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Later
Falcon Chess. Game on an 8x10 board with a new piece: The Falcon. (10x8, Cells: 80)
H. G. Muller wrote on 2016-10-02 UTC

The problem is that 'lame' is an ill-defined concept for 'oblique' moves (i.e. not strictly orthogonal or diagonal). E.g. look at the Xiangqi Horse (Mao). It is a lame Knight. But that in itself doesn't tell you that it can be blocked on the W; squares, rather than the F squares, like the 'Moa'. Or whether it is multi-path, and can only blocked by occupying both squares. So one has to specify the path, square by square.

This can be done by describing the move as a sequence of steps. The Mao takes one orthogonal step, followed by an outward diagonal one. This can be described by afsW: 'a' (= 'again') for indicating there are two steps, and 'fs' behind it to indicate how it bends. So the Mao is described as a two-step Wazir that bends 45 degrees after the first step. The default modality for the first step is 'm', (because another step follows), so it does not have to be written. The Moa would be afsF, and the Moo would be afsK, so it can start in any of the 8 directions.

The notation for the Falcon used here is an extension of that to 3 steps (so there are two 'a', each followe by two descriptions of how the trajectory bends). There are 3 path types: bend early, bend late and bend twice. E.g. bend early can be written as afsafK: the second step forward-sideway compared to the first, and the third 'forward' compared to the second. Unfortunately the twice-bent path has to be written as one left+right and one right+left path, as there is no way to indicate in the third step "now bend in the opposite direction". This is how I finally arrive at afsafKafafsKaflafrKafraflK.

The additional 'm' written in the diagram are really redundant, and act as a reminder only. For non-final leg 'm' is the default, like for a final (or only) leg 'mc' is the default modality. That makes the XBetza system tuned to representing lame leapers. Pieces that capture or hop on their way do need extra modifiers to indicate that.

Aurelian Florea wrote on 2016-10-02 UTC

Hello,

H.G.,

Could you explain the betza notation for falcon for us the more lazy ones.

I was thinking of something more like lame Z or C (L in older version) rather than what you posted which is something I don't understand, and why your choice for the used version , as I'm sure more people could think at more solution to writting the falcon move.

H. G. Muller wrote on 2016-09-28 UTCExcellent ★★★★★
files=10 promoChoice=NBRQF graphicsDir=../membergraphics/MSinteractivedia/ whitePrefix=White blackPrefix=Black graphicsType=png startShade=#FFCC00 squareSize=35 symmetry=none pawn:::Pawn:a2,b2,c2,d2,e2,f2,g2,h2,i2,j2,,a7,b7,c7,d7,e7,f7,g7,h7,i7,j7 Knight:N::Knight:b1,i1,,b8,i8 Bishop:::Bishop:c1,h1,,c8,h8 Rook:::Rook:a1,j1,,a8,j8 Falcon::mafmafsKmafsmafKmaflmafrKmafrmaflK:Hawk:d1,g1,,d8,g8 Queen:::Queen:e1,,e8 King:::King:f1,,f8

## Falcon Chess

This variant also deserves an interactive diagram, so that people can experiment with how the complex multi-path Falcon navigates between the pieces. I picked the starting position that Fairy-Max uses. I also had never rated the game itself, so this offers a nice opportunity for that.

For those who don't feel like working their way through the entire article: A Falcon moves to squares (1,3) or (2,3) removed from it in all directions (the nearest squares not covered by Queen or Knight click). But it does not directly jump there; it has to reach them by stepping along one of the three shortest paths to these squares. If all these paths are blocked, it cannot go there, but if only a single path is open, it can.

H. G. Muller wrote on 2016-09-27 UTC

Well, Falcons make forks, but Rooks make those to a lesser extent too (e.g. when they enter the 7th rank and attack Pawns on both wings). And in addition they can make skewers. All of which also benefits from long-range planning (to open files, make batteries...). To a human the bent motion of Falcons (and even Knights) might seem less obvious than the straight path of Rooks, but to a computer they are just sequences of moves,and it calculates them with precision no matter how far it has to think ahead. So I don't expect specific knowledge on the pieces to make much difference. Also note that even when the Falcon is only marginally more valuable than a Rook, there would be awfully little to fork that would make a juicy bite when protected.

