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Joe Joyce wrote on Mon, Oct 12, 2009 03:45 AM UTC:
Recently, in another thread, Sam Trenholme made the statements found below.
He argues one side of the question very well, saying all the new simple
pieces are used up, and only complicated pieces are left. 

How do you define a 'simple piece', anyhow? Hasn't anything in the last
2 years, say, counted as a simple piece?

2009-10-09	Sam Trenholme Verified as Sam Trenholme	
'What I see ... is that all of the simple pieces a Chess-like game can
have are already invented, and that we’re having to come up with some
pretty convoluted moves to come up with new piece types. 
The simple Chess pieces seem to be:
    * Simple leapers (Such as the knight and the king) I wrote, a couple
of years ago, an essay describing 31 such leapers
    * Simple sliders, such as rooks, bishops, and queens. There are ... 16
symmetrical sliders that can traverse the entire board if the board is a
bounded square; there is also the bishop and Shogi’s lance

It’s possible, of course, to combine leapers and sliders (Can you say
“Capablanca Chess”?), but the only combined leapers + sliders in a
national game are Shogi’s promoted rooks and bishops. There are also
“riders”, sliders whose 1-move “atom” is not to an adjacent square;
the knightrider is the most famous piece of this type.

Once we move past these simple pieces, things get complicated and the
learning curve goes up. One relatively simple piece is a piece that
captures differently than it moves; a piece that, say, moves like a knight
or captures like a bishop.

Betza covered the “crooked rook”, “crooked bishop”, and
“rose”—sliders which change their direction every square they slide.

Chinese Chess, of course, has the “Cannon”, which has inspired all
kinds of pieces that leap before moving or capturing (or a combination
thereof). Speaking of leaping pieces, I’m surprised no one has recently
discussed having a checker’s king in Chess: A piece that moves like a
Ferz, but captures by jumping over an adjacent piece, and can (optionally)
capture multiple times in its move. We can, of course, have a wazir
(horizontal and vertical) form of this piece, or combine it with any other
chess piece.

So, yeah, it looks like pretty much any kind of piece chess can have with
a simple move has been discussed here, so we’re moving on to complicated
pieces that don’t seem very intuitive to me.'

Jose Carrillo wrote on Mon, Oct 12, 2009 03:19 PM UTC:
I consider my Ajax army to be 'simple' in nature.

Just add the moves required to give pieces a Courier Man (Commoner) reach, and you get very interesting 'new traditional' pieces.

These extra 'adopted' moves are non-capturing to not upset some of the tactics (i.e. pins) we are used to and to allow the King a fair chance to defend itself against minor pieces in endgames.

The Ajax Chess complex includes: Ajax Chess (10x10), Ajax Random Chess (8x8), Ajax Modern Random Chess (9x9) and Ajax-Capablanca Chess (10x8)

Sam Trenholme wrote on Mon, Oct 12, 2009 04:44 PM UTC:
Yeah, I think I put the gauntlet down. Can we design new types of pieces whose move is simple?

This is a question that is, by nature, a subjective impression. One person’s simple is another person’s complicated.

OK, let me try to prove myself wrong. I think one simple type of piece is a piece occasionally seen in historical Chess variants:

  • The “hook mover” in Dai-Dai Shogi (and some of the other really huge Shogi variants) There are two versions of this hook mover; one that moves like a rook, then can, at any point, bend 90 degrees and continue its movement; the piece can go to any square on an empty board. There is also the “bishop” form of the hook mover that can go to any square of its color on an empty board.

    We don’t have the complete rules of Dai-Dai Shogi here, but the Wikipedia is your friend; you can also play this game in Zillions (yes, Jeff Mallett deserves your $25 to register the game if you haven’t done so already)

  • The “griffion” in Grande Acedrex. This piece moves out one square diagonally, then turns 45 degrees and moves any number of squares like a rook. A picture is worth a thousand words:
    . . | . | . .
    . . | . | . .
    - - X . X - - 
    . . . # . . .
    - - X . X - -
    . . | . | . .
    . . | . | . .
    ('#' is the piece, and it can move to any square marked 'X', '-', or '|'; the lines are used to show the piece moves like rook in these directions)

