Ratings & Comments

Lovecraftian/Chess related story:

http://www.geocities.com/TimesSquare/Hangar/5176/misc/pirc01.htm

Wait, there's more.

Statements:

A Leaf Pile is subject to the effects of a Basilisk, and a petrified Leaf
Pile cannot engulf anything. 

A petrified Leaf Pile can still engulf things that are pushed onto it, and
it can still engulf things it is pushed onto. 

Conclusion:

Second statement is true, and more fun.

Corollary:

A Go Away pushing a petrified Leaf Pile around can vacuum up all sorts of
impedimenta.


Statement:

Any mobile piece except a Zombie within two squares of a Ghast must flee
the Ghast, and no mobile piece except a Zombie may move of its own accord
to a Ghast Square; the squares within the Ghast's range are called Ghast
Squares. 

Clarification requested:

If several pieces are under compulsion to flee a Ghast, but the Ghast moves
off before the compulsions can all be satisfied, the compulsions no longer
exist if the compelled pieces are no longer on Ghast squares.

Additional statements:

When you are under compulsion, you may make any move which removes the
compulsion, but if you cannot satisfy the compulsion of at least one piece,
you lose. 

The Human moves one square sideways, or one square straight forward, or one
square diagonally forward, but only to an empty non-ichorous square. 

Hypothetical situation:

Alabaster Human on f5, Obsidian Ghast moves to f6, creating compulsion for
human to flee.  Assume there is no other Alabaster piece under compulsion
this move, and no saving move is possible.  The Human can only move to e5,
e6, g5, or g6.  These squares are still adjacent to the Obsidian Ghast.  Is
this a win for Obsidian due to stalemate by compulsion?

I am reviewing the document http://www.panix.com/~gnohmon/nemofull.html and
I need to know if I have interpreted it correctly.


Statements:

[A Leaf Pile] can move onto a non-ichorous non-Ghast square which contains
a Mummy and at least one other piece.

When a Leaf Pile makes its first voluntary move after engulfing something,
it leaves behind a single Mummy; notice that this means no Mummy is left
behind when a Leaf Pile that is digesting something is pushed.

Conclusion:

If a Leaf Pile engulfs a multiple occupancy square including a Mummy, and
then is pushed, there is no Mummy remaining on that square.


Statement:

If the ichor will evaporate after you make your move but before your
opponent moves, you can ignore it.

Conclusion:

That ichor actually lasts nine plies, not five moves.


There will be more questions.

''values of Nemoroth pieces' -- quite impossible.' --- I was just joking
here.  I actually can't imagine how one could assign values, considering
all the interactions.  In regular chess, the only interaction is capture.

'Likewise Nemoroth with Different Armies. The various non-capture effects
have values that are imho impossible to estimate numerically.'  --- True,
but it is possible to imagine other interactions that might be interesting.
 Several spring to mind (nature abhors a vacuum) but they could be as
simple as ichor with different effects.  One could even handicap by
allowing the ichor of each player to dissipate at different rates.

'The useful Go Away has a value that depends entirely on what it can push,
just for one example.' --- A trivially true statement.  Ceteris paribus, a 
Knight that can capture a Queen is worth more than one that can capture a
Bishop.  I consider values to be a statistical guide, not a received truth,
fun as they may be to study and play with.  (Of course, I stink as a chess
player, so what's my opinion worth?)

It is likely that I may soon be playing Nemoroth against another human via
email.  We will be sure to post our observations.

As a sidebar, there is really no assurance that any entity with which one
communicates via email alone is actually human.  We could all be alien
anthropologists, who, thinking we are studying humans, are studying each
other.  The resulting theses would be feces.

It would seem that TERROR CHESS is identical to THE SULTAN'S GAME

http://www.chessvariants.com/large.dir/sultan.html

with the exception that the positions of the marshall and
cardinal are reversed. THE SULTAN'S GAME pre-dates TERROR CHESS
on this web site by three years. 

Nevertheless I still propose that my idea above for a variant
of chess between different armies would be intriguing. 

