualify a game as being "Chess". Anyhow,
onto the question posed by Heraclitus (aka Calvinball) Chess.
The philosopher Heraclitus said, "You can never step in the same river
twice" . So, on this note, I would like to run this concept as part
of the Chess of Tomorrow project. As part of the discussion of the
future of chess, someone brought up Calvinball. They posted a link to
one set of unofficial rules:
http://www.bartel.org/calvinball/
There is one permanent rule they have for Calvinball on that page.
That rule is: You may not play the Calvinball the same way twice.
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)? Changes in rules consist of such things as the change in the
layout of the pieces, changes in what constitutes win conditions,
changes in how pieces move and capture, changes in what is in pocket/
reserve, and other things along these lines.
A softer version of this challenge would be that a person would play
both side (black and white) each once, before moving on to a set of
rules. Another softer version of this question would the prospects of
rules changing DURING a game, so a game which has rules change to
something different in turn 3, would be considered a different game
than one where the same rules change happened in turn 5. So the rules
can change in game. From an abstract strategy game perspective, one
could state such rule changes are either known by players when they
would happen at the start of the game, or are controlled by the
players as to when they happen during the game.
Would this be true for a COMMUNITY of players, that keeps adding new
players, given an infinite amount of time also? The community of
players as a whole would never see the same set of rules twice in the
games they play?
A Heraclitus (aka Calvinball) tournament would consist of this being
unique for each game. During the tournament, a limited set of games,
each game has a different set of rules. This is a practical
application of the whole Heraclitus chess approach.
The question then is: Is Heraclitian (aka Calvinball) Chess
possible? Doesn't mean that most of the games people would play of it
would be good, just if it is possible or not. Then the question
becomes how many restrictions can be placed on it to improve quality,
and still have it be Heraclitian.
Thank you for your time...
- Rich
By the way, this questions does impact the Chess of Tomorrow project
in regards to its objectives. If you care to want to input there,
please feel free to do so. The URL is:
http://chessvariants.wikidot.com/forum/t-51667/chess-of-tomorrow-project-who-is-interested#post-139883
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Date: 17 Apr 2008 22:43:40
From: Rich Hutnik
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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On Apr 16, 6:48 pm, Guy Macon <http://www.guymacon.com/ > wrote:
> Now consider these variants of chess:
>
> Variant 3: standard set of men, 8x6 board. <-- same as in list above
> Variant 3.1: standard set of men, 9x6 board.
> Variant 3.2: standard set of men, 10x6 board.
> Variant 3.3: standard set of men, 11x6 board.
> Variant 3.4: standard set of men, 12x6 board.
> Variant 3.5: standard set of men, 13x6 board.
> Variant 3.6: standard set of men, 14x6 board.
> ...
>
> The above set of variants is also clearly infinite,
> larger than the previous infinite set, and maps
> to the set of fractions. Eventually you get to
> Variant 3.141592653589793238462643383: standard
> set of men, 141415926535897932384626433811x6 board
> and on to any other fraction you choose.
>
> The question of *meaningful* differences is more
> interesting. I don't see any meaningful difference
> between playing on an 8x1000 board and playing on an
> 8x1002 board. But the loss of meaningfulness is
> gradual; where exactly does it reach zero?
Meaningful differences is very important. One could argue that the
look of pieces, or their names, could be considered changes, and that
could be about infinite. But it has no effect on gameplay.
What I do see so far is several things that would lend to chess
variants be unbounded:
1. Time control, being infinite. One could do an infinite range of
time delays for a Bronstein clock. Not practical.
2. Size of board, being infinite. This then means an infinite number
of shapes. Unless the size of the board is infinite, then the number
of boards is finite.
3. Recursion. Here is an example. Say you can Calvinball the rules.
Let's say to implement a new rule, like Gipf introduces a new pieces,
one has to win another game to do this. If the number of possible
games one can play is infinite, then there is an infinite number of
varieties of chess. If then someone else where to go about wanting to
change the rules for the new game to see about the old game, they have
to play yet another game, then it is possible to cause an infinite
recursive set of action in place. This is not practical, but is
arguably meaningful to the game experience as a whole.
Pretty much here, either the parameters of a rule are unbound, or the
number of rules is unbound, or there is an infinite recursive rule
that can take place. If so, then such would be unlimited. The first
two be Heraclitian, and the last one being Calvinball. If anyone can
find any others, please say so.
Now, whether or not there is an infinite number of piece types, or
rules, that is another issue that would need to be considered here.
Anyone have evidence that there is an infinite number of rules that
can come in existence for a game like chess?