    This is, if you will, a limited subset of a hook mover; unlike a Dai-Dai Shogi hook mover, its hook rotation is 45 degrees, not 90 degrees, and it can only make the hook after moving precisely one square

So, based on these two pieces, lets make some hook mover that aren’t three times as powerful as FIDE’s queen:
. . . \ . / . . .
. . . . X . . . .
. . . . | . . . .
\ . . . | . . . /
. X - - # - - X .
/ . . . | . . . \
. . . . | . . . .
. . . . X . . . .
. . . / . \ . . . 
This hook mover is a variation on the Griffion; instead of starting with a diagonal move, it starts with an orthogonal move. If the piece moves more than three squares, it must bend 45 degrees on the third square it moves to, then move outward diagonally.

Here is the same piece’s move if it’s on the edge of an 8x8 board:

. . . . . . / .
. . . . . / . .
\ . . . / . . .
. \ . / . . . .
. . X . . . . .
. . | . . . . / 
. . | . . . / .
- - # - - X . .
Like other sliders, this piece can have its move blocked.

How valuable is this piece? Somewhere between a rook and queen in value.

There’s also the diagonal version of this piece:

. | . . . . . | .
- X . . . . . X -
. . \ . . . / . .
. . . \ . / . . .
. . . . # . . . .
. . . / . \ . . .
. . / . . . \ . .
- X . . . . . X -
. | . . . . . | .
Which is probably a little less valuable than the orthogonal version shown above.

Is this a simple piece? I’m not entirely sure. When I first saw the Griffion in, as I recall, New Rules For Classic Games (or was it Murray’s A History of Chess) I was very confused by this piece, but today it makes perfect sense to me.

We can have versions of this piece that bends after moving only square (the Griffion in the diagonal form), after two squares, after four squares, etc. We can have a version of this piece that bends 90 degrees instead of 45 degrees (the diagonal version of this piece is colorbound). We can limit the range of the piece. Etc.

Jose: Since you mentioned Ajax Capablanca Chess as a game with simple moves (add a non-capturing king move to the pieces), may I suggest Ajax Schoolbook. I should add that as a variant to the Zillions preset for Schoolbook. I really like the bishop + non-capturing Wazir piece; it nicely solves all of the headaches one has coming up with a board setup for colorbound pieces.

Jose Carrillo wrote on Tue, Oct 13, 2009 02:44 AM UTC:
Sam Trenholme: (on the Ajax Bishop)

>I really like the bishop + non-capturing Wazir piece; it nicely solves 
>all of the headaches one has coming up with a board setup for colorbound
I like to keep things simple! ;-)

H. G. Muller wrote on Tue, Oct 13, 2009 05:53 AM UTC:
I tested the Adjutant (BDD), and it is _strong_. A pair of Adjutants beat a
pair of Rooks by 82% when I program its value (slightly) above that of a
Rook, and by 72% when I program it below a Rook. (No doubt because it
starts pursuing trading them for Rooks, which is a waste.) Only 160-190
games so far, but that should have a standard error of ~3%, so all very
significant. An Adjutant might on thus be worth about R+P.

The fact that it is a color-bound piece makes the Adjutant quite
interesting: there should be a pair bonus involved, and because the
Adjutant is quite strong, the pair bonus should also be large. This
effectively makes the first Adjutant much more valuable than the second.
(This explains why building in the drive to trade it for Rook is unusually
detrimental.) So it could be that Adjutant + pair bonus is even larger than R+P, while R < solitary Adjutant < R+P.

It would also be of funamental interest to see how pair bonuses behave between different color-bound pieces. E.g. when you have an Adjutant on the light squares, it stands to reason that a Bishop on the dark squares would be worth more than one that is also confined to the light squares. But would the difference be larger or bigger than when the Adjutant would have been another Bishop?

Too bad Fairy-Max has no pair-awareness, making it a poor tool for answering such questions. Perhaps I should make a version that uses a material table, in stead of strictly additive piece values.