Oh and I would suggest variants with and alternately without
the 'Battle Move' when programming the ZRF for the above proposed
new variant. Players can decide for themselves which they prefer
to use.

How about the Tripunch Terrors, another army to compete against the
Fabulous FIDEs? :-) King and Pawns are standard. The rest of the pieces are
from Tripunch Chess, but they flip as pieces do in Weakest Chess- these
pieces have capturing and non-capturing modes, and can flip (as a move)
from one to the other. To keep the pawn line defended, the Reapers and
Combine start in capturing mode; the others start in non-capturing mode.

If flipping pieces are half as strong as regular pieces (and that seems to
be the estimate in the Weakest Chess article), then the Tripunch Terrors
are about 4 Pawns too strong as described. So we remove the ability to move
as a Bishop from the Harvesters and Combine... and then we should have a
game. So here's the official lineup: the Flipping Reaper, the Flipping
Nightrider, the Flipping Aanca, and the Flipping... the Flipping...

Give me some time. I'll come up with a name for that last one. :-D

Examining this site and The Encyclopedia of Chess Variants, I find the following Ultima Variants:

• Bogart's Chess, which replaces a Chameleon and a Long Leaper with an Absorber (which picks up the capture method of each piece it captures) and a Golem, which only moves two but has to be captured twice (this was the inspiration for Golem Chess).
• Renaissance, which is played on a 9x9 board, and adds a Pusher, a Puller, a Resurrector, and a Bomb, and has a limited form of drops of captured pieces (using the Resurrector).
• Stupid, where each piece can move like an Ultima piece and an Orthochess piece.
• Ulti-Matem, except the Pawns have the moves of the Orthochess pieces they would be standing in front of, except for the King's Pawn which is a Double Knight Pawn which makes two Knight's moves in a row in any pattern.
• Ultimate Ultima which you described in this comment system here.
• Unorthodox Ultima, in which a Long Leaper and a Chameleon are replaced by a Neutalizer (which removes the ability to capture of adjacent pieces) and a Repeller which forces an opposing piece moved next to move as far away as possible.

I still think I'm right, but I'm not as sure anymore...

I think I'm not fully applying the two-path for the f4/d4 - getting the
full two path bonus twice would be 0.91 * 0.7 * 0.91 = 0.57967, just
getting it once is 0.91 * 0.7 * 0.7 = 0.4459, and my method is in my first
comment as 0.51793.  So it is between the values of one and two two-path
bonuses.

Mostly I think it is right because the verbal description seems to be
right, and you agreed with my math on turning that description into a
formula.  I think that formula is properly figuring out how much of a
two-path bonus to give.

Does this seem reasonable to you?

It would seem that I am not the first person to create a CV on an
11 by 11 board. (see my SPINAL TAP CHESS) It  would be interesting
to play a game of TERROR CHESS (for WHITE) vs. SPINAL TAP CHESS
(for BLACK) as a game of Chess Between Different Armies !!!

PETER ARONSON I challenge you to create a ZRF for such a game
IMMEDIATELY!! :-) I could then challenge Brian Wong to a game by
email! (if anyone has his address!) (mine is DavidNYJfan@hotmail.com)

though I suspect that TERROR CHESS has the more powerful army!
Then again who can say for sure?

 
                     TERROR CHESS vs.  SPINAL TAP CHESS

A game of Chess Between Different Armies created by
David Short with thanks to Brian Wong.