- Rich
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Date: 16 Apr 2008 18:58:13
From: Quadibloc
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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On Apr 16, 4:48 pm, Guy Macon <http://www.guymacon.com/ > wrote:
> The question of *meaningful* differences is more
> interesting. I don't see any meaningful difference
> between playing on an 8x1000 board and playing on an
> 8x1002 board. But the loss of meaningfulness is
> gradual; where exactly does it reach zero?
But what about the variant on an 8 x 3,698,201,443,...,828,216 board,
where the ... stands for a number of digits which, if printed in 4
point type, in the pages of a thick telephone directory, would require
enough of those volumes to cover Manhattan Island to a height of one
mile?
The number of practical variants of chess that real humans can play is
strictly finite - yet people keep coming up with unexpected new ideas
for variants.
John Savard
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Date: 17 Apr 2008 11:58:13
From: David Richerby
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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Quadibloc <[email protected] > wrote:
> The number of practical variants of chess that real humans can play
> is strictly finite
Trivially: we only have a finite universe in which to store the rules.
Dave.
--
David Richerby Homicidal Umbrella (TM): it's like an
www.chiark.greenend.org.uk/~davidr/ umbrella but it wants to kill you!
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Date: 18 Apr 2008 06:31:26
From: Ed Murphy
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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David Richerby wrote:
> Quadibloc <[email protected]> wrote:
>> The number of practical variants of chess that real humans can play
>> is strictly finite
>
> Trivially: we only have a finite universe in which to store the rules.
Counterargument: infinite sets of variants can be encoded in a finite
description (e.g. arbitrary board length, as mentioned earlier). Of
course, the set of variants we actually play is not as large as the
set of variants that (individually) we practically could play.
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Date: 18 Apr 2008 16:28:23
From: David Richerby
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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Ed Murphy <[email protected] > wrote:
> David Richerby wrote:
>> Quadibloc <[email protected]> wrote:
>>> The number of practical variants of chess that real humans can
>>> play is strictly finite
>>
>> Trivially: we only have a finite universe in which to store the
>> rules.
>
> Counterargument: infinite sets of variants can be encoded in a
> finite description (e.g. arbitrary board length, as mentioned
> earlier).
Yes but, in order to play a game, we need to know which of those
variants we are playing. We only have a finite universe in which to
store either an explicit presentation of the rules or the parameters
that generate them from your finite description.
Dave.
--
David Richerby Carnivorous Portable Composer (TM):
www.chiark.greenend.org.uk/~davidr/ it's like a pupil of Beethoven but
you can take it anywhere and it
eats flesh!
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Date: 17 Apr 2008 03:40:18
From: John Savard
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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On Wed, 16 Apr 2008 18:58:13 -0700 (PDT), Quadibloc <[email protected] >
wrote, in part:
>On Apr 16, 4:48 pm, Guy Macon <http://www.guymacon.com/> wrote:
>
>> The question of *meaningful* differences is more
>> interesting. I don't see any meaningful difference
>> between playing on an 8x1000 board and playing on an
>> 8x1002 board. But the loss of meaningfulness is
>> gradual; where exactly does it reach zero?
>
>But what about the variant on an 8 x 3,698,201,443,...,828,216 board,
>where the ... stands for a number of digits which, if printed in 4
>point type, in the pages of a thick telephone directory, would require
>enough of those volumes to cover Manhattan Island to a height of one
>mile?
>
>The number of practical variants of chess that real humans can play is
>strictly finite - yet people keep coming up with unexpected new ideas
>for variants.
Here is a more practical variant of Chess which belongs to a class of
variants with a very large number of members.
(Best seen with fixed-pitch font.)
R Q K R
B N N B
P P P P
P P P P
R P - . - . P R
N P . - . - P N
B P - . - . P B
K P . - . - P K
Q P - . - . P Q
B P . - . - P B
N P - . - . P N
R P . - . - P R
P P P P
P P P P
B N N B
R Q K R
The two players have their narrow arrays at the top and bottom of the
board. The pieces in arrays on the side of the board may not be captured
by either of the two players, but they can capture the players' pieces.
These pieces move once after every three ply. That is, the sequence
of moves is:
White, Black, White, Left Pieces, Black, White, Black, Right Pieces
The left pieces, as White, and the black pieces, as Black, when they
move simply replay the moves of the Immortal Game between Anderssen and
Kieseritzky.
If one's piece happens to be standing on a square which was empty in the
game to which a piece moves, then it is captured.
Replace the Immortal by the Evergreen, and you get another variant.
So here is a very practical chess variant belonging to a very large
class of chess variants - as many variants of chess as there are *games*
of chess!
