Comments/Ratings for a Single Item

While there are previous pieces, Duke, I submit my own in a line of all too
little used pieces with effects derived from personality:

Fox is cowardly. When attacked, he will defend himself. Fox is clever.
When another piece is attacked, he can move to any square attacking the
attacker. Dog is loyal. He must defend. Dog is aggressive. He must capture
otherwise, and attacked pieces are immobilized. Ox is stubborn. He will not
stop moving on a path, or standing still. Ox is industrious. He will keep
moving on a path, capturing any pieces. Frog is benign. He does not do much
when attacked. Frog is talented. He will do much when not attacked.

I still need to evaluate soon John Smith's answer to the one quiz question
he answered from the ten questions 3.September.2009. (Scroll all messages
here.) Now on piece-type values, here is a different approach. Let's say
Rook has an established value of 5.0 and Pawn 1.0. The board can be 8x8 or
9x9 or 10x10, and this will work. Instead of defining the type first,
establish the value you want, then design the type. If wanting a piece-type
value of 3.88 with respect to R50 and P10, surely there is a corresponding
inventable p-t. After all, it has been proven that piece-types are unlimited just as CVs themselves are potentially infinite. Joyce would agree, the principle of reasonably-moderate target values is one mainstay of for instance the ShortRange Project, just commented below. So it's not unheard of, but even desirable, to seek a value. You can draw from the lot of sliders, leapers, hoppers, and
contingency pieces compounded at will including multi-path. Bonus Question 11
then to the quiz of 10 is, (11) What p-t has the appropriate wanted 3.88?
[Click back ''all messages'' above for the first ten perfectly serious questions.  To remind the reader, there are #(7) ''Find a CV with railroads.'' and #(8) ''Find a CV with monkeys.'']

To add a bit - fox is ferz, from even 'Middle Ages' shatranj-chess large
board fusions; the dog is still hunting the fox; don't want to rune this
one for anyone, but; and I have to disqualify myself on the frog question.
Oh, yeah: railroads are found in a military chess variant, and monkeys are
found out in the open, under the sky. If you don't believe me, ask
Christine [just in case you weren't sure ;-)].

The Bobo. Let's see there would be 4 Bobos. The system is Bo Bishop, Ro
Rook, Ho Horse, ho-ho-ho bo-ro-ho, the three fundamentals. Systematization
is not insight, but we go along with it because of the European origin of
la mad queena, loca en la cabeza. Now BoBo is like double Bishop. Every
Bobo moves like a regular Bishop plus one more reverse-colour adjacent
diagonal to the ends of the board. There are four potential ''adjacent
diagonals.'' Crisscross. Crisscross. CC. CC. Where he is situated, there
are 4 orientations for the extra diagonal NE-SW up, NE-SW down, NW-SE up,
NW-SE down. We'll further simplify the notations later, but in the array
the four Bobos should of course replace Knights and Bishops like this,
using 'O' for Bobo: ROOQKOOR.  This piece-type makes what was the Bishop
into not being *colourbound*. There is no more need for one of the
non-colourbound fundamentals, Horse, herself overtly colour-switching,
because Bobo goes there too. Value? So approaching Rook as to become
indistinguishable. The next step in the chain of evolution of chess is to
find the perfect hybrid Rook-Bobo and therefore have only
King-Queen-RORORO, or by one equivalent indication King-Queen-XOXOXO. We don't know what that Rook-Bobo hybrid would look like but we can guess the likely name: Boob maybe by acclaim, or better just Book or Koob according to etymological culture; but the above BoRoHo fits logically best when you think about it.  The trouble is when once a name sticks it's hard to change, the very point of Moises' original question. When is
a Tic a Tac? Under what conditions? The beginning or the end? // By the way, Bobo is perfect case of name came first, that we talked about for CVs. This is a case more unusual of piece-type name first, then only then the piece-type fitting the name!
http://www.cmt.com/lyrics/laura-branigan/name-game/251807/lyrics.jhtml

