Comments by HGMuller

Some buttons to pause and scroll through the game might be a good idea. You
should realize, however, that it is only this fast because the full game is
already on the server. If the game is actually being played, the rate at
which the moves would be displayed is determined by how fast the engines
produce them. So in a 5-min blitz game (300 sec), moves would come every 8
sec or so, which is 8 times slower than what you see now. If people on the
average would still consider that too fast, we can play 10-min games.

The fast playback mode is really meant only to catch up with a game in
progress, when you first tune in. It seemed better to have the moves come
by once a second, so that the spectator can at least get a vague idea how
the current position originated, than to instantly flash the current
position. But the display must be a bit fast to catch up with reality.

Once someone is watching, he typically request displaying a new game as
soon as the previous one finished, and at that point there are no stored
moves to display. And it is a good thing that, as soon as people click the
page, they immediately see something happen. If they would have to wait on
average 15 sec for a move to be made, they might already have gone
elsewhere. A 'slow replay' button might be appreciated, though.

This Falcon is a very nasy piece to program. The multi-path character of its moves subverts all properties of pinned pieces on which my engine Joker relies for efficient legal-move generation. There is no longer a well-defined pin line: pieces pinned by a Falcon can often move in multiple directions without exposing the King. Also it is no longer sure that a pinned slider cannot move along its pin line to block a check by another piece (if this other piece is a Falcon). A check by a Falcon can have the character of a contact check (for interposing is not an option if the King is checked through multiple paths) despite being inflicted from a distance.

I guess I will simply generate moves as if the enemy Falcons have no moves, (so generating pseudo-legal moves with pieces pinned by a Falcon, and with other pieces when in check by a Falcon), and then test for their legality afterwards (by testinng if an enemy Falcon happened to be aligned with our King, and then testing all the generated moves for leading to a position where this Falcon is sufficiently blocked). Cumbersome, but I don't see an efficient alternative.

Why is it impossible to give feedback (add rating or comments) on the
CVpage for FFEN / ffen2htm? I wanted to add the following comment:

It seems two separate issues got entangled here: extending Forsyth-Edwards
notation to unambigously denorte positions from Chess-variant games, and
the creation of a graphical tool for generating diagrams from such
positions.

W.r.t. the first issue I see no logical reason why FEN notation should be
limited to boards consisting of a grid of squares. In paricular, the
Xiangqi board is fully equivalent to a board of squares. But also boards
of hexagons (with overal hexagonal or diamond shape) can also be
raster-scanned for description as a FEN with, possibly, unequally sized
ranks.

Indicating if the board is checkered, and what is the color of its
lower-left squares are not part of the game-state at all, and thus do not
belong in a (F)FEN. They are merely input to a diagram-generator tool,
like font information, diagram size, etc.

I don't think it is a realistic desire that an FFEN uniquely specifies
the variant it represents a position from. This problem is well
illustrated in Janus vs Capablanca Chess. These games seemingly share many
positions (after the Chancellors in Capablanca got traded), but as long as
there are Pawns, the positions are still different, as in Capablanca the
Pawns can promote to Chancellor, which does not exist in Janus. In
addition, the rules for Queen-side castling are different. It would be
very inconvenient to require that such details are unambiguously described
by the FEN, as this would quickly make them infinitely complicated.

Note that FENs are mostly used in a context where the game they represent
is known: e.g. in a tag of a PGN file, which also containst a variant TAG.
So if a variant is known to have a diamond-shaped 8x8 board consisting of
hexagons, there is no reason why it could not be represented by a FEN as
would be used for normal Chess. Assuming the variant to be known would
also solve the problem that you run out of latin characters long before
the list of fairy-pieces is exhausted. That problem would not exist if the
same letter represents different pieces depending on the variant. E.g. a C
could denote Chancellor in Capablanca Chess, but Cannon in Xiangqi.