John Savard
http://www.quadibloc.com/index.html
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Date: 16 Apr 2008 15:42:27
From: William Hughes
Subject: Re: Are the number of variants to chess of Aleph nature or not? (was
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On Apr 16, 4:58 pm, Rich Hutnik <[email protected] > wrote:
> On Apr 15, 3:53 pm, Quadibloc <[email protected]> wrote:
>
>
>
> > On Apr 12, 11:08 pm, Rich Hutnik <[email protected]> wrote:
>
> > > 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.
>
> > I think that one can always go 'outside the system' and come up with a
> > reasonable new Chess variant that is not included in any
> > classification system, even if that system embraces an infinite number
> > of variants.
>
> > Yet, the fact that people can only handle games up to a certain finite
> > level of complexity means that the number of Chess variants is finite.
>
> > A large, but poorly-defined finite set, therefore, can behave for
> > practical purposes as if it had properties that, in an exact
> > mathematical sense, can only apply to a set with at least aleph-one
> > elements. This doesn't defy any law of mathematics (and, indeed, due
> > to the subject matter, I've pulled sci.math back in, since it's
> > relevant now).
>
> > John Savard
>
> So, then, to make this more mathematical, are the number of rules
> variants for a game like chess an Aleph of any sort? I will re: this
> topic to have it ask that. Maybe someone else who is more math(y) in
> their knowledge could frame this in a more mathematically proper form.
>
> - Rich
It is relatively simple to come up with an infinite number of
variants.
Consider that in standard chess the king can be captured by a single
attack. Consider a variant where the king can only be captured by
two attacks. This generalizes to 3,4,...,n,... attacks.
(Actually, Simon Smith's argument above falls a bit short. It is
not enough to show there are an infinite number of descriptions
of variants of Calvinball chess (after all for each variant there
are an infinite number of descriptions))
- William Hughes
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Date: 16 Apr 2008 13:58:44
From: Rich Hutnik
Subject: Are the number of variants to chess of Aleph nature or not? (was Re:
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On Apr 15, 3:53 pm, Quadibloc <[email protected] > wrote:
> On Apr 12, 11:08 pm, Rich Hutnik <[email protected]> wrote:
>
> > 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.
>
> I think that one can always go 'outside the system' and come up with a
> reasonable new Chess variant that is not included in any
> classification system, even if that system embraces an infinite number
> of variants.
>
> Yet, the fact that people can only handle games up to a certain finite
> level of complexity means that the number of Chess variants is finite.
>
> A large, but poorly-defined finite set, therefore, can behave for
> practical purposes as if it had properties that, in an exact
> mathematical sense, can only apply to a set with at least aleph-one
> elements. This doesn't defy any law of mathematics (and, indeed, due
> to the subject matter, I've pulled sci.math back in, since it's
> relevant now).
>
> John Savard
So, then, to make this more mathematical, are the number of rules
variants for a game like chess an Aleph of any sort? I will re: this
topic to have it ask that. Maybe someone else who is more math(y) in
their knowledge could frame this in a more mathematically proper form.
- Rich
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Date: 16 Apr 2008 22:48:49
From: Guy Macon
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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Rich Hutnik wrote:
>So, then, to make this more mathematical, are the number of rules
>variants for a game like chess an Aleph of any sort? I will re: this
>topic to have it ask that. Maybe someone else who is more math(y) in
>their knowledge could frame this in a more mathematically proper form.
Consider the following variants of chess:
Variant 1: standard set of men, 8x4 board.
Variant 2: standard set of men, 8x5 board.
Variant 3: standard set of men, 8x6 board.
Variant 4: standard set of men, 8x7 board.
Variant 5: standard set of men, 8x8 board. <--standard chess
Variant 6: standard set of men, 8x9 board.
Variant 7: standard set of men, 8x10 board.
Variant 8: standard set of men, 8x11 board.
Variant 9: standard set of men, 8x12 board.
...
The above set of variants is clearly infinite
and maps to the set of integers.
It even offers interesting play; at, say, 8x32,
do you try to launch an attack on the opponent
right away with your long range men (QBR), or
do you keep them behind a wall of pawns that you
slowly march toward the opponent? And if both
sides start marching pawns, what is the best
pawn structure to have when they meet? Diagonal
line? Arrowhead? V? zig-zag? straight across?
And what is the best knight and king placement?
Now consider these variants of chess:
Variant 3: standard set of men, 8x6 board. <-- same as in list above
Variant 3.1: standard set of men, 9x6 board.
Variant 3.2: standard set of men, 10x6 board.
Variant 3.3: standard set of men, 11x6 board.
Variant 3.4: standard set of men, 12x6 board.
Variant 3.5: standard set of men, 13x6 board.
