Comments by HGMuller

Well, XBoard 4.4.0 should be able to run on a Mac. Hans Aberg was even able
to compile it for a Power-PC Mac. And if you can't install from source:
there was a request on the WinBoard forum for a binary Mac version, and
perhaps some Mac user that is set up for compiling will make one available
for hosting there.

Well, it says 'was patented', pasted tense. I think my strategy for
avoiding conflicts is a lot more sensible than censoring the occurrence of
a certain word in any context, like is done here on CVP...

The source code can be downloaded from:
http://home.hccnet.nl/h.g.muller/capablanca.tar.gz
To my dismay I found out that I can no longer compile it on Ubuntu 9.04
(which I had to run on the server because older versions did not recognize
my network card and left me without internet connection). I get an obscure
error in some script that generates C source files. So I have to compile it
on Ubuntu 8.04 (Hardy Heron), and then transfer the binaries to the EeePC laptop. (I just found out that the mentioned tarball contains a bug; in 
board.c it has swapped the 'A' and 'H' for indicators of Xiangqi Advisor 
and Knightrider, so that Xiangqi did not work.)

The way categories and boards are implemented is by directory and filenames. Each category is a directory name, and each file in that directory corresponds to a board name. So in the standard setup there were files wild/1, wild/2 etc. The contents of the files described the positon. I extended that to also specifying board size, castling type, holdings type, pawn type and of course having more piece types. So the files pretty much describe the game, no matter in which directory they are placed. But the problem is to convey that info to the WinBoard client. WinBoard derives the variant it is playing from the 'Issuing' message of the ICS, which contains as only clue about the variant 'loaded from category/board'. So the naming of categories and boards must be such that WinBoard recognizes the variant that belongs to the position and game rules described in the corresponding file. The WinBoard variant-name parser recognizes wild/# or w/# as the FICS or ICC wild types, but such naming is not very user friendly. It also looks for occurrence of a sub-string equal to a WinBoard variant name. This is why wild/crazyhouse does work as well. I make use of this mechanism by naming the directories after the variant that WinBoard should switch to, and then put all boards belonging to that variant in that directory. So capablanca/bird is recognized as variant capablanca, and the opening array is then taken from the file bird. When no board is mentioned, the filename for it defaults to '0', so capablanca/0 is a file that contains the Capablanca array. When playing on ICS the ICS sends a full board position for every move (even your own) so knowing the opening array is never a problem for WinBoard. There is no restriction on the type of position that can be in the board files.

In my mind this makes these pieces less regular. A Cannon on c1 would not be blocked by Pawn on c2, despite the fact that it does not really move on the first (non-capture) leg of its move.

The most elementary Bifurcator, which does not seem to occur in your list, would be a Slider with a Y-shaped path triggered by a collision. That is, it would be able to make both captures and non-captures to squares on either leg. That means it might not get to the second leg of the path at all.

Anyway, even with your restriction the piece is easy to program. I have started a test now on 8x8, where I replace the Knights of on side by Dimachaers.I gave them a value slightly below that of the Knight, to stimulate trading it for light pieces. A piece like this should decrease enrmously in value in the late end-game, so trading it during the middle game should be a priority. (Similar to Grasshoppers.) This is much less true for the Cannon, which at least keeps its non-captures on an empty board.

After 30 games the Dimachaers-vs-Knights result is still pretty much even.

I have no final verdict on the piece values yet (after 60 games the Knights are slightly leading), but  did form an opinion on the aesthetical value of these kind of pieces:

The square where the two legs are joined creates an ambiguity: does it belong to the first leg, the second, or both? This would involve a certain amount of arbitariness in the design of pieces that have different move rights on each leg.

Now for Bent Hoppers this ambiguity is naturally resolved, because the junction square is occupied by the platform, and not accessible anyway. For the jump-on-1st-leg Bifurcators it would be natural to count the junction square as part of the second leg, because, like the rest of this leg, it is behind the platform. The fact that the bend does not occur at the platform itself it aesthetically slightly displeasing. Note furthermore that jump-on-1st-leg hopping pieces only make sense if they have no capture rights before the hop; otherwise it would not be clear if an enemy piece is a victim or a platform.

The bouncing and hop-on-2nd-leg pieces reek of a non-causality that I strongly dislike. It is not logical that they are deflected by something that is not really in their primary path. Furthermore, they are not true bifurcators: their path does not split. (I guess you could allow them to continue on their first leg and take a later deflection; in that case their bifurction is asymmetrical, and could eventually split in more than two paths.) I like none of that.

The collission-type Bifurcator would be natural if the move rights where the same everywhere, as there is no natural break in the path. I would appreciate a piece that can do zero-or-more steps along the first leg better than one that could do only one-or-more. Of course 'the same everywhere' in practice means that it must be able to capture and non-capture everywhere, or it would be pretty useless. And this raises the concern about the ambiguity of enemy pieces serving as collision partners or capture victims. So I guess that the most logical piece of this type would only collide with friends, and capture foes.

Really interesting would be a colliding Bifurcator that would not lose its bifurcating ability on the second leg. I.e. it could make an unlimited number of collisions with friendly pieces, changing its direction by 45 degrees on each collision. This could be called a Billiards piece.

