Comments/Ratings for a Single Item

David Pritchard's criteria used in the 41-square contest are interesting:
playability, originality, simplicity and elegance. We also generally used
these criteria in judging the 42-square contest, with an added touch of
subjectivity--which should not be ignored. See:
http://www.chessvariants.com/41.dir/report.html

With respect to Shogi and such cases, I think of promotion
pieces as counting 1/2, so Shogi charts at 11/81. Not regarding this 13%
as an outlier, what factor(s) makes 0.13+ work in Shogi? Answer: the
weaker, Pawnlike character of most pieces, also quantifiable. (Piece-type
Density, only one convenient measureable factor, falls off in
effectiveness much below 64 squares, certainly by Tori Shogi's 49.) With
standards like 'simplicity' and 'elegance,' can they ever be
quantified? I think so. Another criterion is Average Moves per
recorded game. I submit there is an optimum that players prefer, about 30
or 35, lower than most chesslike games deliver.  With the prospect of
variants of variants, and thousands of game-rules sets, numerical
relationships help evaluate, and some even fail by the numbers.

Another consideration would be the advantage in the exchange.  No matter
the number of the various pieces, a game might have a significant
difference between the weakest and the strongest.  This allows for the
potential of advantage in the game, even if the exchanges are equal.

Of course this value would be quite difficult to quantify and would vary
from one game to the next, being dependent upon field and goal.

Advantage in the exchange is REALLY difficult to measure, it depends
strongly on position, and FIDE-CHESS is a notorious example. G.M. Tigran
Petrossian, ex-world champion, was famous by a strict positional Quality
sacrifice in some openings, giving its Rook for a Knight without any
apparent advantage. After a lot of moves, say 20 or 25, the advantage was
notorious, but not easy to see at first!.

The advantage of any exchange can be simply expressed by the strength(or
value) of the pieces being exchanged.  If a game was populated with pieces
of near equal value, the advantage of exchange might not be significant. 
But if the pieces were of various degrees of value, enough to clearly
differentiate them, exchanges would hold the potential of an advantage.

Yes, a player can make sacrifices to obtain positional or material
advantage.   This gambit would not be possible unless there was a prior
consideration of the value of such an exchange.  But whether or not the
exchange is a gambit need not be part of the determination of a game's
potential for advantage in exchanges.

One of the reasons I like Shogi so much is that you really do exchange
pieces.  'Advantage in the exchange' takes on a whole new meaning, and
there may be additional advantages to sacrificing a piece for the sake of
being able to drop another.  In fact, the very ability to drop makes the
game so much deeper than FIDE Chess, yet the game seems so much more
refined sometimes.

I would suggest that another criterion, overall clarity, be added to the
list.  Sometimes when I read a new variant that has just been posted on
the CVP, I think to myself, 'I bet it's fun when you figure it out!' 
Some games have learning curves the size of Omaha, and I find that a major
problem.

--Jared

The clarity of the rules is extremely important.  For example, I think
I've figured out the game of Gridlock but I'm still not absolutely sure.
 So I'm reluctant to actually tackle the game.

Whether the game is simple or complex, if the rules are incomprehensible
the game will never be attempted.  The presentation of a game will
definitely effect its overall evaluation.

First let me mention that Pritchard's Encyclopedia of Chess Variants
includes an article on this subject, written not by Pritchard, but by Tom
Braunlich. It's under the entry 'Designing a Variant'. In this short
article, Braunlich describes two criteria: elegance and balance. These are
two criteria I had an instinct for as early as Cavalier Chess, though I
hadn't formalized my thought on the subject. 'An elegant game', he
says, 'combines minimum rules with maximum strategy.' To give one
example from my own games, Metamorphin' Fusion Chess combines the rules
of two other games, Metamorph Chess and Fusion Chess, and the result
transforms the strategy of the game. Unlike its forebears, Metamorphin'
Fusion Chess allows you to increase your material through reproduction.
Now let me contrast that with another of my games that never got uploaded
to the web. Shortly before Jason Whitman introduced a game called
Evolution Chess, I had created a game called Evolution Chess. My Evolution
Chess was completely different. In my game, each piece had a double set of
chromosomes, which is what determined its powers and its gender. Instead
of making a regular move, a player could mate a male and a female piece,
to procreate a new piece whose DNA was a random mixture of the two with
some chance of mutation. I suppose I should release it with an alternate
name such as Procreation Chess or Sex Chess. Anyway, as elegant as both
games are, I think that Metamorphin' Fusion Chess probably handles
procreation in a more elegant way. Procreation simply follows from the
rules, whereas procreation is explicitly built into the rules of my
unpublished game. In general, it is better when the strategic elements of
a game simply flow from its rules instead of being built into them. 