                 a   b   c   d   e   f   g   h   i   j   k
               +---+---+---+---+---+---+---+---+---+---+---+
           11  |*R*|*S*|*W*|*V*|*Q*|*K*|*M*|*W*|*V*|*S*|*R*| 11
               +---+---+---+---+---+---+---+---+---+---+---+
           10  |*P*|*P*|*P*|*P*|*Cr|*Cr|*Cr|*P*|*P*|*P*|*P*| 10
               +---+---+---+---+---+---+---+---+---+---+---+
            9  |   |:::|   |:::|   |:::|   |:::|   |:::|   |  9
               +---+---+---+---+---+---+---+---+---+---+---+
            8  |:::|   |:::|   |:::|   |:::|   |:::|   |:::|  8
               +---+---+---+---+---+---+---+---+---+---+---+
            7  |   |:::|   |:::|   |:::|   |:::|   |:::|   |  7
               +---+---+---+---+---+---+---+---+---+---+---+
            6  |:::|   |:::|   |:::|   |:::|   |:::|   |:::|  6
               +---+---+---+---+---+---+---+---+---+---+---+
            5  |   |:::|   |:::|   |:::|   |:::|   |:::|   |  5
               +---+---+---+---+---+---+---+---+---+---+---+
            4  |:::|   |:::|   |:::|   |:::|   |:::|   |:::|  4
               +---+---+---+---+---+---+---+---+---+---+---+
            3  |   |:::|   |:::|   |:::|   |:::|   |:::|   |  3
               +---+---+---+---+---+---+---+---+---+---+---+
            2  |:P:| P |:P:| P |:P:| P |:P:| P |:P:| P |:P:|  2
               +---+---+---+---+---+---+---+---+---+---+---+
            1  | R |:B:| N |:C:| A |:K:| Q |:Mr| B |:N:| R |  1
               +---+---+---+---+---+---+---+---+---+---+---+
                 a   b   c   d   e   f   g   h   i   j   k


Diagram index:

R- ROOK
B- BISHOP
N- KNIGHT
C- CARDINAL
A- AMAZON
K- KING
Q- QUEEN
Mr- MARSHALL
P- PAWN


Cr- CRAB
S- SQUIRE
V- VICEROY
W- WIZARD
M- MINISTER


Pawns move 1, 2, or 3 squares on their initial move and the en
passant rule is the same as it is in OMEGACHESS.
Each side may castle as its game's rules dictate.

Thanks for cooking my problem. I never claimed to be a good composer.

Now, if you'll pardon me, I'll go sit in a corner and cry.

Now that this comments page is up, I'd like to ask the regular 
readers of www.chessvariants.com to comment on Doublechess.
Doublechess is the first chess variant which I invented, and I
think it is my best one of all the ones I have created. It is my
pride and joy. At the time I submitted it to this site I had learned
that I was just a few months too late to enter it into the Large
Variants contest that was being held at the time. What a pity!
I feel that Doublechess would have been a very strong contender,
but by the time I first learned of this site's existence, the 
deadline for submissions for the contest had passed.

Doublechess' page on this site is unique in many ways. You
won't find too many other games on this site which have sample
games linked to it, and one of the games is annotated in detail.
(The link to my 'Doublechess web site' is no longer valid.)
Doublechess can be played by email on Richard's Play By Email
server, and I frequently conduct Doublechess tournaments on PBM.
The next one may be beginning in a few months and I will post
an announcement about it here (as I did recently for the forthcoming
Omegachess tournament which I will be running on PBM as well) when
I am ready to begin it.

Doublechess is a very simple variant. Simply lay two 8 by 8 chess
boards side by side. Use two chess sets, and replace the second
set of kings with a third set of queens. (if one does not have a
third set of chess queen pieces handy, substitutes can be used until
they are captured. Coins work well, for instance, a penny for a
white queen and a nickel for a black queen.) Set up the first army
of pieces in the traditional setup (RBNQKBRN) in files E to L
and the second army out in the wings (RBNQ, QBNR) in files A to D
and M to P. 

You will notice a few interesting strategic points about Doublechess.
Opposing bishops start along the same diagonals as each other,
often promting them to be quickly traded off if the opportunity
presents itself. If they avoid an early exchange, bishops of like
color can double themselves along the same diagonal to form a battery
in much the same way that one might double their rooks along the same
file in chess. Notice that whereas white begins with two dark squared
bishops on the left side of the board, or queenside (in Doublechess
terminology,
the 'queenside' refers to files A to H, and 'kingside' refers to
files I to P, mimicking the same sides of the boards which these
terms refer to in regular chess), and black has two light squared
bishops on the queenside. Likewise, white has two light squared
bishops to start the game on the kingside, and black has two dark
squared bishops on each side. Each side can try to exploit the other's
weaknesses on light or dark squares on each half of the board.