Variant 3.6: standard set of men, 14x6 board.
...
The above set of variants is also clearly infinite,
larger than the previous infinite set, and maps
to the set of fractions. Eventually you get to
Variant 3.141592653589793238462643383: standard
set of men, 141415926535897932384626433811x6 board
and on to any other fraction you choose.
The question of *meaningful* differences is more
interesting. I don't see any meaningful difference
between playing on an 8x1000 board and playing on an
8x1002 board. But the loss of meaningfulness is
gradual; where exactly does it reach zero?
--
Guy Macon
<http://www.guymacon.com/ >
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Date: 17 Apr 2008 11:56:15
From: David Richerby
Subject: Re: Are the number of variants to chess of Aleph nature or not?
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Guy Macon <http://www.guymacon.com/ > wrote:
> Consider the following variants of chess:
> [for i>3, Variant i: standard set of men, 8xi board.]
>
> The above set of variants is clearly infinite and maps to the set of
> integers. [...]
>
> Now consider these variants of chess:
> [for i>3, j>7, Variant i.j: standard set of men, jxi board.]
>
> The above set of variants is also clearly infinite, larger than the
> previous infinite set, and maps to the set of fractions.
These are properly called the positive rational numbers (i.e., the set
of numbers that can be written as i/j for positive integers i and j).
The set of positive rationals is *not* larger than the set of integers:
it has the same cardinality.
Proof. (Writing N for the positive integers, Q' for the positive
rationals and
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Date: 15 Apr 2008 12:53:12
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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On Apr 12, 11:08=A0pm, Rich Hutnik <[email protected] > wrote:
> 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.
I think that one can always go 'outside the system' and come up with a
reasonable new Chess variant that is not included in any
classification system, even if that system embraces an infinite number
of variants.
Yet, the fact that people can only handle games up to a certain finite
level of complexity means that the number of Chess variants is finite.
A large, but poorly-defined finite set, therefore, can behave for
practical purposes as if it had properties that, in an exact
mathematical sense, can only apply to a set with at least aleph-one
elements. This doesn't defy any law of mathematics (and, indeed, due
to the subject matter, I've pulled sci.math back in, since it's
relevant now).
John Savard
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Date: 12 Apr 2008 22:08:30
From: Rich Hutnik
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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On Apr 8, 5:52 am, Harald Korneliussen <[email protected] > 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
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Date: 12 Apr 2008 22:00:55
From: Rich Hutnik
Subject: Re: Is Calvinball Chess possible?
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On Apr 11, 8:54 am, Quadibloc <[email protected] > 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=D710^-35 meters) is
> > the quantum of distance and the Planck Time (5.3907205=D710^-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
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Date: 11 Apr 2008 05:54:04
From: Quadibloc
Subject: Re: Is Calvinball Chess possible?
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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=D710^-35 meters) is
> the quantum of distance and the Planck Time (5.3907205=D710^-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
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Date: 11 Apr 2008 10:36:26
From: Guy Macon
Subject: Is Calvinball Chess possible?
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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.
--
Guy Macon
<http://www.guymacon.com/ >
|
| |
Date: 10 Apr 2008 18:06:22
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 10, 8:00 pm, Quadibloc <[email protected] > 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
|
| |
Date: 10 Apr 2008 17:57:47
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 10, 4:41 pm, Simon Smith <[email protected] > 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
|
| |
Date: 10 Apr 2008 17:00:33
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 10, 12:40 pm, [email protected] 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
|
| |
Date: 10 Apr 2008 16:53:17
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 10, 2:41 pm, Simon Smith <[email protected] > 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
|
| |
Date: 10 Apr 2008 11:45:17
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 8, 10:19 pm, "Wlodzimierz Holsztynski (Wlod)"
<[email protected] > wrote:
> On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"
> > On Apr 7, 7:55 am, [email protected] 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 here:
http://www.chessvariants.org/index/msdisplay.php?itemid=MSninety-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
|
| |
Date: 10 Apr 2008 11:40:47
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 10, 12:58 pm, Quadibloc <[email protected] > wrote:
> On Apr 10, 10:25 am, [email protected] wrote:
>
> > I believe Heraclitean (or is it Heraclitian, as I am using it, not
> > just full of strife, but never twice) is supposed to be either it is
> > or isn't.
>
> Then I'm probably not using the term the way you are. I'm just
> thinking of my old idea of a basic structure where one chooses one of
> a large number of variants in a way similar to the way Checkers
> players choose one of a number of three-move openings.
As I was discussing Heraclitian, it was meant as a philosophical
boundaries of variant question.
> This isn't like Calvinball, where the rule is to change the rules in
> the middle of play, so as to not take anything seriously except having
> fun.