George Duke wrote on 2016-09-27 UTC

Values -- there H. G. Muller had the values Rook and Falcon worked out 9 years ago. Not much progress has been made, but ultimately I bet texts will show Falcon 5.5 or even 5.75 to Rook 5.0, because of forks Falcon makes with longer term planning the only few programs yet are not told about. But Muller right away was closer than the 5.0 R and 7.0 F I used in the nineties. Now I consider myself player and have lost about 2 to 14 wins at Game Courier.

H. G. Muller wrote on 2016-09-27 UTC

Well, computer programs usually do not rank pieces, the programmers usually do that for them. The quality of play also turns out to have surprisingly little effect on piece values.

Fairy-Max self-play showed the Falcon value to be slightly above that of a Rook, perhaps equal. (Pieces close in value tend to pull their values towards each other, complicating the measurement.)

JT K wrote on 2016-09-27 UTCExcellent ★★★★★

The falcon is an interesting piece!  Arriving at the same square in different ways is a clever concept.  I would be curious to know how a top computer would rank them compared to a knight.

George Duke wrote on 2013-11-26 UTC
```Humphrey Bogart was Chess player with games recorded now at ChessGames,
http://www.chessgames.com/perl/chessplayer?pid=65398.

The Maltese Falcon of 1941 movie has just sold November 2013:
http://www.nydailynews.com/entertainment/tv-movies/maltese-falcon-figurine-fetches-4-million-article-1.1529179,
http://www.pbs.org/newshour/rundown/2013/11/maltese-falcon-bird-statuette-up-for-auction.html.

Bill Wall's Chess and Movies http://www.geocities.com/siliconvalley/lab/7378/movies.htm has Bogart playing Chess in all of 'Casablanca'(1942), 'Knock on Any Door'(1949), and 'Left Hand of God'(1955) films.  For Chess Variant, see 217 The Blood of Heroes.

http://www.chessdryad.com/articles/wall/art_01.htm -- his Bogart and Chess has shot of Peter Lorre and Humphrey Bogart at Chess in 'Casablanca'.```

George Duke wrote on 2010-07-30 UTC
That last section the commenter (Frolov) is right referring to, ''More Variants,'' as really for another article. It was to be lead to further expansion on Falcon combined with Shogi and also Xiangqi never completed. Immediately, proliferation in CVs occurred, and the last section on other variants is overtaken and substituted instead by the general reference article 6 years later in 2006 ''91.5 Trillion Falcon Chess Variants.'' Korean Chess Elephant is non-leaping Zebra. In CVs there are also a few non-leaping Camels used. Two of those are Cardinal Super-Chess, and Camblam. There may be no other non-jumping Camels, except as incorporated in partial destinations of all-range hook movers like the magisterial 13th-century Gryphon and recently of course such as Winther's bifurcators having multiple target squares, not just (1,3) or (2,3). However, a type that leaps like Knight and then slides to Camel gets used historically, but that would not be non-jumping. The same for piece-type of Knight leap, then slide to Zebra. Both those are in 1994 Pritchard occasionally, and for some reason not in CVPage CVs, although CVPage has by now two or three times more the attributed CVs than 'ECV'.

Anonymous wrote on 2010-07-30 UTC
```I like falcon. It's interesting stronger version of Korean elephant. By
the way, have anybody thought about using moo in Korean chess instead
normal horse (mao) and falcon with only zebra's moves (without all camel
But, i think that section 'Other variants' should be removed from this
page, and each variant, described here (shogi generals instead pawns, for
example), should have separate page, they are not logical continuation of
falcon, they may be used for FIDE chess to (as Betza says, 'for
without it, but these variants are interesting to.```