The way the board is set up, as players begin to develop their pieces
and pawns, the pieces tend to engage each other on each half of the
board in about the same amount of time as they do in regular chess.
In the middle game it is often the case where pieces will be interacting
with each other and threatening each other on each half of the board
completely independent from what is going on on the other side of the
board. In some ways then, Doublechess is like playing two games in one,
though one really needs to look at the board as a whole to truly
understand and appreciate the game.

There are other strategic differences between Doublechess and regular
chess which make my variant exciting and unique. It is more common
to sacrifice material for attack in Doublechess than it is in regular
chess, since one has so much material at one's disposal to attack with.
In Doublechess then, obviously king safety becomes extremely important.
Thus another axiom of dc is that it is quite possible to win despite
a material disadvantage, more often than one can overcome such a
deficit in regular chess. As long as one has enough pieces to launch
an attack, they can make things interesting.

I should also point out that the one rule that is unique and 
distinctive to Doublechess is the castling rule (see dc's page for
full explanation of the castling rule), and the pros and cons of
long castling vs. short castling can be long debated. It's another
twist to the game which makes it interesting. 

One advantage that my variant has over other CVs is that it only 
uses orthodox pieces, so it is very easy to learn how to play.
Perhaps more than any other CV, Doublechess has the 'feel' of regular
chess. There is a ZRF file available for download at the bottom of
Doublechess' page. I urge everyone who has not played it yet who owns
ZILLIONS OF GAMES to download Doublechess and try it out.
I welcome comments from everyone, pro or con, as to how they would
rate Doublechess as a chess variant. What are this variants'
strengths and weaknesses? Finally I would say that, although I 
realize I am very biased in the matter ;-)  I feel that Doublechess
is such an excellent variant that it deserves consideration as one
of this site's 'Recognized Chess Variants'  and as inventor of this
game I am necessarily disqualified from nominating it to that position.
Might someone else who has an equal appreciation for this game take
up the gauntlet and nominate it along with an eloquent essay on my
game's merits?

'Why is it that when I encounter an Ultima variant, it inevitably seems
more complex than Ultima, not less?'

What defines an Ultima variant? Is it possible that no game simpler than
Ultima fits your definition of 'an Ultima variant'?

At some unspecified time (1970s most likely) I collaborated with John
Ishkanian on an Ultima variant named 'Ultimate Ultima'; I still have a copy
and have seen it within the last few weeks but it would take me years to
find it again (Phil Cohen probably still has a copy and can find it
quickly). The premise was based on my idea that the duration of a game
depends on the ratio of power to space; and we tried to create a playable
game with so much power to space that games would rarely last longer than 4
moves -- this would be a great game for playing at lightspeed radio against
an opponent in another star system!

Four pages of dense and terse single-spaced typewriter text with characters
out to the narrowest margins. Rules not all that complex, but interactions
beyond belief. The Carrier (is this the right name?) could move like Q, but
at each single step could pick up or drop pieces; and if you drop a Mixer
it can rearrange all adjacent pieces (all of this happening within the
context of the single=move multi-square move of the Carrier) and by
rearranging a Transporter it could cause pieces to teleport to other
squares, and if you teleported a Converter it could make enemy pieces yours
and so on.)

We spent probably 3 months hashing out the rules and then played 2 games,
which lasted maybe 5 plies between them (I won both).

That's my idea of complex.

Compared to that, the Game of Nemoroth is so simple!

'But crazyhouse is better' -- interesting comment.

What you call Crazyhouse is, I think, the 'Double Bughouse chess' to which
the mimeographed magazine 'New England Double Bughouse Chess' was devoted
in the 1970s. (That's how people communicated then. Inconvenient, slow, and
expensive compared to the internet, but would you believe it people
communicated with each other even before there was an internet! What a
mindblowing idea, no?)