This is the way I implemented the FEN reader in WinBoard_F. Which, btw,
could also be used as a tool to generate diagrams as GIF files for many
variants (only with square boards of conventional topology, though). For
instance, the Xiangqi array would look like this:

http://home.hccnet.nl/h.g.muller/XQpetite.gif

OK, I can now do all 3-men EGTBs on 2n x 2n boards upto 16x16. (For odd-sized boards the reflection symmetry works differently.

King + Carpenter can almost always perform checkmate on 10x10, but hardly ever on 12x12.

This is the one where you went wrong:

| 3.  Winboard F requires SMIRF-o-glot to be with it in the same 
| directory to work.

you can put Smirfoglot in any place, as long as you tell WinBoard (in the
startup dialg) the full pathname of the engine, AND ALSO the directory in
which the engine should look for its files (through the /fd or /sd
option):

'D:\engines\smirf\smirfoglot /H128' /fd='D:\engines\smirf'

So engines that look for files (like Smirfoglot is looking for the engine
executable, but also engines that look for opening books etc.) do need the
/fd (/firstDirectory) option to specify where to look (which does not
necessarily have to be the directory where the executable is, although
this usually is the case).

For the second engine you need to use /sd in stead of /fd.

So it is possible to keep several different versions of Smirf, each in
their own directory, each containing their own copy of Smirfoglot. This is
the way I usually do it. I think that you could even put a single version
of Smirfoglot in the WinBoard directory, as long as you tell it with the
/fd argument where to look for the engine DLL (untested):

'Smirfoglot /H128' /fd='Smirf_1'

if the Smirf_1 directory is a subdirectory of the WinBoard_F directory.
(Note that my double quotes get mangled to single quotes here.)

Betza's HFD (= (1,1)+(2,0)+(3,0) leaper) can mate a bare King (with the
aid of its own King) even on a 14x14 board. With white to move the K + HFD
vs K end-game is 100% won. There really isn't a single position that is
not won. (Some KXK end-games have a few draws when the X is trapped in a
corner by the bare King, or when they cannot lift a stalemate condition of
a cornered King that attacks the X. But not when X = Half Duck) The number
of moves it takes is:

14x14: 94
12x12: 66 
10x10: 42
 8x8:  27

On 16x16 it is usually draw: only 7.78% of the positions with white to
move is won. The longest win on 16x16 still takes 65 moves, though, from
the following position:

 k . . . . . . . . . . . . . . . 16
 . . . . . . . . . . . . . . . . 15
 . . . . . . . . . . . . . . . . 14
 . . . . . . . . . . . . . . . . 13
 . . . . . K . . . . . . . . . . 12
 . . . . . . . . . . . . . . . . 11
 . . . . . . . . . . . . . . . . 10
 . . . . . . . . . . . . . . . . 9
 . . . . . . . . . . . . . . . . 8
 . . . . . . . . . . . . . . . . 7
 . . . . . . . . . . . . . . . . 6
 . . . . . . . . . . . . . . . . 5
 . . . . . . . . . . . . . . . . 4
 . . . . . . . . . . . . . . . . 3
 . . H . . . . . . . . . . . . . 2
 . . . . . . . . . . . . . . . . 1
 a b c d e f g h i j k l m n o p
White to move, mate in 65.