George Duke wrote on 2009-07-20 UTC
[Incomplete description corrected. The reason I had 8x7x5 around was to see if certain natural pathways of 8x7x7 and 8x7x5 balanced out. It's better to get them all 8x7x6 as below.] The following is abstract summary about Chieftain, not Falcon. I filed the 2x2x2 comparison at Gilman's M&B04. The 48/336 is going to come up again within M&Bxx. Of course 336/48=7. The full Rule to get 8x7x6=336 requires logical Chieftain of Jetan restriction between loose and strict, and these three subrules are convenient to gamesters. Chess in motion is not only math. 8 steps to choose, then 7 to choose, the first two are obvious, then 6 the third step we have to be careful, all three one-steps for the full three-steps, numbering the 336 pathways. (1) In the three-step there is no return to same square already passed over. (2) 0-degree, 45-degree, and 90-degree changes of direction are all permitted. (3) If there are two 135 changes to choose to get the total 6 choices for the final one-step, use clockwise preference. The full rule makes always 8x7x6=336 three-steps (without subrule 3 there are cases of 8->7->7); and Falcon uses 48 movements from among them. Falcon's movement rule is far simpler, and the foregoing is for Chieftain of Jetan, out of which Falcon is carved. Falcon can be stated as simply as: ''three-steps outward both of at least one straight and one diagonal.''

Joe Joyce wrote on 2009-02-04 UTC
```There are elements of interest found in higher-dimensional chess that are not found in 2D variants. But many think the 2D surface is the best to play upon. Even if the game is 3 or 4 dimensions, playing on a 2D surface is generally easier. For an interesting take on this topic, let me recommend Mapped Chess, by S. Burkhart, found here:
http://www.chessvariants.org/index/msdisplay.php?itemid=MSmappedchess```

Adrian King wrote on 2009-02-04 UTC
```>  3-Ds are just 2 or more layers of 2-Ds, unnecessary contrivance, when you could just lay the whole smear end to end in nice flat canvas.

Strictly speaking, of course, 2-dimensional games can also be represented as 1-dimensional games. A 1-dimensional layout is simpler mathematically (and game-playing software often stores a game's positions in a 1-dimensional array), but the human visual system generally does better with 2 dimensions than with either 3 or 1.

Exactly what this says about the relationship between mathematical tidiness and playability, I'm not sure.```

George Duke wrote on 2009-02-03 UTC
In famous comment this thread here 17.July.2007, Editor Good, if I may call him editor, calls Falcon ''the greatest chess innovation to come along in 500 years (scroll back).'' He is right because Falcon-Bison complement Rook, Knight, Bishop mathematically, as nothing else conceivably could, not in 100 years ahead. Guaranteed. Specific Falcon in question is just more precise Bison to achieve that full sought-for-a-millennium complementarity. The theorem does not address actual Falcon games per se; for all I know they may be mediocre by consensus, just the piece. Gilman should not waste time with 3-D. By and large that has been one very limited success in CVPage -- having few successes in 15 years. Namely, to reject 3-D forms is credit to CVPage. Give them up is the message out of CVPage. No one plays them at Game Courier and whenever new ''3-D'' pops up it is not complimented much here. 3-Ds are just 2 or more layers of 2-Ds, unnecessary contrivance, when you could just lay the whole smear end to end in nice flat canvas. John Smith has 100 CVs in couple of months, and none of them are 3-D, so that proves it. So, given 3-D as probable lost cause, and nothwithstanding there are 91.5 Trillion Falcon CVs at article ''91.5 Trillion...,'' Gilman may well have some good idea for 2-D not yet presented. I suggest Gilman collaborate, if wanting to make FCV #91,500,000,000,020. The ''twenty'' (20) is because there are Bifocal Chess and couple of others. Charles, please find some best use on 8x10, 10x10, 8x12, flat and 2-D, and I'll add equal material to round it out, by Charles G. and George D. Precedents in collaboration include everybody else: Duniho & Lavieri, Duke & Aronson, Brown & Havel... Gilman has 200 Lone Ranger CVs only. Out of right field don't play left out: too sinistre.