The Heraclitian question asks initially if the starting rules to the
game can be infinite (if they don't change during play). A version of
the Heraclitian question, which refers to changes during play, would
be the Calvinball variety of Heraclitian. Such changes can be done in
a strategic manner.
> Nor is it like IAGO Chess, where different pieces are dropped on the
> board during play - but made more complicated.
If you speak of your game, it looks like a variant on Chess960, but
with fantasy pieces. As far as the IAGO Chess System goes, it is
meant to have a framework where you can use the drops at the start.
In fact, in Near Chess, which would fit in the IAGO Chess System, the
pieces enter the game at the start, before any moves. If you allow
entry not just at the start, it makes for a deeper game that calls
upon judgment, and makes the game less likely to be solved
(mathematically speaking). This is why I had proposed in the IAGO
Chess (game) it be done via gates and dropping. The game is also
meant to introduce people to the fullness of chess variants, which is
why the C-Class version has you doing a start of the game drop on the
queen space.
> Let's say, for example, one plays on a chessboard where the squares
> have numbers printed on them in a random arrangement. The last two
> digits of the sum of the numbers on the squares that are occupied by
> both players' Pawns (think of this as a hash function of the
> position)... indicates one of a hundred different Fairy Pieces - and,
> on any turn, a player can choose to either drop a piece in hand for
> dropping, or *drop the piece indicated by this number* which also
> gives his opponent the same type of piece in his hand to drop later.
So, you are using a shuffle to decide where the pieces go (rather than
deterministically). A shuffle is good for mixing things up, but has
the definite risk of leaving pawns unprotected and forcing players to
use moves to compensate for poor starting position. I will say it is
a good thing to have as one of the ways to play, but I don't see a
shuffle alone as being the answer to the migration path.
> So as the game goes on, the type of pieces on the board varies
> "randomly", but it's all from the same starting position and rules.
>
> Some rule would have to be added to prevent the board from having on
> it almost as many pieces as there are squares, but this is just a
> thought example, not a serious variant yet.
>
> But if this is the sort of direction you're thinking of, I don't know
> of a good direction to go in to make that kind of variant.
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.
- Rich
|
| |
Date: 10 Apr 2008 09:58:20
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 10, 10:25=A0am, [email protected] wrote:
> I believe Heraclitean (or is it Heraclitian, as I am using it, not
> just full of strife, but never twice) is supposed to be either it is
> or isn't.
Then I'm probably not using the term the way you are. I'm just
thinking of my old idea of a basic structure where one chooses one of
a large number of variants in a way similar to the way Checkers
players choose one of a number of three-move openings.
This isn't like Calvinball, where the rule is to change the rules in
the middle of play, so as to not take anything seriously except having
fun.
Nor is it like IAGO Chess, where different pieces are dropped on the
board during play - but made more complicated.
Let's say, for example, one plays on a chessboard where the squares
have numbers printed on them in a random arrangement. The last two
digits of the sum of the numbers on the squares that are occupied by
both players' Pawns (think of this as a hash function of the
position)... indicates one of a hundred different Fairy Pieces - and,
on any turn, a player can choose to either drop a piece in hand for
dropping, or *drop the piece indicated by this number* which also
gives his opponent the same type of piece in his hand to drop later.
So as the game goes on, the type of pieces on the board varies
"randomly", but it's all from the same starting position and rules.
Some rule would have to be added to prevent the board from having on
it almost as many pieces as there are squares, but this is just a
thought example, not a serious variant yet.
But if this is the sort of direction you're thinking of, I don't know
of a good direction to go in to make that kind of variant.
John Savard
|
| |
Date: 10 Apr 2008 09:25:59
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 9, 10:52 pm, Quadibloc <[email protected] > wrote:
> On Apr 7, 8:40 pm, Quadibloc <[email protected]> wrote:
>
> > But my version, on the 12 by 8 board, offers up to 16,200 variants -
> > all tidy and symmetrical like normal Chess, so it might meet this
> > particular goal.
>
> I kept the original set of versions of Random Variant Chess, and the
> 10 by 8 version I added at the last, but I've replaced the other
> recently added versions (Historical Random Variant Chess and Mutable
> Random Variant Chess) by something which has included their best
> features, but made more organized and rationalized, which I call
> Progressive Random Variant Chess (the Progressive part has to do with
> the placement of the Camel and the Giraffe on the board if they are
> used) and which offers more possibilities - up to 172,620 possible
> variants of Chess on the 12 by 8 board.
>
> Perhaps this might be Heraclitean enough...