Solution:
1. Hc5, Kb15 2. Hc8, Kc14 3. Hc11+, Kd14 4. Kf13, Ke15 5. Kg14, Ke14 6. He11+, Ke15 7. Kg15, Kd14 8. Kf14, Kd13 9. Kf13, Kc13 10. Ke13, Kc12 11. Ke12, Kc13 12. Hd10, Kd14 13. Hd13, Ke15 14. Kf13, Kf15 15. Hg13, Ke15 16. Hh12, Kf15 17. Hh14, Kf16 18. Kf14, Kg16 19. Kg14, Kf16 20. He14, Kg16 21. He16+, Kf16 22. Hf15, Ke15 23. Hf13, Kd14 24. Kf14, Kc14 25. Ke13, Kb13 26. He12, Kc13 27. Hd11, Kc14 28. Hd14, Kb13 29. Kd12, Kb12 30. Hd11, Kb13 31. He10, Kb12 32. Hc10, Ka12 33. Hb9, Kb13 34. Kd13, Ka12 35. Kc12, Ka11 36. Kc11, Ka12 37. Hb12, Kb13 38. Hd12, Kc14 39. Kc12, Kc15 40. Kd13, Kd16 41. He13, Kc15 42. Hf14, Kd15 43. Hg15+, Kc15 44. Kc13, Kd16 45. Kd14, Ke16 46. Ke14, Kd16 47. Hd15, Kc15 48. Hd13, Kb14 49. Kd14, Kb15 50. Hb13+, Kb14 51. Hb11+, Kb15 52. Kd15, Ka14 53. Kc14, Ka13 54. Kc13, Ka14 55. Hb14, Kb15 56. Hd14, Kb16 57. Kc14, Ka14 58. He15, Kb16 59. Hb15, Ka15 60. Hb13, Ka16 61. Kc15, Ka15 62. Ha12+, Ka16 63. Ha14+, Ka15 64. Ha11, Ka16 65. Ha13#

'On 2008-07-06 H. G. Muller concluded that King and Bison can force checkmate on boards as large as 12x12. '

That was actually even 14x14. King + Bison vs Kings is absolutely won on 14x14 and smaller, with white to move. (i.e. not a single draw position.) The Bison cannot be trapped in a corner; its large stride simply makes it leap out of trouble. In addition there are no corner stalemates (such as in KNK:

 k N . . . .       ), because a Bison can alway check the square
 . . . . .            next to it in 1 move. 
 K . . . .
 . . . . 
 .

The longest mates (against perfect defense) are:

BOARD MOVES (K,Bi,k)
16x16: 76 (a4,b7,b1)   (but 90% of all wtm positions are draw) 
14x14: 82 (a1,n14,c3)  (100% won)
12x12: 55 (a1,L12,c3)      '
10x10: 40 (a1,j10,c3)      '
 8x8:  27 (a2,b2,b4)       '

Some more data about mating potential of the short-range leapers:

Betza NR  NAME              Longest mate (if generally won)
                             8x8  10x10 12x12 14x14 16x16
F      4  Ferz              color bound
W      4  Wazir             pure alternator
A      4  Alfil             color bound
D      4  Dabbaba           color bound
N      8  Knight            pure alternator
FW     8  Commoner            18    29    49    62    -
FA     8  modern Elephant   color bound
FD     8  ?                 color bound
WA     8  Waffle            no mates
WD     8  Woody Rook          29    52    -
AD     8  Alibaba           color bound
FN    12  ?                   22    32    44    59   100
WN    12  Vicar             pure alternator
AN    12  Kangaroo            35    63    -
DN    12  Carpenter           31    44    62    92    -
FWA   12  Crowned Alfil       15    22    31    41    53
FWD   12  Crowned Dabbaba     15    20    27    33    40
FAD   12  ?                 color bound
WAD   12  ?                   26    39    -
FWN   16  Centaur             13    17    21    28    33
FAN   16  High Priestess      17    23    30    36    45
FDN   16  ?                   14    19    25    31    38
WAN   16  ?                   22    31    43    57    74
WDN   16  Minister            17    23    30    36    45
ADN   16  Squirrel            19    24    31    38    46
FWAD  16  Mastodon            13    19    24    29    36
FWADN 24  Lion                 5     7     9    10    12

Note that the Lion does not need King assistence to perform the checkmate,
which is why it can be so fast. It is easy to prove it can mate on boards
of any size, and indeed on an infinitely large board (which is not the
same!). It does not even need a corner, just an edge.

'no mates' means that the piece does not cover two orthogonally
neighboring squares, which is the minimum requirement to create a
checkmate position (in a corner). Being color-bound, or a pure color
alternator implies this.

Because I am still struggling to implement the Falcon in Joker80, where efficiency is a hallmark, I decided to add a few lines of code to Fairy-Max to implement support for multi-path moves. Fairy-Max is inefficient anyway, and does not know about pins and check tests; it simply plays on until the King is captured.