Charles Gilman wrote on 2009-02-03 UTC
```I am further inspired to write in defence of the Falcon piece, at least, by comments on some variants of mine that do not use it. Yes, the Falcon is weaker than the Bison, but too much of a strong piece is not always a good thing.
Comments on variants using compounds of two oblique leapers have made me reluctant to use them further unless a theme calls for them. They can just about get by on a board of squares, or more sparingly on a hex-prism board, but on a cubic board they can be overpowering. A Gnu, Gazelle, or Bison in the centre of an 8x8x8 board can reach 48 cells, and a Buffalo 72. The same could of course be said of the Churchwarden, Samurai, Overon, and Canoe but at least that lot are confined to the second preimeter.
`	Being blockable a Falcon does not dominate even the cubic board to the same extent, and suggests a logical set of fellow pieces. Where, by mixing Wazir and Ferz steps, it complements the Knight corresponding 3rd-perimeter steppers can be devised mixing Wazir and Viceroy steps to complement the Sexton - call it the Vulture - and mixing Ferz and Viceroy steps to complement the Ninja - call it the Kite. Even their own compounds are not unthinkable with sufficient blocking pieces - say Merlin for Falcon+Vulture, Kestrel for Falcon+Kite, Osprey for Vulture+Kite, and Eagle for the triple compound. In fact I might try out a cubic variant with the compound pieces, if George Duke does not object.```

George Duke wrote on 2008-12-11 UTC
Let's say you are patenting a Micrometer. It has some unique, novel, inventive inner mechanism. Within the calipers, or connected to them, are some special gear(s), or spring, or device, it does not matter what, that the group thinks will benefit precision measurement conditionally and sufficiently to bother patenting; and researches show it to be untried or thought of before. You know some spacing, or gap, or aperture within, has to be over 3 centimetres for it to work. The specifics are not important. It would be poor to state some exact spacing, like ''4 centimetres.'' Then someone else could make one 4 1/2 centimetres that works just as well and basically the same. So, this patent would be worded minimally concretely as ''at least 3 centimetres'' at that juncture for its particular inventive mechanism to function -- presumably the inventive step. It means there could be untold thousands, millions of very specific embodiments, if anyone gets ''technical,'' i.e. 3.1, 3.2, 3.8, 3.85... Similar reasoning is why, for example, the moves of Rook, Knight, or Bishop are not specified, and instead called or indicated as ''rook-like.'' Cannon for Rook would still be USP5690334 if 8x10 and up, because Cannon then becomes the added element, departing from the norm and making a superset. Elements ABC and D just have become elements ABCD and E: also patented by age-old practice. And so on. It is not a very interesting subject. CV strategy and tactics would be more interesting, but TCVP has never even advanced to that stage, instead being never-ending compilers of so-called ''new'' rules-sets. Hey, with an Author for each and every one, fully to his or her credit. That is except perhaps for Sam Trenholme (in Schoolbook having built some depth), who started it all around 1995, posting assorted CVs from the historical record. See few comments back Trenholme's article ''List of CVs'' from the 1990s at his membership for some great CVs culturally-accepted.

George Duke wrote on 2008-12-11 UTC
USP5690334 covers all 453,600 initial arrays. This repetition is to clear up mis-statements last fall over a month ago, not current comments I have not read. I had all arrays in mind during 1994-1996 and used the wording and technique, of many prior patents going back to 1970s to extend the coverage correctly that way, in legal consultation. There is no going one by one by one, but all of them together in the Claims wording ''all at predetermined locations.'' Also covered is Bison and any other piece going to squares (2,4) plus (3,4), such as exclusively orthogonally multi-path, or two-path, instead of three-path, Falcon. Also, whimsically are the 91.5 Trillion ''supersets'' now extended, in mirroring CVPage purely artistic over-proliferation, turning it to humour, to some 10^50 CVs. ''Superset'' is not legal term, but makes it understandable to math-types. Anticipating proliferation, I did not at all patent the piece, as I could have. So, for example, anyone can slot Falcon into 8x8 (as Antoine Fourriere does with Bifocal Chess). Also, if there are some important pieces you want to combine with Bison-Falcon on 8x10 and larger, inform me and we can set up co-authorship. That works with Complete Permutation Chess of Aronson. Sorry, to Peter Aronson, Tony Quintanilla, Jeremy Good, who have understood realm of intellectual property involved all along, for repetition to parties that shall not be named not getting it the first time, and to newcomers. What field of endeavor has no patenting for several hundred years? Virtually none. Patenting, and formal copyrighting are far and away the norm (put your money where your mouth is); and CVPage, to the extent increasingly ignoring prior invention/discovery, becomes the aberration to dispassionate informed viewers. For eventual contact with the outside world, how many CVs will be welcome, or tolerated, by the world's billion chess players? Who wants to see a thousand rejects or how the process was arrived at? The scrap paper and uncompiling programs? That is the purpose of NextChess threads, to get the right 100 or so CVs -- an interesting project, if it can be completed, and counterpoint trumping proliferation.

George Duke wrote on 2008-10-13 UTC
Think of Falcon as having all the Pawn's moves, 1 or 2 straight, 1 or 2 diagonal, the very last of those concatenated over two moves, for example, two Pawn captures in back-to-back moves, as e3xd4 then d4xc5 by the same Pawn capturing twice. That could happen also in dual-move CVs in only one turn. Falcon was ''two-way'' multi-path from January 1988 until December 1992. Then Vera Cole and I were talking about what expansion to 8x10 would mean, and all of the sudden it was realized there was middle path, S-D-S and D-S-D, to the same never-used squares of very old Camel and more-recent 19th-Century Zebra. So, the standards became D-D-S, D-S-S, S-S-D, and S-D-D with then the newest ones called split block and split diagonal, the above DSD and SDS, making all attainable squares three-way, the three-fold way established. Now actual claims USP5690334 numbering 20 retain, by the way they are worded, the (incomplete) two-way Falcon along with three-way Falcon. Lengthy claims have never appeared in CVPage, and are immediately accessible through USPTO site. The discovered first of the 4 fundamental Chess pieces, the mathematical template from which Bishop, Knight and Rook derive, has characteristics of each of those three she makes possible, and moreover traits of Western Pawn embedded in Falcon's very logic and unfolding. Incidentally, it takes all three pathways for accurate mathematical complementarity, but that would be for longer demonstration than room here allows. In this way over-all, Falcon interfaces and links Pawn and Piece, tying all the normal units together.

H. G. Muller wrote on 2008-10-06 UTC
```You keep stressing how many variants are covered by your patent.