Bobos number four, four piece-types. Bo-Bo is like double Bishop, but the
second is only 1/4 of the possibilities, yet fully 1/2 of a second Bishop's capabilities. There are upper left, lower left, upper right and lower
right Bobos(orienting from lower left). The extra diagonal allowed, adjacent and opposite colour,
removes colourboundness from Bobo. Let's call the 4, BoboUL BoboLL, BoboUR
and BoboLR for now. The standard Bobo array goes ROOQKOOR on 64 squares. There is no need for Knight any more. We can start to think about hybrid of Bobo and Rook. We don't know yet what that would look like. If we achieve hybridization, then there is only one piece-type, like Battle Chieftain,
 to go with King and Queen. Reductio ad absurdum, versus proliferation in some sense. Polar opposites with some sense. Because of often observed cumulative effect, operable most cases of lower-value pieces, the accrued value is not 3.0 plus 1.5 only equal to 4.5. Actually there is initially a damping for the 1.5 to maybe 1.0 if that, the half a Bishop leg, and thereupon, once that is guaged properly at (below) 1.0, the accruing to nearly 5.0, not quite to Rook, 3.0 plus a temporized ''1.0'' here compounds to 4.6, 4.7. These are preliminary, that we would still slightly give edge Rook to Bobo.  Bobo is a good-valued piece in a useful range, like Bifurcators or Bent optional second leggers, if Joyce would scale them back somewhat.

Footprint of the Bobo. Bobo derives from Bishop-Bishop, but standard Bobo
is 1.5 Bishops. The footprint of the Boboll, where 'll' is for the lower
left Bobo, from a starting standing square e5 is f6, g7, h8, d4, c3, b2,
a1, d6, c7, b8, f4, g3, h2 -- those so far are standard Bishop -- AS WELL
AS f5, g6, h7, e4, d3, c2, b1. Boboll is blockable so the pathway to the
latter b1 is through the e4-d3-c2-b1. The tag 'll' determines the
across-the-board diagonal from initial orientation of lower left. The other 3 Bobos also use ''lower'' orientation to find their respective
different additional diagonal, one for each. Identification is by the
suffixes upper(ul), lower right (lr), upper right(ur), and their names are
Boboul, Bobolr, and Bobour. The 4 Boboll, Boboul, Bobolr and Bobour are in
lieu of Knight and Bishop, because they are genuine hybrids of Knight and
Bishop. Hybrid is not compound. Compound is another animal, a different
concept. Compound of Knight and Bishop is Carrera Centaur(BN).
Hybridization takes visualization in a best sense from higher, or more spatial
dimensions, at least one more than regular 3-space. To hybridize N and B
gives the entity a whole new diagonal, not just the one spot we see as
Knight target square in 3 dimensions. Thus subsumed by the hybrid are what
were called Knight and Bishop. They are smeared across the others' paths. There are 4 orientations for this entity, hence
the 4 Bobos. The argument will be further developed as (time dimension)
allows. Now ''Bobo4'' will represent conceptually all 4 Bobos as if one
-- which are not interested in when thinking of the practical chess pieces. Further hybridization, namely of Rook and Bobo4, will yield the footprint of long-speculated Bo-Ro-Ho. For follow-up, Bo-Ro-Ho is now discovered and open to speculation on the whys and wherefores. One piece-type fits all.

Brainking has a new CV since I last logged on today, well, since I last
played a lot anyway. Behemoth Chess. The Behemoth introduces a random
factor. The indestructible piece moves 1-4 spaces in a random direction
after every player move and destroys everything in its path. The CV may be
imbalanced to Black. (Two kinds of imbalances, arrays and results, may be
loosely connected, but Behemoth has no unbalanced array.) The results at
Brainking so far. White wins 4537 for 47.16%. Black wins 4667 for 48.51%.
Draws 416 for 4.32%. That's not too scary. The imbalance is logical if you think about it. The Behemoth has to be somewhere, and to move first puts you more likely in the path.