Funny thing is, your comment makes me think that the last time I played
that game you hadn't been born yet. Stalling was a bad consequence of the
rules as they were then; have they fixed this?

If you say it's better, you should say why you think it's better. By
providing reasons, you might get people to respond with counter arguments,
and once in a while they would convince you you were wrong and once in a
while you would convince them and most of the time you'd have fun arguing
but you wouldn't get anywhere. Welcome to the internet.

Does the game you call crazyhouse require 4 players? Did you know that in
the 1970s I described how you could play it with 2 teams of 100 players?

Thank you for finding my error. I'm wrong, so I take back my nyaah nyaaah.
But you're also wrong.

When you're really stuck with probabilities, you can use the laborious
case-by-case analysis. With a zFF going from e1 to e5, if e3 is occupied it
can't get there and f4/d4 deserves no two-path bonus. If e3 empty and both
f2/d2 occupied, no twopath. If e3 empty and one of f2/d2 occupied, no
two-path. If e3 empty and both f2/d2 empty, I was in error, twopath
applies. I haven't worked out the correct number, but it's higher than
mine, lower than yours, closer to mine than yours. You applied twopath in
too many of these cases.

I'm not sure to write this in a more general manner. (for example, zFF
going from e1 to e9 on a larger board).

I haven't worked out the number the laborious way, pending your agreement
to this.

You found an error, I think, but I think you were also wrong. 

I know you'll reply!

'rarely seen as much chatter' -- it's a combination of two things, I think;
first the story is pretty good. You must understand that after I wrote it,
I also read it, and even I was affected by it. The idea of the ancient
Lovecraftian city that existed before the world was finished being built
kinda grabs me. And the details that make it real (by the way, the reason
that Nemoroth was destroyed when Luna was floated up into the sky after
being built in its harbor was that the project was given to the lowest
bidder) -- well,when I wrote it, in the heat of the moment I thought it was
merely corroborative detail intended to add artistic verisimilitude to an
otherwise bald and unconvincing narrative, but when I read it, it sounded
so suspension-of-disbeliefable and I could picture the city and the harbor
and the Moon and the little boats carrying pieces of craters to the work
site, and golly gee gosh how amazing.

The second thing is that the game itself is pretty interesting. Although I
was so caught up in the story that I really did a bad job of describing the
game, it's non-trivial and it's very different (in terms of how it feels to
play it) than most chesslike or ultimalike games.

This *will* cause chatter, even in the most silent of times.

Since The Game of Nemoroth came out shortly after I had said strongly that
there wasn't enough chatter, well, what would you expect. :-)

'values of Nemoroth pieces' -- quite impossible. Likewise Nemoroth with
Different Armies. The various non-capture effects have values that are imho
impossible to estimate numerically. The useful Go Away has a value that
depends entirely on what it can push, just for one example. 

In practice, I think the Zombie is most valuable, and the second tier
contains the Go Away, the Basilisk, and the Leaf Pile. The Leaf Pile is so
easy to use; an advanced Basilisk, even if it gets petrified (but you gotta
calculate if the foe can push a Leaf Pile onto it!) can be crippling, and
the Go Away transforms positions completely.

But even the humble Human is strong. Leaving one's Basilisk at home invites
the Humand to advance and petrify themselves in blocking positions. 

The Ghast is so powerful that it is outside the range of values. However, I
have not yet played a game against myself where I captured a Ghast, so in
effect the Ghast is always neutralized by the enemy Ghast. Pushing a statue
to d4 or d5 neutralizes the enemy Ghast and allows you to reposition from
b6 to f6; this happened once and was very strong. All in all, I like the
way the game works.

I am attempting to locate one variant from the Sung Dynasty China (0960),
Which has an extended king row, forward of which are two rows of pawns,
forward are two major power pieces  [ either named lance or archer] ,
forward of the archer is yet another row of pawns. Any info you might
have
on this game would be greatly appreciated.
			Thank You

Ultima is very interesting, I play it with Zillions (not strong).
However,
I tried to find game annotations and I could not find any. It would be
nice
if you could give some games and some open sources. I wonder if there
exists opening and endgame theory.