So it is possible now to define pieces like Falcon in Fairy-Max (in this as yet unreleased version), so that I could already start running some games for asymmetric play testing.

The initial results suggest that a Falcon is not worth nearly as much as mensioned somewhere below. As the Falcon seems a piece similar to the Rook, initially hard to use on a crowded board, but reaching its full potential as the board gets empty, I decided to test it against Rooks. So I took a Capablanca setup, and replaced both Rooks of one side by Falcons. If the Falcon would be really worth 6.5, against a Rook 5, this would mean the Falcon player is leading by 3 Pawns from the outset. Such 'piece odds' games normally produce 80-90% scores. (Simple Pawn odds results in 62% for Capablanca Chess with Fairy-Max.)

The setup seem to be completely balanced, however. Currently it is at 39.5-37.5 for the Falcons, far below the level of significance for determining which piece is better (Rook or Falcon), but almost ruling out completely that the Falcons convey a +3 advantage.

I would currently be inclined to value the Falcon a quarter Pawn above the Rook.

Indeed,this is a known problem with Smirf. Because the underlying piece-value model is linear in the average piece mobility, the piece values become additive, and a the value of Q becomes that of R+B, and that of A that of B+N. For A this is more disastrously wrong than for Q, but trading Q for R+B is still quite bad (like blundering away a Pawn).

For the short-range leapers I found a clear non-linearity in the relation between (maximum) number of target squares N and piece value V:

V = (30+5/8*N)*N (centiPawn).

The methodology of basing piece values on board-averaged mobilities seems flawed to me: it overestimates the impact of bad squares where the moblity is low. In practical play you avoid putting the piece on such squares. e.g. take a few thousand positions randomly chosen from grandmaster games, and count how many of those had a Knight on a corner square. It seems a safe bet that this will be FAR LESS than 4/64 = 6%, and in fact I would be really surprised if it is more than 0.6%.

It would be interesting to observe the frequencies with which pieces visit each board square in grandmaster games, and determine how this correlates with the mobility of the piece.

I had never heard of the term 'darter' and the only image it brings to mind is this silly game of throwing arrows. I can't really relate that to Chess pieces. 'Lame leaper' OTOH seems intuitively obvious. The qualification 'lame' is not intended to be a complimnt: it is a clear disadvantage over an ordinary leaper. If that leaper covers a range of 2 or more, that is. Ferz and Wazir cannot suffer, but it would be better to call those 'steppers' than 'leapers' (i.e. the same distinction as between 'sliders' and 'riders'). A Mao is almost exactly worth half a Knight, when you let it participate in a normal Chess game.

Of course the Mao is a worse-than-average example of a lame leaper, as the paths for its moves overlap, so that two moves can be blocked with one piece. The Falcon in multipath, but also suffers from this effect, partly undoing the multipath advantage. 

Perhaps it would be useful to define an 'effective number of paths', as the conductivity of a network of 1-Ohm resistors connecting the squares through which it moves. This would result in 8 for a normal Knight, but would reduce to  2.66 for a Mao, while 8 moves that could be independently blocked on non-intersecting paths would have 4. The calculation for a Falcon would be a complicated problem in cicuit theory, though.

The point you are trying to make escapes me. What the heck do you mean by
'with the latter determinin who moves first'? K + (BN) vs K is a totally
won end-game even on 16x16. With white to move, there are no draws. With
black to move, there are of course always draws when the blck King can
capture an undefended (BN), and it dos not care much if it was a (BN),
(RN) or Q it was capturing...

Some of your other aguments seem to be directed against (BN) and (RN)
occurring only once in the Capablanca (and related) setup. It says nothing
about the pieces per se. You could have said exactly the same thing about
Rook and Bishop being fatally flawed, if you have one of each (like in
Shogi). Or the Knight and the Falcon.

