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Falcon Hexagonal Chess. The Falcon into the Hexagonal world. (Cells: 121) [All Comments] [Add Comment or Rating]
Ezra Bradford wrote on 2008-08-07 UTC
I wonder about a more Wellisch sort of Falcon. This one would make three steps, divided in the customary Falcon way but between any two adjacent wazir directions. It can move to any of twelve squares, each along any of three paths. These twelve squares are exactly those reachable in three wazir steps but not hit by rook or Wellisch knight (Glinski ferz), analogous to the rectangular Falcon's sixteen destinations that are those not reachable by rook, bishop, or knight within three steps (wazir or ferz) of the origin.

George Duke wrote on 2007-09-15 UTC
[Before going on to 'noncolourboundedness' etc.] 'Triangulate' is just defined as three moves returning to the same square as in the ordinary OrthoChess term itself we overlook. It means no more or less for exotic CV pieces. In '91.5 Trillion..' article, in a different concept using the name, we have a new Mutator defined in Rule Number 13 called 'Triangular Transference': 'Three same-side pieces that form a right triangle positionally, even if 2 or more are adjacent, mutually transfer the moving power of those 2 pieces that define the hypoten(e)use'. For another clarification, CGilman's latest Comment's last sentence assumes everyone well understands there are four(4) Dabbaba bindings in squares. To the question of 'significance', on Sibahi's and Glinski's hexagonals, one already stated is for the problem theme of Tours reaching every hex. The verb 'to matter' can have as wide or narrow scope as you want: bindings, or alternations among them, *matter* foremost for just their mathematical reality one supposes. In a case, maybe it *matters* to move in three not to same square (1,1), as in triangulating, but instead (1,2) or (2,1)-- using our notation for squares as blocks not steps: thus(1,2) is Wazir step one-path, or leap.

Charles Gilman wrote on 2007-09-15 UTC
Colourswitching is something that I first read about on these pages (for
and understood very quickly. The significance is that if a piece
alternates between two bindings, then the one that last moved from is the
one that it will next move two. You can glance at a Knight at any stage of
a square or cubic game and correctly predict that after it has made [insert
number] more moves it will be on a [insert light or dark] cell. It was
analysed long before I knew anything of it. What is the significance of
moving from one for another of three bindings, or even four? The King
(once it can no longer castle) always moves to a different Dabbaba
binding, likewise the Gnu, but both can triangulate. Moving between
Dabbaba bindings matters only to the likes of the Ferz and Camel, which
alternate between only two of these.

George Duke wrote on 2007-09-14 UTC
[Taking exception to Gilman's 'never has a switching property' for a later Comment, let's start with basics:] With also ARS's indulgence, the colour changes get interesting in hexagonal. In squares the categories Slider, Leaper, and Multi-path are descriptive enough that we usually omit a colour-describing trailer. For example, a Dabbabah-Rider is understandably colour-bound. Most of us are content with using 'colourbound' for such as Bishop and Camel too. Easily understood. On the other hand, we hardly bother with 'colour-switching'...except Gilman. Now Knight is 'colour-switching', an informative description, in that each successive move alternates White to Black, and we would like to preserve the quality and integrity of the definitions from squares to hexes. First, in hexes new adjective 'colour-changing' we propose for a (mandatory) move to either of the other 2 colours, as with Glinski-FHC Knight and Falcon both. By their three-colour alternations they can reach every square, a desideratum for design. Please refer to the extended definition of 'colour-changing' in our earlier Comment. The famous problem theme of Knight Tour and Falcon Tour becomes possible when all squares and/or hexes can be reached. Are there 1000 possible Knight tours on these 121 hexes? Are there 10,000 Falcon tours on ARS's 121? We have no idea immediately even an approximation the answer to this topic for research. ['Noncolourbound' also to be taken up separately]