Gert Greeuw
grw@geodelft.nl

Hi,

I have worked out a slightly different method of setting up Fischer random
chess positions with a single six-sided die.   It's fairly easy to
memorizem because it follows logically from the positional rules of the
game.   As far as I can tell it will create all possible positions. Here it
is:

All die rolls are counted from the left side of the board from white's
point of view and apply to remaining empty and 'legal' squares only.

Because the king must be between both rooks, it can only occupy the central
six squares on each side.  Roll a die and place the king on one of the six
'central' squares.

Now place the rooks.   Roll a die for the left rook.  If the number exceeds
the number of squares on the left side of the king, roll again.    Repeat
for the right rook.  If there is only one square to the right or left of
the king, skip the rolls and simply place the rook.

Now place the Bishops.   Place the first bishop based on a die roll.   If
the roll value exceeds the number of remaining squares, roll again.   Place
the second bishop in a similar manner counting only the available squares
of the opposite color of the already placed bishop.

Place the queen with a die roll.  If the die number is 4-6 then subtract 3
from its value (to minimize the number of rolls necessary.)

Place the two knights on the last two squares.

I have yet to study this method in detail to determine if it favors certain
positions.


A modification of the die roll procedure to minimize re-rolls is as
follows:   If there are 2-3 'legal' squares for the rooks or the second
bishop take the remainder of the die in the 'modula' of the number of
remaining squares.  For example, if there are two legal squares for the
left rook, and one rolls a 5, one counts this as a '1', as 1 is the
remainder when one divides 5 by 2.  If the roll had been a '4' one would
count this as a '2'.   In the case of 3 empty squares, one a '5' would
count as a '2'.  A '6' would count as a '3' and a '4' would count  as a '1'
(as in the queen roll, which will always have 3).   

This method will not work without bias when there are 4-6 legal squares
remaining, and re-rolls must be employed.  However, statistically speaking,
fewer rolls will be necessary in such a case anyway.   

It is possible, though highly improbable, that one might require a very
large number of rolls to finally 'nail down' a position for the rooks and
bishops.  But once they are placed, only 1 roll remains.

What do you think?

Brad Hoehne- Columbus, Ohio.

I have rarely seen so much chatter as for this game. (N.B. there is
significant commentary on Nemoroth in the Yellow Journalism thread.)

A couple of points:

Is Nemoroth a chess variant?  If gnohmon says it is, who am I to gainsay
him?  I am an 'inclusionist' when it comes to chess variants, anyway.  It
actually seems more like an Amazons variant, and there are other more
chess-like games that make use of the 'shrinking board' mechanism, but what
the heck.  (Bob Abbott, who invented Ultima, did not think it was chess,
because it did not use replacement captures.  He was an 'exclusionist'.)

When Nemoroth is refined, and the rules settle down, may we expect pages on
'The Value of the Nemoroth Pieces' and 'Nemoroth with Different Armies'? 
Should we reserve the name www.nemorothvariants.com?

If interest remains high, how about the CVP sponsor a contest in Nemoroth
problem composition?

>My verbal description is saying that the choice between the two paths is
made
>only once, and therefore the two-path probability correction should be
made 
>only once in the calculation

This works fine if the first step forces you to make a choice, but
sometimes both directions are unblocked after the first step, so you
still
have a choice of which way to go when you get to the third step.  A piece
that moves 2 squares as a Crooked Bishop then started moving as a Rook
would be easier to block than a Crooked Bishop is, as it would only get
the
two-path correction once.  Likewise, a piece that made bigger zig-zags,
going to c3 or g3 instead of e3, would get the higher number.

Nyaah, nyaah! :)

'First off, it is quite interesting to instead of picking a magic number
as
the chance of a square being empty, calculate the value for everything
between 32 pieces on the board and 3 pieces on the board.  Currently I'm
then just averaging all the numbers,'

I've done that, too. The problem is, if the only reason you accept the
results is because they are similar to the results given by the 
magic number, then the results have no special validity, they mean
nothing more than the magic results. So why add the extra computational
burden?