>
> John Savard
I believe Heraclitean (or is it Heraclitian, as I am using it, not
just full of strife, but never twice) is supposed to be either it is
or isn't. If one wants to argue whether a game itself is Heraclitean
in the possible number of moves it could have (aka unbounded or
infinite), then perhaps one wouldn't need to have an infinite number
of rules or staring configurations to reach a Heraclitean game state.
Also, another question is whether or not a game that is Heraclitean in
number of game states could ever be solved, or that there is always a
counter strategy or line to the one that is developed. Heraclitean
game rules, not just a Heraclitean GAME, would end up being infinite.
- Rich
|
| |
Date: 10 Apr 2008 09:20:24
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 9, 1:48 pm, Quadibloc <[email protected] > wrote:
> On Apr 9, 9:30 am, [email protected] wrote:
>
> > On Apr 7, 9:41 pm, Quadibloc <[email protected]> wrote:
> > > On Apr 7, 12:02 pm, Guy Macon <http://www.guymacon.com/> wrote:
> > > > My name is Guy Macon. Not George.
>
> > > I was wondering if this was a Freudian slip... perhaps he was imputing
> > > the "we will adopt no chess variant before its time" viewpoint to you.
> > There is someone on the chessvariants site named George I discuss and
> > debate with. Even after checking that, I likely had his name on mind.
>
> Ah. Not the George Masson wineries. Ah, my memory was faulty. That was
> the Paul Masson wineries.
>
> John Savard
The Masson masonries have to deal with chess variants? :-)
- Rich
|
| |
Date: 10 Apr 2008 06:37:15
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 9, 8:52 pm, Quadibloc <[email protected] > wrote:
> On Apr 7, 8:40 pm, Quadibloc <[email protected]> wrote:
>
> > But my version, on the 12 by 8 board, offers up to 16,200 variants -
> > all tidy and symmetrical like normal Chess, so it might meet this
> > particular goal.
>
> I kept the original set of versions of Random Variant Chess, and the
> 10 by 8 version I added at the last, but I've replaced the other
> recently added versions (Historical Random Variant Chess and Mutable
> Random Variant Chess) by something which has included their best
> features, but made more organized and rationalized, which I call
> Progressive Random Variant Chess (the Progressive part has to do with
> the placement of the Camel and the Giraffe on the board if they are
> used) and which offers more possibilities - up to 172,620 possible
> variants of Chess on the 12 by 8 board.
>
> Perhaps this might be Heraclitean enough...
I have now added notes to my page on Spectral Realm Chess to cover how
the various Fairy Pieces in Random Variant Chess would be modified in
respect of the possibility of half-step diagonal moves, and I have
added a page on what I call "Half-Shogi Chess" to reduce draws, with
inspiration from Shogi, but without having full unrestricted drops in
the manner of Shogi, which has already been proposed (Neo-C from 3M/
Mad Mate/Chessgi) by others.
John Savard
|
| |
Date: 09 Apr 2008 19:52:40
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 7, 8:40 pm, Quadibloc <[email protected] > wrote:
> But my version, on the 12 by 8 board, offers up to 16,200 variants -
> all tidy and symmetrical like normal Chess, so it might meet this
> particular goal.
I kept the original set of versions of Random Variant Chess, and the
10 by 8 version I added at the last, but I've replaced the other
recently added versions (Historical Random Variant Chess and Mutable
Random Variant Chess) by something which has included their best
features, but made more organized and rationalized, which I call
Progressive Random Variant Chess (the Progressive part has to do with
the placement of the Camel and the Giraffe on the board if they are
used) and which offers more possibilities - up to 172,620 possible
variants of Chess on the 12 by 8 board.
Perhaps this might be Heraclitean enough...
John Savard
|
| |
Date: 09 Apr 2008 10:48:53
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 9, 9:30=A0am, [email protected] wrote:
> On Apr 7, 9:41 pm, Quadibloc <[email protected]> wrote:
> > On Apr 7, 12:02 pm, Guy Macon <http://www.guymacon.com/> wrote:
> > > My name is Guy Macon. =A0Not George.
>
> > I was wondering if this was a Freudian slip... perhaps he was imputing
> > the "we will adopt no chess variant before its time" viewpoint to you.
> There is someone on the chessvariants site named George I discuss and
> debate with. =A0Even after checking that, I likely had his name on mind.
Ah. Not the George Masson wineries. Ah, my memory was faulty. That was
the Paul Masson wineries.
John Savard
|
| |
Date: 09 Apr 2008 08:30:39
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 7, 9:41 pm, Quadibloc <[email protected] > wrote:
> On Apr 7, 12:02 pm, Guy Macon <http://www.guymacon.com/> wrote:
>
> > [email protected] wrote:
> > >I want to thank George Macon in he future of Chess thread for bringing
> > >up Calvinball, and bringing attention one website that offered one
> > >spin on it,
>
> > My name is Guy Macon. Not George.