George Duke wrote on 2007-09-13 UTC
Colour-changing is well-defined in my Comment about hexagonal Falcon: it just may not be Gilman's term. Broadly 'Non-colourbound' has unique meaning when there are three colours, so 'changing' seemed to be better as a new term, when making a second Comment about FHC. I noticed Gilman's 'colourswitching' without even trying to get his full Comment and then approached the Knight-Falcon-tour idea from that colour-changing vantage to highlight one ordinary feature. I need to review the distinctions here, because they seem interesting in this context, but they appear descriptive not evaluative, and not what someone designing would dwell on for piece-move choices, involving as they do a Move 2, Move 3 and so on. Okay, Charles, I will organize the concepts and get back, and the last couple sentences may be somewhat off the mark. 'Note that it's colour-switching like the Knight' in the text may be ARSibahi usage exactly like ours above using 'colour-changing', and it just does not happen to be Gilmanese: we are not sure whether your particular 'colour-switching' has caught on.

Charles Gilman wrote on 2007-09-13 UTC
Well, coincidences do happen, I suppose. It did look uncannily like a reply
to my original comment, which was referring to the 'switching' in the
text. I'm not sure what 'changing' means in this context. Is the Rook
colour-'changing', or the King, or the original Falcon, or the Cardinal,
or the Gnu? Is it, in fact, simply a synonym for non-colourbound?
	Note that I am not criticising the variant, only pointing out that a
symmetric hex piece never has a switching property, regarding multiples of
2 or 3 or any other number of moves. It can retract its last move (return
in 2) or triangulate (return in 3), and any larger number of moves can be
a sum of multiples of those. I also like how this page hints at an
exploration of hex analogues to square-board pieces and where they break
down - the conflicting orthogonal and diagonal definitions of 'Camel',
for example.

George Duke wrote on 2007-09-13 UTC
I had not even read Gilman's (nor Joyce's) Comments when rating FHC 'Excellent'. Aware of FHC for six or eight months now and already having opinions, the point of our Comment is that a Falcon's tour is possible. We credit Abdul-Rahman again for a job well-done in adapting the 15-year-old fourth fundamental square-board Chess piece to its reasonable, probably optimum, Hexagonal counterpart. Our word is 'colour-changing' not 'colour-switching'. Now looking over Gilman's, they seem to be analysis without the evaluation, that's fine.

Charles Gilman wrote on 2007-09-13 UTC

George Duke misses my point. Switching has nothing to do with reaching the entire board. Consider the following pieces on a square board:

The Rook is neither bound nor switching, but can reach any square in an odd or even number of moves. Likewise the Falcon, as stated above in contrast to its analogue here.

The Camel is both, as it is bound to a single Bishop binding, but that binding comprises two Dabbaba bindings of which the Camel always moves from one to the other. Likewise the Ferz.

The Halfknight (Heavenly Horse) switches between the Bishop bindings but is bound to alternate ranks, a binding which is also a pair of Dabbaba bindings.

George Duke wrote on 2007-09-11 UTCExcellent ★★★★★
It should not be necessary or desirable to change Knight to Gnu just to complete access to some surrounding set of hexes. As it is, Falcon being colour-changing goes from 1 of 3 'colours' to either of the other 2. Then whichever colour of those two it reaches, from that arrival square, now the new departure square, Falcon again follows the pattern of going to one of 2 colours other than its own very departure-square colour. Following through with a large enough sequence of moves Falcon, like Knight but unlike Bishop, can reach every hexagonal space on the board. Great concept.

Charles Gilman wrote on 2007-09-11 UTC
Sorry to have taken so long to get round to commenting, but I've been busy. The concept of colourswitching doesn't really work on a hex board. The significance of this property is that alternating between a board's only two colours prevents a piece 'losing the move', that is, gaining positional advantage by returning to a cell in an odd number of moves. On a hex board all fully symmetric pieces can do this, because there aren't just the two colours. Indeed they can do it in three moves forming an equilateral triangle, even if that means using cells of all three colours.