Braunlich describes balance as being between pieces. He points out that
changes in various parameters can upset the balance between a game's
pieces, and these 'must be reconstituted in some way to prevent the game
from becoming too straightforward.' A game that is too straightforward
would be one that has too much clarity and not enough depth. So he is
getting at something of the same thing as Mark Thompson writes about. As
an example, let me compare Cavalier Chess with an early version of the
same game. In Cavalier Chess, most pieces get additional Knight powers,
and the Knight itself moves as a Nightrider. In an early version of the
game, Pawns were replaced by Knights. This made the game too
straightforward, for the Knights quickly captured each other, leaving the
other pieces too easily exposed to each other. I fixed this by replacing
leaping Chess Knights with the lame Knights used in Chinese Chess. These
could be used for blocking, which allowed the powerful pieces behind them
to be used more strategically.

Clarity in the rules?. Well, the game of Nemoroth is not exactly the
example of this, but it seems to be a good game very playable (at least I
have seen that in the two test games I have tried). I´m not sure anyone
can stablish standard measures for all games. If you want to have a better
idea about a game, play it, test it and obtain preliminary conclusions. It
is best that any other theoretical consideration.

I'd like to discuss Thompson's four criteria in a separate comment. These
are all important criteria. I especially like the focus he puts on
balancing complementary elements. Tic-Tac-Toe is a perfect example of a
completely unbalanced game. It has complete clarity, no depth, complete
decisiveness, and no drama. A game I've been working on recently, Magic
Chess, a Chess game played with cards, is high in drama but has been
lacking in decisiveness. In one game that I played against myself, each
side kept getting the upperhand over the other for a while, only to lose
it again. I'll have to focus on making that game more decisive.

The rules for the game of Nemoroth, though complex, was completely
understandable.  The various moves and powers were well defined.  The only
area of  non-clarity would the the potential inter-relationship between
all the effects when a specific move is preformed.  This makes strategic
planning very tough, if not impossible.  It can strain the limits of the
mind.  And the developer gave all players fair warning about its nature.

It can be used as an example of a well-defined complex game.  

[BTW, the Gridlock game I referred to in an earlier posting was Paul
Leno's Gridlock, or Gridlock's Ruins or New Wave Chess.  I've been able
to decipher about ninety percent of it, and it has caught my interest.  I
will post a few of questions about it on the appropriate pages.]

Define an 'Event', generally applicable, as either a Capture or a
Check. An interesting game, one likely to have a high baseline for all
four Depth-Drama-Decisiveness-Clarity, should have event frequency 33-50%
per paired move. In other words, by move 30 say, there should ordinarily
be 10 or 15 captures or checks, either way B-W and W-B.

To go with Depth-Clarity-Decisive-Drama, the first-order generalities,
there are now numeric Piece-type Density, Game Length(# moves), and Event
Frequency [(Checks + Captures)/#Moves]. [Cited by Michael Nelson from Ralph Betza's 
constructs:] Power Density makes four quantifiable factors so far to evaluate 
a given set of game rules, or any of millions.  Power Density, not even
requiring database of games played, makes ideal a priori evaluative
criterion.  PD trades off with PTD: other things being equal, a lower PD
tolerates a higher PTD.  
Larry Smith's Gradations in piece powers are measureable, rigorous as any
other way, by, with n the number of piece types and PV piece value:
[PV1/PV2 + PV1/PV3...+ PV1/PVn + PV2/PV3...+PV2/PVn...+PV(n-1)/PVn]/
((n!/(n-2)!)/2)
--now five measureable quantities, three without any records of play
needed at all--absolute standards if one will.

Michael Howe's All-Rooks' 1/64 is beaten by Craig Daniels' Battle
Chieftain's 1/84. There is a chess game in EnclCV, not in CVP, with
pieces on every square to start, but it may have only ten piece types; 
so the upper limit for Piece-type Density is one(1.0)

George is quite correct. While I think I can lay claim to the term 'Power
Density', the concept is Ralph Betza's.

Subject: Game Length:(#M)= Z(Ptd)/(Pd)G; see below.
Ralph Betza frequently submits games-variants not yet played. Randomly
under 'C', under RB: Captain Spalding 'However, my impression is that
the experience of playing the game will not be very Chesslike at all.' 
Castlingmost 'It will probably be fun to play OOmost Chess a time or
two.'  Chatter Chess 'Therefore, I would expect the game to be quite
enjoyable.' Chess with Mixed Pawns 'Although I haven't examined it yet,
I suspect that it will be a very interesting game.' In fact, I would say
descriptions of majority of Betza's 150(?) games give impression of no
test by across-the-board opponent.
Roberto Lavieri says today, 'All of us are mortal people,' about
avoiding Tai Shogi on its 25x25 and Taikuyoku 36x36. Now I go so far
as to say only a favored sample of us will live 33,000 days.(approx.) Take
that optimistic subset. Even if one starts playing Chess at age 3, as
super-Grandmasters are wont to do, that leaves 30,000 day/nights. Now a
good variant surely warrants 10 days; think of that as 3 games played a
day for a total of 30 games over 10 days, or 4 serious games for a total
of 40, or as one will...
But 2000 variants more or less list on CVP and another 2000 such in
Pritchard, and 4000 variants already exceed the allotment. (4000x10=40,000
days, longer than humans can be expected to live.) Therefore, it can help
to have criteria, other than subjective or self-promotional, to evaluate
CVs,even without playing them.  And why a formula too to estimate Game
Length benefits. The included variables are already spelled out in
comments. Where #M is game length in number of moves, Pd Power Density,
Ptd Piece-type Density, Z Board size in squares, G Smith's Piece
Gradient, (#M)  = (Z(Ptd))/((Pd)G) , first approximation showing
correlations.