>
> I was wondering if this was a Freudian slip... perhaps he was imputing
> the "we will adopt no chess variant before its time" viewpoint to you.
>
> John Savard
There is someone on the chessvariants site named George I discuss and
debate with. Even after checking that, I likely had his name on mind.
- Rich
|
| |
Date: 09 Apr 2008 19:26:41
From: mudshark
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
Wlodzimierz Holsztynski (Wlod) wrote:
>
> On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"
> <[email protected]> wrote:
> > On Apr 7, 7:55 am, [email protected] 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.
>
> ... too easy.
>
> > Furthermore, for a greater variety, I have 255
> > of such different sequences [...]
>
> 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).
>
> Wlod
You still are - "conservative" Wlod. You will _never_ free yourself from
the stultifing 'milieu' into which you were born. It is your destiny, to
forever long & linger over what might have been had you had the fortune
to be born in Britain. Just think of it. You could of had a first class
education & with your natural Polska brilliance conquering all won an
oxbridge scholarship! Then, after the Tripos they might even have
crowned you 'wrangler' (google it if you're not sure) @ which point _it
is_ -behoven- [now that's a word] upon you to announce the variegated
peregrinations of the 'optimes'. The juniors & seniors, the wooden spoon
etc. But no! You chose instead the saturated pastures of Amerika just
like Innes & look @ 'im if you can - a bloated fish awash with his kids
hanging on to a wifes bloody rag. Ptew! What disgustment, what lack of
freedom. Huge, large Maori people - doing 'hakus' & eating ionised fish,
scare the shit out of the Parr/Innes & by proxy Evans gambit. Won't do.
Huge dislike of these bone-marrow sucking vampires. These vile human
entities who are @ the fore everytime & all the time - sucking vampires.
Righto, I'm awaiting your opinion regarding the Karpov..
|
| |
Date: 08 Apr 2008 19:19:40
From: Wlodzimierz Holsztynski (Wlod)
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"
<[email protected] > wrote:
> On Apr 7, 7:55 am, [email protected] 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.
... too easy.
> Furthermore, for a greater variety, I have 255
> of such different sequences [...]
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).
Wlod
|
| |
Date: 08 Apr 2008 18:40:16
From: Wlodzimierz Holsztynski (Wlod)
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
On Apr 7, 7:55 am, [email protected] 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 have a very long, regular sequence of such
variants. Each is very much like standard chess. Each next one differs
only a little from the previous one. You use the standard chess
board, and standard pieces, only possibly more than in the standard
chess, depending on the game (the starting position is always the
same).
Furthermore, for a greater variety, I have 255 of such different
sequences (plus standard chess on the top of it :-)
I claim that each sequence is very long and not infinnite
because I am talking about games which are essentially
different, and not just formally -- if we treat the repetition
rule seriously then I consider each of my 255 sequences of
variants to be finite. (There are still more than plenty of them :-)
Regards,
Wlod
|
| | |
Date: 10 Apr 2008 21:41:57
From: Simon Smith
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
|
In message <fc9209bf-6fe8-447f-8f9f-d6bfd023ee6c@p39g2000prm.googlegroups.com >
[email protected] wrote:
> On Apr 8, 10:19 pm, "Wlodzimierz Holsztynski (Wlod)"
> <[email protected]> wrote:
> > On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"
>
> > > On Apr 7, 7:55 am, [email protected] 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 here:
> http://www.chessvariants.org/index/msdisplay.php?itemid=MSninety-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
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Date: 08 Apr 2008 02:52:14
From: Harald Korneliussen
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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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 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.
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?
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.
Nor do the fact that big games include very many other games as their
subgames matter much. They have to stand on their own merit. I don't
feel that Magic: The gathering is an all that varied experience, for
instance, although the number of possible games probably dwarfs even
Go.
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.
(* technically a directed acyclic graph. Whether the rules say so
explicitly or not, all rules have an equivalent of the fifty-move
rule, because players aren't machines.)
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Date: 07 Apr 2008 18:41:36
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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On Apr 7, 12:02 pm, Guy Macon <http://www.guymacon.com/ > wrote:
> [email protected] wrote:
> >I want to thank George Macon in he future of Chess thread for bringing
> >up Calvinball, and bringing attention one website that offered one
> >spin on it,
>
> My name is Guy Macon. Not George.
I was wondering if this was a Freudian slip... perhaps he was imputing
the "we will adopt no chess variant before its time" viewpoint to you.