It just doesn't make any sense. So the Cardinal and Marshall are mixed
slider-leaper compounds. So what? You seem to judge pieces by the abstract
symmetries underlying their design. But the rest of the World judges them
for the beauty and marvelous complexity they display in action, when
participating in games. You seem to live on another planet...

Seems to me you are ripped off for the 10x10. Where I live, the World is
saturated with them.

Also 10x8 is produced and commercially available in the U.S. for $30,
including pieces. It is not allowed on this website to refer to their
supplier, though.

So (BN) is flawed because it cannot enforce mate on 3x3 now? What kind of
reasoning is that? Falcon cannot do that either. In fact, it cannot even
move on a 3x3 board. Does that mean it is even more fatally flawed?

I think it is a mistake to consider using a different array as creating a
new variant. I usually refer to such things as sub-variants. In the
WinBoard GUI, 10x8 games like Carrera, Bird, Embassy are all played as
'variant capablanca'. If not actually playing Capablanca, the user will
have to provide the opening setup (as FEN).

I guess (BN) and (RN) are so popular because their play is appeling in
practice, and they blend in well with the usual crowd of FIDE pieces.

On a price-comparison website, the cheapest draughts set (wooden 10x10 board
+ chips) is only €11:

http://www.twenga.nl/dir-Games-Speelgoed%2CGezelschapsspellen%2CGezelschapsspellen-Intelligentie%2CDammen

The Buffalo is upward compatible with the Bison, and adds the Knight moves
to it. Although this does not endow it with more speed, it helps
tremendously in accelerating the checkmating of a bare King. The long
stride of the Bison makes for very awkward manouevring. The Bison mates
are very tedious, the average mate is only some 10 moves shorter than the
longest mate. On 14x14, of the 18.5M positions (with the white King in a
given quadrant), only some 100,000 have a DTM < 60. After that it
explodes, the most common DTM shared by 203,408 positions being 73.
Apparently there is a very easy initial phase, probably just walking the
winning King to the center, driving away the bare King from there with the
aid of the Bison. But after that, a very painstaking drive towards the
corner starts, in which the Bison can only barely prevent that the bare
King nescapes back into the open.

The extra Knight move of the Buffalo allows you to cutt off the bare King
much more efficiently:

               8x8  10x10 12x12 14x14 16x16 
Bison:   (CZ)   27    40    55    82    -
Buffalo: (CNZ)  18    24    31    38    45

The remaing Camel/Knight/Zebra compound, the GNU or Wildebeest (NZ), has
no mating potential. There are only 2 irreducible checkmate positions, and
they cannot be enforced on any size board. Similar to KNNK, the bare King
would voluntarily have to step into a mated-in-1 position.

For the Griffon no computer is needed to give the proof. The system is
similar to the Rook, and works even in the corner of an infinite board.
(So certainly for boards of any size.) It is even easier, because the
Griffon immediately traps the bare King in a corner, without the latter
being able to attack it, like it could do for a Rook.

In fact, with the Griffon there is even a much faster method than with the Rook, as a Griffon can trap the bare King in a narrow corridor, its own King acting as a piston to push the bare King to the edge.

King and Queen are different, and most variants have only one of each. Does
that mean you also consider the Mad Queen game flawed, and advocate use of
King + Commoner?

What exactly is this supposed to add to the game compared to orthodox castling? It seems to me it would be strategcally foolish not to castle to a square one step away from the corner. Standing in the corner is in general a weakness, as your King defends one less Pawn, and has fewer escape squares. Standing further away from the corner leaves a gaping hole n the undefensible side of the King. If in a certain position it is not allowed to castle the maximum distance, because you would castle through check, it would be suicidal to castle in that direction in the first place.

So the only application I see of a variable King destination is that in Q-side castling one now will always go to b1/b8 in stead of c1/c8. But to get that, the much simpler symmetric castling rules as in Janus Chess would suffice.

The variable Rook destination might have some use, although this is largely spoiled by the fact that we are not allowed to give check. (After all, this would be the main reason why you need the Rook immediately in a certain position, rather than allowing an extra move for it.) Usually castling is done in a game stage where there are no open files yet, so the position of the Rook is rather indifferent. So why not put it always next to the King?