I wonder if Brainking.com got permission from Donald?

Oh, yes, they mention him, Peter. I'll go over there and copy the wording.
''Behemoth Chess is a chess variant invented by Donald Seagraves and adds a random factor to the classic chess rules -- a Behemoth, which destroys everything in its path.'' -- their first sentence in the Rules
http://en.wikipedia.org/wiki/Over_There
Through Uwe Kreuzer Brainking was supposed to have Falcon
Chess, but I have kept putting them off, because Europe is well over there, as they said in World War I.
What I admire about Brainking is restricting to 37 Chess Variants making them very intensively played. What I dislike about Brainking is the lack of interaction among players or personalities. It's cut and dried like playing a computer only. There's no highlighting one or a few, or all, CVs for champions, but they have full ratings within each individual CV of everyone who ever played it.

Hybrid of Bobo4 and Rook? Bobo4 has four orientations in Boboll, Boboul,
Bobolr, and Bobour. The key to this hybrid is to ask, what Rook? So you
thought there was only one Rook. Not so. Now Bobo4 is hybrid (not compound)
of Knight and Bishop(scroll back this thread). It doesn't matter which
Bishop. It doesn't matter which Rook either, but you have to deal with
them one at a time. All this will be explained in follow-up if no one does
so first. The object is to specify which board squares comprise the hybrid
Bo-Ro-Ho. ChessboardMath is a specialty many mathematicians would not get
right away. Can a Rook always perform a tour whatever square he starts on,
or does it depend on the (required-)rectangular board size? Instead if Rook has to go directly to an edge, then aren't more board sizes tour-prohibitive from some squares?

http://www.chessvariants.org/index/listcomments.php?subjectid=ChessboardMath10.
Triangle/Triangle = Square/Square, Tetraktic in threes and fours like DNA.
Triangles afford readily natural movements of Queen analogue, but other
fundamental movements will differ according to interpretation, as in
Hexagons, such as throughout hexagonal Glinsky versus McCooey once at ''Pieces'' of Man & Beast 14 above:
http://www.chessvariants.org/index/displaycomment.php?commentid=25203.
Gilmanesque interpretation can have a field day, but one should
carry the day.   In triangles, Knight is logical piece-type leaping through one side and one vertex in the same direction. So Queen and Knight go to differing exclusive triangles from a starting square. On 6^3 Queen from corner reaches 19 of the 36 spaces and centrally Queen 22 of 36. Naturally Queen subdivides into Rook and Bishop. Unlike squares, triangular Rook and Bishop move in the same direction, but to different alternating cells. Put a board in front of you to follow logic of symmetry-separation for piece-types Knight, Bishop and Rook. From any starting cell, R, B, & N are mutually exclusive, as in squares. There is next the expected fourth fundamental, Falcon, fully present, having two destination-type cells but one being paired for three altogether, the two being two-way and the other solitary (central) one three-way. The larger the board, the lower percentage of triangles Queen reaches. The generic designer would not employ actual Queen as piece-type on 36 or 25, since she is too strong when reaching over half the cells. Start using Queen on 64 triangles, then ideally 81 and 100(10^3). By the same token, on 64 triangles (8^3), no one should be greatly interested in the exterior movement mode of piece-type B, which perfects elementary non-trivial Tetraktys (3^3, 9 cells).
ChessboardMath11, now for triangles, has isolated comment with 5x5x5 triangles sketched, 
http://www.chessvariants.org/index/displaycomment.php?commentid=25200, and continues CM10; the topic of triangles is in both -10 and -11.