Joe Joyce wrote on Tue, Oct 13, 2009 08:10 AM UTC:
Sam's griffon-type pieces have the property of being more powerful at a
distance than up close. Once they get past a certain number of squares,
they switch from attacking 4 squares at each range to attacking 8 squares
at each range. The R & B attack 4 squares at each range, the queen 8. This
stronger at a distance attack of any bifurcator is also a property of the
bent shaman [and hero] and the twisted knight from Atlantean Barroom. It's
an interesting property when it's not trivial, as in the case of the D,
the 0,2 leaper, the H, the 0,3 leaper...] Are there other pieces that share
this property, and how?

H. G. Muller wrote on Tue, Oct 13, 2009 10:20 AM UTC:
>Sam Trenholme: (on the Ajax Bishop)
>>I really like the bishop + non-capturing Wazir piece; it nicely solves 
>>all of the headaches one has coming up with a board setup for colorbound

Actually I tested such pieces once, to figure out how much of a handicap
color-boundedness actually is. To my surprise the extra non-captures are
not worth that much, at least when you play the piece in pairs. I tried
augmented Bishops with 1, 2, and 4 Wazir (non-capture) moves, and it seemed 
each move added about 15 cP to the piece. The fact that this was nearly
additive suggested that it was due more to tactical mobility than breaking
the color-boundedness (for which a single move would already have been
sufficient). This was further corroborated that adding Wazir non-captures to a Knight, which does not suffer from color-boundedness, caused a nearly identical value increase.

I guees the most important thing is that the pair bonus becomes
incorporated in the basic piece value, which is something you would not
notice when you play them in pairs.

H. G. Muller wrote on Tue, Oct 13, 2009 11:21 AM UTC:
> Mats: This is a piece that is easily graspable, very agile, but not 
> trivial to exchange. Due to its great value it cannot simply block 
> enemy pieces. It would be a good substitute for the mad queen, then.

Indeed, I like the Adjutant. It really adds new aspects to the game: a
jumping Slider, interesting pair interactions with the Bishops, and
something to bridge the Rook-Queen value gap.

The Nightrider is another piece that tested as more valuable as a Rook,
despite its lack of mating potential. In fact mating potential is a bit of
an overrated property. In practice Pawnless end-games hardly occur. It is
the piece that is more effective in supporting Pawns in the battle for
promotion that is most valuable, and the mating potential becomes only an
issue when the number of Pawns has fallen to one (so you can sac your piece
for the last Pawn). I also tested an augmented Bishop with a single extra
backward capture (BbW). This move endows it with mating potential, but has
not much tactical value. It added about what I expected from the tactical
value (15-20 cP). There hardly seemed to be a bonus for the mating
potential, although at the time-control where I tested Fairy-Max was
definitely able to find the mate with this piece against bare King.

Sam Trenholme wrote on Tue, Oct 13, 2009 04:36 PM UTC:
I see Mats Winther has recently created a new piece that
  • Has a simple move
  • Has not been, to the extent of my knowledge, thought of before
I’ll give you guys Mats’ description of this new “Warlock” piece:
This magic piece can change movement capability by using up a move to transform itself. A Warlock rook can change into a Warlock cannon by turning the rook upside down, or vice versa. The Warlock cannon uses Korean Cannon movement: it moves as a rook after having jumped a piece. If it cannot jump then it cannot move. As such, it is somewhat weaker than a knight, but its tactical capacity is great. In any case, the Warlock cannon can always transform itself back into a Warlock rook. After the piece is transformed it must make a move before making yet another transformation. So it's not possible to stay put and make continual transformations on the same square.
OK, this is something I haven’t really seen before: A piece that can, at the cost of a tempo, change its nature. We can have all kinds of pieces of this form: bishops that can become knights and vice versa, Jumping Marshalls (Korea Cannon Rook + Knight) that can become Queens, as just two examples. This is best for pieces that are strong, but don’t develop very well in the opening, or pieces that alternate between two pieces of about the same value (bishops becoming knights on an 8x8 board, or bishops becoming augmented knights on larger boards).

The only time I’ve seen something like this before is Betza’s “Weakest chess”, where a piece has to lost a tempo to go from a moving piece to a capturing piece (and vice versa). Here’s an idea for people who want a game that computers do not play well: Multi-move weakest chess!