John Savard
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Date: 07 Apr 2008 18:40:08
From: Quadibloc
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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On Apr 7, 9:55 am, [email protected] wrote:
> A Heraclitus (aka Calvinball) tournament would consist of this being
> unique for each game. During the tournament, a limited set of games,
> each game has a different set of rules. This is a practical
> application of the whole Heraclitus chess approach.
>
> The question then is: Is Heraclitian (aka Calvinball) Chess
> possible? Doesn't mean that most of the games people would play of it
> would be good, just if it is possible or not. Then the question
> becomes how many restrictions can be placed on it to improve quality,
> and still have it be Heraclitian.
I would think that each variant should be used twice - once for one
player as White, once as Black, for a series of two games between two
players. Just like the openings drawn in Checkers.
Since I am not discussing whether or not one could have a near-
infinite number of variants of Chess, I've removed sci.math.
But my version, on the 12 by 8 board, offers up to 16,200 variants -
all tidy and symmetrical like normal Chess, so it might meet this
particular goal.
John Savard
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Date: 07 Apr 2008 14:32:30
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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On Apr 7, 5:13 pm, Guy Macon <http://www.guymacon.com/ > wrote:
> (Who snuck sci.math into the newsgroups line? *WAY* off-topic there!)
I was looking for a group that would deal with the mathematical
theoretical issues regarding the idea that a set of rules to a game
could have an infinite varieties. Perhaps there is a better "game
theory" newsgroup.
> [email protected] wrote:
> Hey, as long as I am in the "thanks to" section when CalvinChess
> makes you rich (don't laugh; do you have any idea how much they
> made off of Smess? It was a huge hit!) I will be happy. :)
Well, you will be made mention if Calvinball Chess (by whatever its
name) will get discussed, in regards to its history (and you will be
referred to as Guy :-) ).
> BTW, here is a place to get some interesting ideas:
> [http://www.sjgames.com/knightmare/] and at the "specific
> cards" section here:
> [http://www.sjgames.com/knightmare/kc_faq.html].
Drops and gating, shuffles (FRC/960), and the ideas in Knighmare Chess
are what I was actually thinking of regarding Calvinball. With
Nightmare Chess, I believe you deal out a bunch of cards, and players
alternate turns taking one. Players know what can come into play, but
players decide when they come into play. You need to balance the
scoring somehow so it is fair, and have players both have the same
choice picking which cards to use. So long as you can keep spawning
more and more rules, Calvinball is in effect.
The idea you see in Knightmare Chess has been discussed as
"mutators". These are rules that change the rules of the game as you
play. They can be applied to the start, or possibly throughout the
game.
- Rich
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Date: 07 Apr 2008 21:13:22
From: Guy Macon
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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(Who snuck sci.math into the newsgroups line? *WAY* off-topic there!)
[email protected] wrote:
>
>Guy Macon <http://www.guymacon.com/> wrote:
>
>> [email protected] wrote:
>
>> >I want to thank Guy Macon in he future of Chess thread for bringing
>> >up Calvinball, and bringing attention one website that offered one
>> >spin on it,
>>
>> My name is Guy Macon. Not George.
>
>Sorry for that. I stand corrected here. I should of said Mr. Macon
>instead. And to think, I went back to make sure I got your name
>right. I did fix it above.
Hey, as long as I am in the "thanks to" section when CalvinChess
makes you rich (don't laugh; do you have any idea how much they
made off of Smess? It was a huge hit!) I will be happy. :)
BTW, here is a place to get some interesting ideas:
[ http://www.sjgames.com/knightmare/ ] and at the "specific
cards" section here:
[ http://www.sjgames.com/knightmare/kc_faq.html ].
--
Guy Macon
<http://www.guymacon.com/ >
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Date: 07 Apr 2008 10:29:35
From:
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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On Apr 7, 1:02 pm, Guy Macon <http://www.guymacon.com/ > wrote:
> [email protected] wrote:
> >I want to thank Guy Macon in he future of Chess thread for bringing
> >up Calvinball, and bringing attention one website that offered one
> >spin on it,
>
> My name is Guy Macon. Not George.
Sorry for that. I stand corrected here. I should of said Mr. Macon
instead. And to think, I went back to make sure I got your name
right. I did fix it above.
- Rich
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Date: 07 Apr 2008 17:02:21
From: Guy Macon
Subject: Re: Is Heraclitian (aka Calvinball) Chess possible?
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[email protected] wrote:
>I want to thank George Macon in he future of Chess thread for bringing
>up Calvinball, and bringing attention one website that offered one
>spin on it,
My name is Guy Macon. Not George.
--
Guy Macon
<http://www.guymacon.com/ >
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