If, on the other hand, you had a sound and convincing theory of why 
averaging the results was correct, that would be a different story.

'This concept seems to be directly related to distance.' Actually, I
think
I'd call it 'speed'. I'm pretty sure that I've played with those numbers
but gave up because I couldn't figure out what to do with them. 
Maybe you can; I encourage you to try.

>>   Would 0.91 times 0.7 times 0.7 be correct? Yes, this is the answer
>>   to 'it can move there if either d2 or f2 is empty AND e3 is empty
>>   AND the corresponding square (d4 if d2, or f4 if f2) is empty'.

>  This isn't right (I think). It can move there if e3 is empty and
>  either d2 and d4 are empty or f2 and f4 are empty. So that's 0.7 * (1
>  - (1 - 0.49) * (1 - 0.49) ), which works out to 0.51793, as compared
>  to 0.4459. I think the generalized equation, where X is the (always
>  even) number of squares moved, would be 0.7^(X/2 - 1) * (1 - (1 -
>  0.7^(X/2))^2)

(We're talking about the probability of the zFF being able to make a four
step 
move, for example from e1 to e5.)

My verbal description is saying that the choice between the two paths 
is made only once, and therefore the two-path probability correction should

be made only once in the calculation; this gives me a simpler formula 
for doing the calc by hand. Upon review I am even more convinced that
this is correct, but in order to feel perfectly secure I must find 
your error. 

You are saying 'if e3 empty and ((d2 empty and d4 empty) or (f2 empty and
f4 empty))'. The verbal description is clearly correct, although it
makes things more complicated when you extend to 4 step and 6 step moves.
The probability that d2 empty and d4 empty is 0.49; the probability that
p or q is (1 - ((1 - p) * (1 - q))). Ouch, that's convincing.

Wouldn't another fair way of stating it be 
'(d2 empty and e3 empty and d4 empty) or (f2 and e3 and f4)'?
But that gives me a completely different number, even higher.

Aha! '(d2 and e3 and d4) and (f2 and e3 and f4)' is incorrect because 
in effect it applies the two-path correction to e3, but e3 non-empty
blocks both paths!

But then by the same token, your 'e3 and ((d2 and d4) or (f2 and f4))'
must apply the two-path correction twice!! 

I'm right, you're wrong. Nyaah, nyaah! (If I were a licensed
mathematician
I would be able to say Q.E.D., but since I'm not I can only say nyaah
nyaah.)

That was difficult. My head hurts.

'Yellow is the color of mystery in Italy' is an arcane little i18n joke. A
paperback pulp mystery story is colloquially called 'un giallo' (a yellow)
because of its yellow cover. Even the publisher Mondadori uses the term, as
its series is titled 'Il Giallo Mondadori'. Number 1331, 'Quella Bomba di
Nero Wolfe' (Please Pass the Guilt) was published in 1974 and it is weekly,
therefore the series began around 1948; but it also says 'new series', so
the usage of a yellow in this sense may be older.

This is *not* the sort of color usage that can get you into i18n trouble,
though it sounds like the typical 'White is the color of death in China'
warning, and that's the little joke.

For true madness and horror, you should look into the methods of
internationalization that were used in the days before the current
standards existed....

Various and sundry ideas about calculating the value of chess pieces.

First off, it is quite interesting to instead of picking a magic number as
the chance of a square being empty, calculate the value for everything
between 32 pieces on the board and 3 pieces on the board.  Currently I'm
then just averaging all the numbers, and it gives me numbers slightly
higher than using 0.7 as the magic number (for Runners - Knights and other
single step pieces are of course the same).  One advantage of it is that it
becomes easier to adjust to other starting setups - for Grand Chess I can
calculate everything between 40 pieces on the board and 3, and it should
work.  With a magic number I'd have to guess what the new value should be,
as it would probably be higher since the board starts emptier.  One
disadvantage is that I have no idea whether or not the numbers suck. :) 
Interesting embellishments could be added - social and anti-social
characteristics could modify the values before they are averaged, and
graphs of the values would be interesting.  It would be interesting to
compare the official armies from Chess with Different Armies at the final
average and at each particular value.  It might be possible to do something
besides averaging based on the shape of the graph - the simplest idea would
be if a piece declines in power, subtract a little from it's value but
ignore the ending part, assuming that it will be traded off before the
endgame.