Sam Trenholme wrote on Tue, Oct 13, 2009 05:53 PM UTC:
Actually I tested such pieces once, to figure out how much of a handicap color-boundedness actually is. To my surprise the extra non-captures are not worth that much, at least when you play the piece in pairs.

The issue I have is that having to place bishops on opposite colors reduces the number of possible setups. There are 126,000 possible Capablanca Chess setups where the queen is to the left of the king and the bishops are on opposite colors. There are, however, 226,800 possible Capablanca Chess setups if we allow bishops to be on the same color of squares—something we can only do if we allow the bishops to shift colors.

Speaking of strong colorbound pieces, in addition to the Adjuntant (Bishop + Dabbah-Rider), there is the Sage (Camel + Bishop), and The Way of the Knight has a piece called the 'FAD' (Camel + Ferz + Alfil + Dabbah). There’s also, if you want a really powerful colorbound piece, Sage + Dabbahrider (or think of it as a Adjuntant + Camel), or even the diagonal hook mover I recently mentioned (a very ancient piece, older than Mad Queen Chess).

(Edit: 226,800, not 453,600 possible setups because the queen should be to the left of the king—we shouldn’t count mirror images)

Peter Aronson wrote on Tue, Oct 13, 2009 06:30 PM UTC:
Actually, the Warlock is a bit like the Can(n)on from Antoine Fourrière's Jacks and Witches 84 or Bilateral Chess, which in turn was inspired by the Rotating Spearman from John William Brown's Centennial Chess. Admittedly the details are different, but the idea of a piece that can move or transform is not particularly new. (There are also games where the Pawn promotes as an entire move, instead of moving and then promoting as part of the same move -- this has some similarity.)

Joe Joyce wrote on Wed, Oct 14, 2009 01:25 AM UTC:
Gary Gifford used 'spearman' pawns, that had the ability to either move 1
square the way the spear was pointed, capturing anything in that square, or
change its direction of movement [and capture] one step, the three forward
directions being available. 

I'm currently playing a game of Grand Ducal Chess with John Ayer, which
uses a pair of lame bishop-dabbabah-riders, This game, 2009 by John, was
adapted from Emperor Chess, 12x12, 1954 by HR Lambert, NYC, which uses the
lame bishop-dabbabah-rider as the title piece. I would suggest this
somewhat weaker early version of the adjutant might be more suitable in
some games, being far more blockable than Mats' adjutant.

John Smith wrote on Wed, Oct 14, 2009 04:25 AM UTC:
I've had an idea about static move sets which pieces on that square can
move as for a while. However, this in practice is rather boring as the
positions are always essentially the same, just with different colors or
simple modifiers like one square or infinite. Then, I got this idea:

What if the movements were separate from the pieces, but moved

As if the movements were normal people, leading their dull lives, when
they become vessels in a fight between foreign spirits...

Jeremy Good wrote on Wed, Oct 14, 2009 04:36 AM UTC:

The Can(n)on is similar to the Warlock in that it changes into a somewhat related piece but also has the ability to morph as an option, as a move in itself. Unlike Warlocks, the Can(n)ons change / switch automatically at the end of every move.

In the notes to Jacks and Witches 84, Antoine Fourriere mentions (in a different context) David Howe's delightful Chess on a Longer Board with a Few Pieces Added, which has the changeling pieces, a halfling bishop that changes into a halfling rook at the end of every turn and vice versa. There is no option to change there. It is entirely automatic.

David Howe in his notes to his changeling variant cites John William Brown's Flip Chess which has pieces that can optionally flip back and forth - pawns/berolina pawns, ferzes/knights, rooks/bishops and after being captured can optionally be dropped back in as their flip sides.

I like the idea of a piece that has the option of turning into a completely dissimilar piece. 'Warlock' is a good name for a piece that transmogrifies but the Winther rook/cannon flip piece seems like a conservative implementation of a 'warlock'. A good piece though.

A piece that is somehow compelled to turn into a dissimilar piece - a werewolf piece - is a nice idea too.

Regards and advance happy Halloween!