Apart from this, I like the jump-on-1st-leg piece without capture rights on the 1st leg best. And to not lose its value in the extreme in the end-game, it should have non-capture moves along the first leg. I would expect it to be able to capture directly after the hop, though. If not, I think a Bent Hopper would be more regular, and thus nicer.

I wonder if Mats agrees with the 2s I replaced by 3s? Can the Bifurcation pieces really end on those squares with the same type of move as they are allowed to make to the 2s?

. 2 . 2 . . . .        2 . . . . . 2 . .
. . 3 . . . . .        3 . . . . . 3 2 2
. . X . . . . .        . X . . . X . . .
. . 1 . . . . .        . . 1 . 1 . . . .
. . 1 . . . . 2        4 4 4 # . . . . .
1 1 # 1 1 X 3 .        . . Z 4 1 . . . .
. 4 Z 4 . . . 2        . . . 4 . 1 . . .
4 . . . 4 . . .        . . . 4 . . X . .

I don't have Zillions, and perhaps I should learn how to read ZRF files. But the simplest way still seems to ask Mats! ;-) What was a bit ambiguous, and was also not explicit in Sam's diagrams, was what happens in the presence of the piece Z with a Colliding Bifurcator. Does it create moves to the 4s? Not for Mats' pieces, but you could make stronger versions that could.

After 404 games the Knights were leading against the Dimachaers by 56.2%. The statistical error should be about 2%, so I guess this should be taken as a significant advantage for the side with the Knights. IIRC Pawn odds results in a 68% score, though, so the difference is only about 1/3 of a Pawn. This is for a pair, so a single Dimachaer seems about 1/6 of a Pawn weakr than a Knight. With the Kaufman Knight value of 325cP, this would make the opening value of the Dimachaer equal to ~ 310cP (+/- 5cP). This value is consistent with the value I programmed for the test, which would encourage trading Dimachaers for Knights (and the Knights to avoid such trades).

For a really reliable value I should also test Dimachaers against a pair of Bishops. But I want to focus attention on the Secutor first, as this would not lose value in the end-game as steeply as the Dimachaer. Fairy-Max uses fixed piece values during the game, which might still not be perfect for the Secutor, but at least should be a better approximation than it is for the Dimachaer. The Secutor is Cannon-like, and I noticed that the Xiangqi Cannon only starts losing value if the board population gets really, really sparse. With just a few (friendy) pieces it is still quite useful. With orthodox Kings it retains its mating potential in combination even when assisted only by the weakest pieces (a single Ferz or Wazir).

Well, I play them in pairs, so that doubles the advantage in the starting position to 1/3 of a Pawn. And Pawn odds is a pretty large advantage in normal Chess: it creates a score of about 68%. The white advantage has been estblished (from statistics of Grand Master games) to create an advantage of 53-54%, which is about 1/6 of a Pawn.

I guess the reason the Dimachaer is worth nearly a Knight is because in the early game phase when the board is still densely populated it has a very good forward forking ability, while every non-Pawn is a potential target. So it is almost always possible to force trading it for at least a Knight. I could run another experiment programming the value to between Knight and Bishop. This would already cause a major strategy change in the handling of the Dimachaer, as the program would not spontaneously rade it for a Knight anymore, but would wait for a chance to trade it for a Bishop. If this is good strategy, the value might go up to being close to a Bishop. OTOH, it might on average not be able to force such a trade, and then it would be stuck with a worthless Dimachaer in the end-game so often that it hurts more than it helps. The fact that it tests less valuable than a Knight now already suggest that it is already inferior to a Knight in the early middle game, as even when it could always be traded succesfully before th end-game, it is present for at last part of the game in every game, and does not seem to be able to creat an advantage during that time (e.g. by gaining Pawns).

I guess that pieces dependent on sceens and platforms only start to suffer when the population density starts to fall as low as about one piece per rank or line. Before that they will virtually always find a platform on their path, and it does not help much if there are two or three on their path: they can only use the first one. In fact the Colliding Bifurcation pieces, which do not only need a screen, but need a distant screen, might start to suffer again if the population density gets really high, because they can be blocked.

Well, I tested the Xiangqi Cannon once in the Western context, and its opening value was also only slightly below that of a (Western) Knight. I guess the Secutor suffers a lot from the fact that it can be blocked, while the Cannon cannot. Another factor might be that captures contribute more to piece value than non-captures, while the Cannon has the more powerful orthogonal Slider move as capture.

As to the handling: You should not forget that I test with Fairy-Max, which also has no kowledge on specific handling of orthodox pieces. In a program with more knowledge (e.g. piece-square tables) the value of the Secutor might go up, but the value of the Knight likely would go up too, meaning that the relative value would be much less sensitive to this. Fairy-Max does distinguish pieces that should be centralized (P,N,B,K in orthodox Chess) and pieces that roam freely, though. I programmed the Secutor as a piece that could roam freely, because it is long-range and actually needs distance to its platform. For the Lion (FWADN) the value went up about 50cP by centralizing it! (It is short-range, so perhaps this should be expected, but before I tested it I had the belief that centralizing very valuable pieces was not good because it would make them easy chase targets. Of course the value increase by better handling should be seen relative to total value, and Lion > Q, so it is only ~5%.)

>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
>>pieces. 

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.

> 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.

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.