George, finally, you give a good reason for measures. There are things that
you are not going to be capable to see with theoretical considerations,
but I admit that not ever you, or me, are going to be interested in
feeling the invisible essence of one specific game.

On the contrary, Hetacomb proves effectiveness of relational measures, of
which there will be many more. If Hetacomb is 64 squares, its two piece
types make PTD of 2/64, so low that it tolerates a very high Power
Density, other things equal. While true that PD is useless alone, as
evaluative systems develop (necessary for sheer number of alternatives),
PD stands as important measure subsuming extensive ideas of Ralph Betza
and others on piece values (mobility, forwardness).

It's also possible that some of these numbers have non-linear
relationships. For example Hectacomb with Amazons instead of Queens might
not be that much different in playablity in spite of the high PD
difference (aout 40%)--the PD is huge in either case.

Simiarly, assuming an 8x8 board, a game with 100 piece types might be
scarely less clear than a game with 50 (clarity approaching zero in both
cases), while 10 piece types vs. 5 makes an easily perceptible
difference.

It is also very possible that numerical criteria are best at comparing
games of somewhat similar types, and become more and more 'apples and
oranges' as the game types diverge.

The latter is why I objected to George comparing PTD in Fugue to PTD in
Chess. Compare it to Ultima and Rococo and it doesn't look so bad by
this criteria. It is by this measure less clear than Ultima or Roccoco 
but the difference in not as extreme as the the difference with Chess.

A Comment says that comparing Games is like apples and oranges. The analogy
speaks for itself:  we know that biochemically, Apples and Oranges (trees)
are mostly alike sharing 95%+ of their 30,000 (60,000?) genes,
partly-sequenced basis to compare. So, Chess Variants compare strict
equality or not in board size, pieces, and Power Density, Piece-type
density. piece Gradient, Event Frequency, if one cares to try  other
than entirely subjective approach, and also not to dwell on the extreme values
where theory less effective. Clarity and Depth alone seem too
general unless something measures Clarity-Depth, besides opinion poll.  After all
topic of interest is Game Design not Preferences.

Although Game Theory can be used to quantify real-world events into a Game
Design, a Game Design is not subject exclusively to Game Theory.

Particular aspects of games cannot be quantified as they exist purely on
the emotional level of the players.  For example, how do you evaluate the
potential for frustration or joy?  Each player will react subjectively,
some enjoy frustrating games.

But objective values can be assigned so that a potential developer can
make decisions while designing a game.  But this will not cause a
developer to create a good game.  Their own prejudices will often effect
their design.  Some might never develop a large game while others will not
develop small ones.  And some do not appreciate game with themes, while
others will not try the pure abstract.

George, 

Men and women are about than 2% genetically different--but it's a really
important 2%! Similarly, some people love apples and hate oranges and vice
versa.

I believe that you are making a real contribution to the 'Science of
Chess Variant Design' while denigrating the 'Art of Chess Variant
Design'.

I think we need both. 

Preferences and not the be all and end all of design, but neither are they
irrelevant--what is the point of designing a 'mathematically perfect' CV
that no one wants to play? And aren't clarity/depth and
drama/decisiveness important precisely because they speak to game
players' preferences?

One CV by way example, Isis posted week of 25 March, design analysis:
# squares: 48
# piece types: 5
Piece-type density: 10.4%
Est. piece values: P1, B3, K2, Q4, M8
Initial piece density: 50%
Power density: 68/48 = 1.42  [Orthodox Fide's is about 1.25 or 1.30]
Exchange Gradient: G = 0.425, using range of values here 1,2,3,4,8
[Orthodox Fide is about 0.50, and Isis shows better exchange potential
with lower G]
Ave. Game Length projected:  #Moves = (4(Z)(ptD)/(PD)(1-G)) = 
(4)(48)(0.104)/(1.42)(0.575) = 24 Moves
So, Isis games should not be very long because small Z (board size) and
high potential advantage in exchange (low G).
Other features: River reduces value of Q.
Comments: Obviously, some values are estimates not completely amenable to
analysis.  From description only, comparing different games shows trends
in useful, compact numerical information, able to complement
clearly-written game rules.