[Updated: Gary Gifford deserves some mention here too, I think. Another variant with automatic flipping is Gary Gifford's Bishop Knight Morph Factor. I seem to recall some other variants where a piece morphed depending on what color square it rested on, but can't think which ones at the moment...In Gifford's Pillars of Medusa, the Morphs change into the pieces they capture, an idea he takes further in his remote sensing variants...]

[Updated again: See this comment David Paulowich made about his idea for a piece that automatically changes from Rook to Knight to Bishop and back to Rook again (if I understand it correctly). He calls this piece the Rotator and has a mate in three problem at the link above, using the Rotator.]

[Update 3, See Proteus a game where each piece is on a dice on the face of which is a piece, each dice containing a piece for all eight of its sides (Gifford mentions it above Paulowich's comment.). There are other such variants...

Jeremy Good wrote on Thu, Oct 15, 2009 04:16 PM UTC:
This discussion and the one about Wusses inspired me to create a new chess variant this morning containing a piece I am dubbing the Werewolf (a Mamra that turns into a Wuss and vice versa) and kings and queens that transform into one another. I call them Transvestites. Preset may take a while as it would be no fun unless it's rules-enforced.

H. G. Muller wrote on Thu, Oct 15, 2009 08:06 PM UTC:
I did a test of 400 games with a single Rook -> Adjutant substitution, and
the Adjutant won by 63%.

Then I did two 600-game matches giving additional Pawn odds to the
Adjutant (deleting f2 or f7). One where I set the Adjutant value slightly
above R+P, one where I set it slightly below. They ended in 52.7% and 52.3%
victories for the R+P side.

So it seems a single Adjutant is worth almost as much as R+P. Note this is
opening value, and that the opening value of the Rook for me always tests a
little bit below the classical 500, though. There was no pair of Adjutants
in this test, but there was a pair of Bishops. So the empirical value might
include some Bishop-Adjutant pair value.

Sam Trenholme wrote on Fri, Oct 16, 2009 04:19 AM UTC:
OK, I have a new idea for a piece: A piece that does not move 90 or 45 degrees, like all the simple sliders in Chess, but a piece that can move 22.5 degrees.

This is akin to a Knightrider, but unlike a knightrider, it doesn’t hop over any squares.

A picture is worth a thousand words:

. . 1 . . . 2 . .
. . . 1 . 2 . . .
8 . . 1 . 2 . . 3
. 8 8 . 1 . 3 3 .
. . . 7 # 3 . . .
. 7 7 . 5 . 4 4 .
7 . . 6 . 5 . . 4
. . . 6 . 5 . . .
. . 6 . . . 5 . .
Or on the edge of a board:
1 . . . . . . . 2
. 1 . . . . . 2 .
. 1 . . . . . 2 .
. . 1 . . . 2 . .
. . 1 . . . 2 . .
. . . 1 . 2 . . .
8 . . 1 . 2 . . 3
. 8 8 . 1 . 3 3 .
. . . 8 # 3 . . .
This piece is in the same general class as the crooked rook, crooked bishop, rose, and other sliders that change direction as they slide: The piece goes out one square orthogonally, then turns 45 degrees to the left or right, goes out one square diagonally, then turns 45 degrees back to go outwards orthogonally again, goes one square, turns diagonally the same direction, etc.

Another way of looking at this piece is that it’s a “bent queen”, instead of going from its origin 0 degrees, 45 degrees, 90 degrees, etc., this piece goes from its origin 22.5 degrees, 67.5 degrees, 112.5 degrees, etc. Since Chess is quantized to its squares, the move is a little more awkward-looking on the grid.

There are, of course, a lot of ways of making other pieces based on this idea. There is the same piece starting with a diagonal instead of an orthogonal move, there can be versions of this piece whose rotation from the queen’s move is not 22.5 degrees, but some other rotation. We can have a “Betza Crab” version of this piece, etc. There are the forms of this piece that are “Bent rooks” or “Bent bishops” which are not left-right symmetrical. There is the possibility of combining this piece with other leapers and sliders. And so on.

