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(21) Posted by Rosie Fay [Wednesday, Jul 28, 2021 08:07]

I found two 5-unit directmates which PDB claims show the Banny theme in the first 3 plies:

Martin Wolfgang Hoffmann
Variationen über zwei dreizügige Mattführungen mit dem Turm, 1976
P1132755
(= 4+1 )

8/8/2P5/8/k1K1R3/8/2P5/8
#3

Tries: 1 Re2? {A} zz Ka3 {a} 2 c3 zz Ka4 3 Ra2#, but 1 ... Ka5! {b};

1 Kc5+? {B} Ka3! {a};

1 Re3? Ka5!;
1 Re1? (thr 2 Ra1#) Ka3!;
1 Re8? (thr 2 Ra8#) Ka3!;
1 Re5?/Re6? zz/Rd4?/Rf4? zz/Rg4? zz/Rh4? zz/c7? zz Ka3!
Solution: 1 c3 zz
Ka3 {a} 2 Re2 {A} zz Ka4 3 Ra2#;
1 ... Ka5 {b} 2 Kc5 {B} zz Ka6 3 Ra4#
---------
François Fargette; Bruno Fargette
1478 Themes-64 43, Jul 1966
P1142958
(= 4+1 )

3k4/3N4/3K4/8/8/3S4/8/3B4
#4

Tries: 1 N3e5? {B} zz Ke8 {b} 2 Be2 zz/Bg4 zz, but 1 ... Kc8! {a}

1 N3c5? {A} zz Kc8 {a} 2 Be2 zz Kd8 3 Ne6+ Kc8 4 Ba6#; 3 ... Ke8 4 Bh5#, but 1 ... Ke8! {b}
Solution: 1 Be2 zz Kc8 {a} 2 N3c5 {A} zz Kd8 3 Ne6+ Kc8 4 Ba6#; 3 ... Ke8 4 Bh5#;

1 ... Ke8 {b} 2 N3e5 {B} zz Kd8 3 Nc6+ Kc8 4 Ba6#; 3 ... Ke8 4 Bh5#

(Is Black's first move in each try-line moot?)

Not sure comparisons with Nim will be useful. In Nim (as in all impartial combinatorial games) if a position isn't itself zugzwang, the best move from it is to a zugzwang position. (A combinatorial game is a two-player game where the players take alternate turns and there are no random or hidden elements. It's impartial if any position which can occur with A to move can also occur with B to move, and the sets of legal moves are identical in the two cases, and if the game is over then the respective outcomes for the respective turn-players are the same.)
 
   
(Read Only)pid=21400
(22) Posted by Juraj Lörinc [Wednesday, Jul 28, 2021 09:14]

As a response to Andrew's idea I dare to point a basic treatise of new-strategical school contained in Conflictio issues 13-17 and 19-21*. Juraj Brabec** explains main ideas of changes of play and move functions, together with three different formal systems describing them (Z- notation, MOVR notation and tables). Banny theme appears in the system in the issue 20 (look for symbol BAx-BAx-), it is one of basic themes in the area of move function changes (that starts in the issue 17). It is a very good example of what is called anti-paradox, hinting non-paradoxical nature, as pointed earlier in this thread.

* Previous Conflictio issues available at https://juliasfairies.com/articles/#conflictio
** Juraj Brabec wrote his text in Slovak, using Slovak terminology, and I was trying to translate it into something like English, with some obvious terminological difficulties.
 
 
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(23) Posted by Andrew Buchanan [Wednesday, Jul 28, 2021 11:20]

Rosie said:
 QUOTE 
Not sure comparisons with Nim will be useful... impartial...

My intended point was just to show that Banny is extremely common. So I showed the most trivial instance. I had thought about generating instead a partizan game position which does the same. E.g. red-blue-green Hackenbush, https://en.wikipedia.org/wiki/Hackenbush, where the three stacks are now G RG BG. So Red can remove R or RG but not just G from the middle pile. But the additional complexity would have served no purpose.

Clearly, impartial games can't cover all of the alphabet things, because threats (which many of these alphabet things contain) can't be embedded in an impartial game - the opponent could play the threat instead!

It's obvious that chess problems differ from chess in the notion of the clock, and hence the game tree gets pruned savagely. But it's less obvious that alphabet chess problems differ from other chess problems in the significance of the notion of *move* being valid across multiple positions. Nim and hackenbush both have this notion of move. However a general game (defined purely in terms of left & right options) does not, as a move is only defined locally as an option in the context of a particular game state.

Juraj: do you plan to find a permanent home for these ideas being described in sequential issues of Conflictio?
 
   
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(24) Posted by Juraj Lörinc [Wednesday, Jul 28, 2021 20:53]

Andrew: The series of 8 articles mentioned above was actually written on my impulse as a brief summary of theory explained in the Juraj's book "Za všetkým hľadaj motív" (can be translated as "Look for motivation behind everything"). Unfortunately, it is written in Slovak and thus largely difficult to read for composers abroad, even if I recommend it in my extended English review in Conflictio 9 (https://juliasfairies.com/wp-content/uploads/conflictio_009.pdf).

Why the name of the book? My view: "Thematical area of changes is often accused of formalism. The authors are said to concentrate too much on the algebraic description of the themes shown in their works. But almost anyone working in the style of new-strategical school could retort that behind every formal theme there has to be a motivation, and this is actually often more important than tables or patterns accompanying solutions. This is in my view the main reason for choice of the book name. Look for motivation behind everything."

So the book covers both formal themes, systemise them, notation of themes and also provides large amount of examples showing that motivation is important and even alphabetic themes can be beautiful in the classic strategical sense.
 
   
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(25) Posted by shankar ram [Wednesday, Aug 4, 2021 14:03]

One recent example of Kontrawechel/Banny in an S#2 using the fairy condition Breton (When a piece is captured, a piece of the same kind of the capturing side, if any are present, also disappears):

Udo Degener, FA1903
StrateGems 2020
(= 10+10 )

S#2
1.Sc6 A (zz)? Bd2 b 2.Qd8+ C Kxb7 (xb1)# but 1…Sd2 a! (1…dxc6 (xb1) 2.Bb8+ Kxb8 (xc1)#)
1.Sa6 B (zz)? Sd2 a 2.Qd8+ C Kxa7 (xc1)# but 1…Bd2 b!

1.Qd8 C (zz)!
Sd2 a 2.Sa6+ B Kxa7 (xc1)#
Bd2 b 2.Sc6+ A Kxb7 (xb1)#
 
 
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