Secondly, I'm not sure what to do with the numbers, but it is interesting
to calculate the average number of moves it takes a piece to get from one
square to another, by putting the piece on each square in turn and then
calculate the number of moves it takes to get for there to every other
square.  So for example a Rook (regardless of it's position on the board)
can get to 15 squares in 1 move, 48 squares in 2 moves, and 1 square in 0
move (which I included for simplicity, but which should probably be left
out) so the average would be 1.75.  I've got some old numbers for this on
my computer which are probably accurate, but I no longer know how I got
them.   Here's a sampling:

Knight: 2.83
Bishop: 1.66 (can't get to half the squares)
Rook: 1.75
Queen: 1.61
King: 3.69
Wazir: 5.25
Ferz: 3.65 (can't get to half the squares)

This concept seems to be directly related to distance.  Perhaps some method
of weighting the squares could make it account for forwardness as well.

Finally, on the value of Kings.  They are generally considered to have
infinite value, as losing them costs you the game.  But what if you assume
that the standard method is to lose when you have lost all your pieces, and
that kings have the special disadvantage that losing it loses you the game?
 I first assumed this would make the value fairly negative, but preliminary
testing in Zillions seems to indicate it is somewhere around zero.  If it
is zero, that would be very nifty, but I'll leave it to someone much better
than me at chess to figure out it's true value.

I'm not really a mathematician or stastician - I merely enjoy math and am
somewhat talented at it.

I have read your general theory of piece values - in fact, I think I've
read it roughly ten times, starting back when you were still adding to it. 
I'm afraid I can't tell you how accurate it is, as I feel very much the
midget when it comes to playing chess. (I think I may have read your theory
of piece values more often than I have played chess in the last five
years.)

I've meant to e-mail you with various comments about it for many years now,
but I never got around to it.  This handy comment system makes it easy
enough that I'll finally stop procrastinating, though.  I'll start some new
threads, I think.

I hesitate to mention it because I'm currently working on the revision
(which should suck less), but Fantasy Grand Chess is my chess variant with
different armies.  I didn't analyze things very thoroughly (mostly I just
guessed at what looked right), and mostly assumed values would be the same
on an 8x8 board as 10x10, so it needs work.  (Which is what I'm currently
doing.)  I'm also making changes to help the theme, and dropping it down to
a more manageable four armies.

If there are any other numbers in particular you want me to check, let me
know.  I'm currently calculating for a Crooked Rook, which should be simple
after the Bishop, and then I'm going to do mRcpR and RcpR.

Excellent for the feedback, that is.

You have no idea how hungry I have been for so many years to find a
mathematician or statistician who would be in the mood to criticize my
numbers or my methods and point out the errors that must be there.

With all due respect, I give you this instant reply, but I do not examine
the specifics of what you said nor do I respond to them. I am in the midst
of other things and not in condition to reply.

I give you my double-barrelled platinum promise that the specific numeric
algorithmic probabilistic things you said will be closely and extensively
examined by me and that a serious reply will be forthcoming.

Meanwhile, literary criticism of your reply suggests that you agree with my
basic method but merely cavil at a few of my specific applications. Is this
right? If so, I celebrate. If not, I cerebrate.

If you haven't read my general 'theory of piece values', please please do
and if you can (though I hope you can't) tell me I'm full of it.

The general public here believes in my numbers more than I believe in my
numbers. Perhaps you can have the deciding vote, since paolo has declined
to speak up.

Did you know that a giant standing on a midget's shoulders can see further?
Well, in doing this math stuff about piece values let me tell you I've
always felt like a midget. But right now I can only write silly answers. I
just spent a few hours writing serious. The promises I made in previous
paragraphs are serious, though.