Antoine Fourrière wrote on Fri, Oct 16, 2009 06:41 AM UTC:
I tried some time ago a (seemingly lost) zrf for Comet Chess, a rather dull 10x10 variant which merely used a CRNBQKBNRC setup, with augmented Knights (color-changing NW) and Comets, parabolic, colorbound curve riders which moved (1,1), (2,4) or (3,9). (So, advancing a Rook's Pawn threatened to exchange a Comet for a Bishop.) The Comets, the Bishops and the NW had approximately the same value, if I recall correctly.

Jörg Knappen wrote on Fri, Oct 16, 2009 09:49 AM UTC:
Hey Sam, you just rediscovered the Rhino, have at look at the Piecoclopedia
entry for more information about this really nice piece:

Sam Trenholme wrote on Fri, Oct 16, 2009 03:59 PM UTC:
So someone else independently came up with the same idea? Hmmm...

Like I said before, it looks like pretty much any simple piece a Chess Variant can have has been thought up before. Maybe it’s time to devote less energy to trying to come up with new pieces and opening setups, and more energy to coming with with ways we can develop opening theory for setups, figuring out how to make a Chess variant that comes as close as possible to having high depth, short games, no draws, and no advantage for the first player (or deciding how important each of these four factors are), and finding ways to come up with opening theory, endgame theory (which pieces can mate the king, etc.), and what not.

I’ve actually been working on opening theory for the one variant I have “officially” invented; White has about a 7% advantage and I’m trying to come up with ways Black can equalize. 1. e4 d5 2. exd5 Nb6 equalizes things for Black and Black has a better game after 1. f4 c5; I’ve been spending the last two weeks looking for a good reply to 1. c4 (right now, 1. c4 Mh6 looks like the most equalizing line for Black; 1. c4 e6 is refuted by 2. g4).

I personally think the Rhino makes more sense on a hexagonal board. Here is how a hex-Rhino would move:

. . . . 1 2 . . .
 . . . . 1 . . . .
B C . . 1 2 . . 3
 B B C . 1 . 3 3 4
. . B B 1 2 3 4 . 
 . . . A # 4 . . .
. . A 9 8 6 5 5 .
 A 9 9 . 7 . 6 5 5
9 9 . . 8 7 . . 6 
 . . . . 7 . . . .
Here, we see the hex-Rhino (This may also be considered a hex-crooked-Rook) travels like the usual piece people use as a hex-Bishop, but stops at the squares in between, and can take two paths for each of the six directions it can go in a straight line, resulting in 12 total paths.

Speaking of Hex chess, I never liked the idea of the “bishop” as normally implemented in Hex-chess, nor the knight or the queen.

I used to play hex-based wargames with my dad when I was a kid and, in those games, there is no “diagonal”; the only movement allowed is to one of the six fully adjacent hexes; some pieces could move two, three, or more hexes, but never diagonally.

M Winther wrote on Fri, Oct 16, 2009 04:30 PM UTC:
H.G., after this thorough research it is clear that the Adjutant is worth 6, which
is very good. I have updated the Zillions files in which I've implemented
this piece, tweaked its value and changed the documentation:
Pioneer Chess
Pilgrim Chess
Alternative Chess
Accessory Chess
Adjutant Chess

The latter program now also contains a variant that implements the
'Orthobishop'. The Adjutant can be viewed as a combined piece:
bishop + orthobishop. The latter is probably less useful than the
Adjutant, but it could be interesting to investigate its properties. The
Orthobishop can only visit a quarter of the board squares. So I assume
its value is very low, probably only 2. So the Adjutant is 3 + 2 + 1
(surplus value) = 6. The low value of the Orthobishop means that it can
be sacrificed for two pawns, thus breaking up the position. So it could
perhaps be a useful piece in game construction, anyway. In the variant
implemented it replaces the bishops. Below I give an example of
Adjutant tactics:

1.Rxb7! Bxb7
2.Ba4+ ...
forces the black king to a black square, which
means that Ab8 doesn't cover the rook on h8 anymore
2.... Kd8
3.Axh8+ ...
and white has gained a pawn, whilst maintaining
the initiative.