George Duke wrote on 2007-09-10 UTCExcellent ★★★★★
Thanks Graeme, for excellent Preset. Abdul-Rahman has it right since we have exchanged information on Falcon Hexagonal Chess since beginning 2007.

Joe Joyce wrote on 2007-09-09 UTC
Hey, Graeme, yeah, I've seen that rationale, too, but I don't believe it's valid. [I still figure that these things are usually done by chessplayers that have been so conditioned by the external trappings of FIDE that they often unconsciously bring them along.] My last post was already overlong, so I didn't add this part - figured I'd do it if someone said something. 

I'd argue a better extrapolation would be to note pawns promote on the rank behind the one their opposite numbers start upon. The 'parallel neighboring diagonal' lines the pawns would be set up on are, in color/shade D-L-D-L..., the promotion lines would be the 2 'parallel neighboring diagonal' lines directly behind the setup, colored/shaded L-M-L-M-L-M... This allows each pawn to move directly forward to its own promotion hex. 

This is a general 'argument' [ie: discussion] about the best spots to set up pawns in hex chess variants, and is in *no* way meant as any sort of criticism of the fine game upon whose page this discussion appears.

Graeme Neatham wrote on 2007-09-09 UTC
'I've never understood why they are set up in two 'V's with the points almost touching and the legs extending away from each other.'

I'd always thought the main idea behind the pawn positioning was to have them start the game equi-distant from a promotion hex.

Abdul-Rahman Sibahi wrote on 2007-09-09 UTC
Graeme .. Thanks for the rating and the diagram! And no, since the Falcon Chess patent only covers the Square version. (You might want to include the 'Gnu-instead-of-Knight' variant, but it's your choice.)

(Speaking of ZRFs, the variant in the following link might interest you as well.) Link

Thanks again ..


Thank you for the comment.

As for the pawn structure, this game was intended as a re-modeling of Glinski's Chess to include the Falcon. So almost all the setup 'ideas' are borrowed from that game. As I understand the philosophy of Glinski's Chess, this setup ensures that all pawns are protected (they protect each other,) AND that all the pieces can move in the opening setup.

Your idea of the zig-zag line was used by Christian Freeling in HexDragonfly. It is probably just as workable as anyother setup. Link

Joe Joyce wrote on 2007-09-09 UTC
Very nice adaptation of Falcon to hex, Abdul-Rahman. It appears very traditional [if I may use that word for something as new as hex chess], but you obviously did some thinking about the game; you trimmed the 6 corner hexes off the board. [And Graeme's graphic does justice to your game.] Even though I have very little experience in hex chess and have great trouble wrapping my head around the 'diagonal'move in hex games, this one looks like fun to play.

I do have one question about this style of hex setup in general, though, and that's with the pawns. I've never understood why they are set up in two 'V's with the points almost touching and the legs extending away from each other. The distance between facing pawns ranges from 1 to 6 hexes. To me, this destroys the whole pawn skeleton, a major part of chess. Further, this setup exaggerates the values of the center pawns and diminishes those of the flank pawns, as far as I can see.

Has anyone tried the following? The 3 hex board colors can be called Light, Medium, and Dark. The pawns are now set up in an orthogonal line that goes L-M-D-L-M-D... Drop the 3 center pawns back 1 hex each. Move the 2 end pawns on each flank up 1 hex. Now, you've moved 7 pawns per side 1 hex, and the pawn lines are each along two parallel neighboring 'diagonal' lines. The pawns are now set up on an L-D-L-D-L-D... 'wavy' line. This puts all facing pawns either 3 or 4 hexes apart, in an alternating pattern. This gives a more 'chesslike' pattern to the pawn setup, and gives up very, very little, just the possibility of matching an opponent's double step pawn move with one of your own on occasion. Practically, the 1 step reply still results in the pawns blocking each other along the centerline of the board.

Graeme Neatham wrote on 2007-09-09 UTCExcellent ★★★★★

Always happy to see a new hex variant. Would it infringe any patents if I produced a zrf for this?

BTW here's a not-quite-so-ugly graphic:

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