It seems to me that this adds very little to Chess, other than complexity we could do without.

OK, I finally got to setting up a live demonstration match. It can be
followed at

http://80.100.28.169/gothic/falcon.html

Currently, you can watch a match of Falcon Chess there, between two
versions of Fairy-Max: one programmed to value a Falcon higher than a
Rook, the other programmed to value it lower.

Let me know if the link works for you.

George, let me know if you object to using Falcon Chess for this purpose.

'The Cavalier is a sort of multipath Gryphon, which cannot stop on any
adjacent square. Benjamin C. Good wrote (March 13, 2002) that this piece
cannot, in general, force mate - because it does not attack adjacent
squares.'

Well, pieces that do not attack at least two orthogonally adjacent squares
obviously can not checkmate. But the Cavalier obiously attacks lots of
adjacent squares. I think the percieed problem was that the rays covered b
the Cavalier are not 'air tight', but have a hole in them, allowing the
bre King to escape its confines by approaching the Cavalier. A Cavalier,
unlike a Rook, can not change to another position alog the ray it covers.

The mate is very easy, though, (even on infinite boards) as a Cavalier can
also do things a Rook cannot do. You don't even need a corner, just an
edge (say 1st rank), and it works on an infinite board.It works like
this:

1) Cut off the bare King from moving away from the edge, (a rank, say),
and walk your own King to be further from the edge than he is.

2) Cut off the bare King moving laterally away from the file your own King
is in, and step towards his file, staying further from the edge than he
is.

3) When the Kings are nearly in the same file, position the Cavalier in
the file of the bare King, so that he gets trapped in the 'corridor'
between the Cavalier's attack lines.

4) Use your King to push the bare King towards the edge, walking on the
same file, until he reaches 1st rank (on f1, say).

5) Lift the stalemate danger by moving your Cavalier to a file far away,
so you can safely take opposition on 3rd rank.

6) We now have to get the bare King into opposition twice, once for
driving him back to 1st rank with check along the rank, second time for
checkmating. In both cases we shephard him into opposition by first taking
opposition ourself, and when he steps sideways, cut off the file two files
away from our King. He then either has to step back into opposition, or
step back immediately.

The main problem is keeping enough distance, as the Cavalier has thes
'holes' in its attack set nearby. So in general, when advancing towards
the edge, for sideway checking, we move one file away from the bare King.
On a small board this might not be possible, and we have to manouevre a
bit. This takes some extra moves, but the principle remains the same.
e.g.:

w: Kd4, Cd8 b: Kd2

1. ... Kd1, 2. Cg7 (out of the way), Kc2 3. Ca8 (cut off b-file), Kd2

Now we would have liked to check from the side, but our Cavalier is on  on
the a-file, and the b-file is too close to cover c2. So we nudge him to the
other side:

4. Cb6 (cut off c-file), Ke2 5. Cg7 (cut off f-file), Kd2 6. Ch3+ (got
him!), Ke1 7. Ke3 (opposition), Kf1

Now we would have liked to cut off the g-file, but our Cavalier is already
on the h-file, and too close to cover f2. And even if he was, we are in
zugzwang. So again some delay displacing the position sideways to gain
room, and then nudge him to the long side:

8. Kf3 (opposition), Ke1 (only move, g1 was attacked) 9. Cc5 (cut off
d-file) , Kf1 10. Cb2#.

Easy as pie...

Well, as I explained, I cannot imagine who would ever want to use other King destinations than those to b- of g-file. Adding moves that are not attractive to use, will hardly lead to more variation in play. You can make variants where it is allowed to remove your own pieces from the board, in stead of moving them, or cpture own pieces, or teleport your King to e4 in stead of castling, but it will essentially stay the same game, as no serious player would ever consider it.

I have a strong suspicion that this castling rule flls in the same class: strong players would virtually never use the extra possibilities.