M Winther wrote on Sat, Oct 17, 2009 06:44 PM UTC:
The Consul is a new relative to the Adjutant. It also slides on the
orthogonals, but only on the same colour. It also jumps like a Camel (3+1).
This means that it is a colourbound piece, too. I guess it's worth 5. I
added it as a variant in my Pioneer Chess so it can be evaluated together
with the traditional pieces. This, too, seems like an attractive piece that
can be used in diverse contexts. The colourbound orthogonal slide seems to
be a fruitful concept. Beside the Adjutant and the Orthobishop, I have used
it in the Vicuna and the Guanaco, too, however in the latter two pieces the
capture capability is restricted. I suppose it could be combined with
knight-jumps, too, continuous or single, but somebody else will have to try

Joe Joyce wrote on Tue, Oct 20, 2009 05:34 PM UTC:
I have a question involving piece types and values. Consider 4 pieces, the
standard RN and BN, and the DWN and FAN. Using HG Muller's values, we see:

 RN = 9.00
 BN = 8.75
DWN = 6.33
FAN = 6.50

DWN/RN = 70%. FAN/BN = 75%. This says something about the value of
leaping, because I think lame 2-square pieces would test out as less than
70-75% of the archbishop and chancellor values. But the thing I find
interesting is the flip in relative values between the pairs of pieces. 

Why the flip?

The FAN has 8 forward squares to the DWN's 6, but the BN, from a
'rearward' central square has 11 forward moves compared to the RN's 8
from that same central square, so that doesn't account for the flip in

I've considered the relaxation of [color] boundedness. It seems pretty
feeble to me, but the numbers point in the right direction. The rook is
unbound, visiting all the squares on the board. The bishop is singly color
bounded, visiting half the squares on the board. The RN and BN combos are
unbound, so the bishop visits twice as many squares as it did by itself. 

The dabbabah is doubly colorbound, visiting 1/2 x 1/2 or one quarter of
the board. The DWN is unbound, allowing the dabbabah to visit 4 times as
many squares. The alfil is triply bound, visiting 1/2 x 1/2 x 1/2, or one
eighth of the board, and the FAN is unbound, allowing the alfil to visit 8
times as many squares. 

Like I said, feeble. Suggestive, but feeble. Who's got any ideas? They
can't possibly be much worse than what I just suggested. Maybe
blockability, as one pair is unblockable and the other partially blockable.
Well? ;-)

Sam Trenholme wrote on Wed, Oct 21, 2009 03:10 AM UTC:
[see above]

Sam Trenholme wrote on Wed, Oct 21, 2009 03:11 AM UTC:
H.G.Muller: Do you have any interest in adding support for other pieces besides the Capablanca pieces to Joker80? You seem to have a lot of interest in the Adjutant piece—perhaps you will consider giving Joker80 support for this piece.

The biggest issue I see with giving Joker80 support for this piece is properly evaluating the piece, and having it possible to have the pawn promote to this piece—is there a way we can give Winboard a subset of pieces which we only allow the pawn to promote to?

Given a setup where we have the two rooks in the corners, the king on the F file, two bishops on opposite colors, two Adjutants on opposite colors, two knights, and the queen, we have 216 possible setups.

One issue I have with the Adjutant on a 10x8 board is that there’s a lot of smothered mating threats in the opening. For example, in the RANBQKBNAR array (A = Adjutant), black can threaten Af4# by opening with 1. h4. Black’s only reasonable reply to this is 1. h4 e5; after 1. h4 Ng6 2. h5 Black loses his knight; 1. h4 c5 2. Axb8 Rxb8 and Black can no longer castle on the queenside; 1. h4 g6 2. hxg5 and Black loses a pawn; 1. h4 f5 2. Af4+ and Black loses castling privileges; so that leaves us with 1. h4 e5 2. Nd3 and now Black is probably best doing a Slav-style defense with 2. ... d6, though 2. ... Bxh4 also looks interesting. This Slav-style defense also works against other White threats like 1. h4 e5 2. f4 d6.

When I investigated six different Capablanca setups to see which one was most balanced for White, the one setup with a first-move mating threat scored really poorly; being fifth place out of six (White had a really strong advantage). We can also consider using the RBNAQKANBR array, which doesn’t have any first-move mating threats. Then again, it’s an open question whether RANBQKBNAR is better for white than RBNAQKANBR, or what the most balanced Adjutant array is.

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