More relevant would be: how many of those are actually played? How many of these variants have regional or national championships for them? On how many internet servers can people play these variants? How many people World-wide have equipment to play any of thee variants?

It seems to me that all this is a lot more important than wether you cover a billion or a trillion variants...```

George Duke wrote on 2008-10-06 UTC

H. G. Muller wrote on 2008-08-07 UTC
```George:

I am close to releasing a new version of the WinBoard Chess GUI, which I expect to become widely distributed amongst Windows and Linux users. Most of the people no doubt will only be interested in playing 'normal' Chess, but I planned to include Fairy-Max with the distribution, as it can both play normal and many variants. The distribution package would look a lot like the experimental version that can be downloaded from the link I gave in the post below.

In this new WinBoard I included some support for Falcon Chess in the menus: people can click 'Falcon' as one of the options in the variant menu, and will then be able to use WinBoard as Graphical User Interface for an engine that could actually play it, provided they use one of the wildcard pieces supplied by WinBoard to represent the Falcons. I suppose you have no objection against this, and as WinBoard itself does not play the game, but only acts as a display, it probably does not fall under the patent anyway. As it would only be useful to use WinBoard this way if you did have a Falcon-Chess-playing engine, and the user can communicate with such an engine only through WinBoard, I make WinBoard pop up a licensing message, mentioning your name and the patent number. (Similar to what I make WinBoard do in Gothic Chess.)

Fairy-Max, in the download below, does include Falcon Chess as a pre-defined variant, in its fmax.ini file, and when programmed by this preset, actually does play the game (as you could watch in the broadcast). Can I leave this in, or would you prefer me to take out the Falcon-Chess game definition?

Please let me know ASAP, I hope to be able to releas this weekend.```

George Duke wrote on 2008-08-06 UTC
True, this is not a Rules-set, instead as it says an essay. It adds to official 1990's copyrights variance-material to suit CVPage in 2000. Right away under the first picture, it refers to having five Pawns as alternative, as Chinese Chess. (Later Overby in Beautiful Sun adopts similar starting array.) Of course, five Pawns would be just ridiculous artwork of no playability. Still in Chapter I, under ''other embodiments'' I mention replacing Queen on 8x8 with Falcon -- something close to what 2008 Seirawan-Chess derivatives might envision in back-rank piece substitutions. Also speculated are 9x9 set-ups. We like to think that preliminarily we are anticipating in 1996-1999 the 10^50 or so CVs (one for each atom between Sun and Mars) using Falcon developed later in 2005 ''91.5 Trillion...'' article including under Comments. What's one hard and fast Rules-set in early going of inevitable widespread experimentation? Figure 23 establishes Free Castling, invented in 1992-1993 along with Falcon, now becoming more prevalent on large boards, whether King goes 1 or 2 over, and always going more at option. Chapter IV ''Symmetrical Expansion'' lays the groundwork for Scorpion, actually described here and publicized fully-definitionally in 2003 ''Passed Pawns, Scorpions and Dragons.'' Elsewhere copyrights show Scorpion, Dragon really invented 1996. Only one of several rationales within Chapter Five ''More Variants'' is illegal infringement of USP5690334 and accompanying copyrights. For example, Rook is still Rook if going 1-, 2-, and 3 steps only, but we would probably not object if someone implements new Falcon along with all fully-short-range movers like Squirrel, Dabbabah, Ferz. That raises the 20 claims of this patent that have never actually appeared in any website, other than USPTO itself online.

H. G. Muller wrote on 2008-07-21 UTC
```I put up the zip-file with Fairy-Max, a confiuration file including Falcon Chess, and the WinBoard_F GUI, all packed together as a ready-to play combination on my website. For those who want to try it out, the download link is:

http://home.hccnet.nl/h.g.muller/WinBoard_F.zip

(Beside Falcon Chess it also contains definitions for normal Chess, Capablanca Chess, the unspeakable variant, Knightmate, Shatranj, Courier Chess, Cylinder Chess.)```

George Duke wrote on 2008-07-16 UTC
```In response to recent inquiries> Falcon is interpolated from Rook Knight, and Bishop, not extrapolated. Falcon (including special case Bison--Bison being first implemented in patented Falcon 8x10,9x10,10x10) is of the implicate order, out of which RNB emerge, their template, vernacular cookie-cutter if one will. From another standpoint, RNB and F can be said to intersect at common origin, having further mutually-exclusive cells for destination. Knight can be awkward when children first learn Chess lessons at age 6. Knight is potentially confusing until broadening horizon and starting to see entire board(s). Bishop is awkward without using checkered bi-colour board begun in 12th Century.
Actually, undoubtedly the King came first. Knight, King and Rook are of course unchanged since 6th-Century Indian Chaturanga. But everyone knows (think Jungian archetypes) the first tiled patterns took tentative one-steps King-like through either triangles or squares. The plain checkered board came from fishing nets tens of thousands of years ago. Non-technological civilisations, more sustainable than ours,  and their tiles and nets and fields and stone patterns of geometrical shapes. Adjacent triangles have diagonals, like squares do, sides and vertices, so the Knight was not far behind, going through line and corner one each.```

George Duke wrote on 2008-07-11 UTC
```In  the standard model, the symmetry of the six quarks was established at CERN, Geneva, with finding of the top quark in 1998. Table of Quarks(Joyce, Finnegan's Wake 1929). The glue that holds Bishop, Knight, and Rook together, beyond mnemonics the reason why section two is so long, most skimming it still do not move Falcon correctly in application. The article itself thoroughly panned by the now-conventional free-expression artistic community here, but in the long run thoroughly necessary rudiments, even upon taking any act overseas.
SYMBOL    NAME     CHARGE         FALCON MOVE        O = Orthogonal
U         Up         2/3          Orth-Orth-Diagonal
D         Down      -1/3          Diag-Diag-Orthogonal
C         Charm      2/3          Diag-Orth-Orthogonal
S         Strange   -1/3          Orth-Diag-Diagonal
T         Top        2/3          Orth-Diag-Orthogonal
B         Bottom    -1/3          Diag-Orth-Diagonal
Top and bottom, the more charming ones called split block and split diagonal. The point would be that these are the movements, period,  not ''Camel away'' or ''Zebra away.'' Pawn 1 e4  d5  2 e4xd5 is common enough opening (imagine FRC), but we do not say Pawn moves to Camel square in two moves, or Pawn Camel away. Knight reaches Camel square in two, or Zebra square in three, but talking that way is secondary. (to be continued)
[For WB_F and F-M, my usual provider has chosen this week for major upgrade, so will contact easily next week conveniently the implementations. However, please have Scharnagl or other circles try it before I do right away, no problem.]```

Later