Offhand the piece-types of Klin Zha Star Trek are at best ambiguous in
deliberate imitation of Martian Jetan. Lancer as ''1,2, or 3 unobstructed
spaces straight in any direction'' or Swift as ''2, 3, or 4
unobstructed spaces in any direction or combination'' may achieve reasonable
definitional clarity with no small effort. It is rude to write up rules
that way, dumping the interpretation on the player. Does ''any direction'' mean through and across each vertex as well as side? [Near the end, before ''Notation,'' it says no ''point-to-point,'' only ''side-to-side,'' for later comment.] Interior triangles with 3 others adjacent across sides, have 9 more across vertices, for 12 altogether. Whether pathways may retrace is unknown. Even once
ambiguity resolves, they are not very good inspiration as piece-types for
couple reasons. One, overlap in functionality with so many, including those
other than Lance and Swift, going to similar squares from a hypothetical common
departure square, each alternatively placed. Two, on 81 cells, there is nothing compelling about 3 or 4
spaces as the outer limit.  Why not five, or all the way across?  Klin Zha probably falls within a cross-category of ''from the outside-in'' without empathy for the carrying power of the spaces themselves and
the mode-units forced to follow more or less arbitrary rules. Whether or not Klin Zha's rules, once fully in mind, may have redeeming over-all coherence is left for follow-up to this preliminary appraisal.

It is just as easy to plan strategy in triangles (/_\s) as hexagons, and the more
basic triangles are more interesting than hexagons. In equilateral triangular boards,
Queen is broken down into Rook and Bishop, and there are the expected more than one
Bishop binding(details under review). Rook always starts a move across a side, and Bishop the
cell just beyond the accepted Rook side, she between his pathways so to
speak. Rook and Bishop move parallel in the same direction. Eventually Rook
could get to that Bishop's path-spaces one and all along the ways, but that
Bishop never could get to that adjacent Rook's cells. Two opposite Bishops pairwise never
will cohabit. For example, number 5^3 as 1;234;56789;10,11,12,13,14,15,16.
Then Rook at 17 moves along 18,10,6 to 3 if four-stepping. Bishop from 17
would go -10,5,2,1. All four longstanding fundamentals are there, but Falcon more than
the others needs practically at least 6^3. As well, more effective for 7^3 and up
would be long-range leapers (4,0), (4,1), (4,2), (5,0) etc. as the boards
enlarge. Of course all those have arrival cells beyond Knight and Falcon and between
Rook and Bishop. There is not the dual subdivision per quadrant between
Rook and Bishop of straightforward smoothed-out squares and rectangles.
Instead, all the ''oblique'' ones have the full set of spaces between
Rook/Bishop and Rook/Bishop, 120-degree separated, to themselves in any given
notional move from a same hypothetical starting triangle. It is better to
study the concepts on at least 8^3. In off-Chess science, as noted before, whether squares or triangles, ''oblique'' just means directions not Bishop-like and not Rook-like. So for instance in squares, along the Bishop diagonal is not oblique, as supposed to be in math.

Falcon first-steps like the Knight, but Falcon is always three steps and
blockable. In equilateral triangles, Knight leaps more in a straight line,
differently from squares. Knight leaps either through a vertex or through a side for
6 destination cells, not squares' eight. Where Knight goes through a side,
Falcon has three potential arrival cells, just described, 
http://www.chessvariants.org/index/displaycomment.php?commentid=25201.
Where Knight would go through a vertex, corresponding Falcon manoeuvre is called back-Falcon, who is three-way to the three logical spaces.  Falcon, front or back, can
never use Bishop's cells en route. The four basic moves, R-N-B-F quickly
become second nature in any regular geometry, square, triangle, hexagon.
http://www.chessvariants.org/index/msdisplay.php?itemid=MSfalconhexagona
Abdul-Rahman Sibahi already worked it out here in less manageable hexagons. With all the foregoing movement formulae, there is complete mutual exclusivity of arrival squares, with the understanding that Queen's assuming Bishop and Rook modes offsets appropriately their individual infinities.

Few CVs have triangles. They work symmetrically for two-player  .
Chess as well as three. Here is suggested starting array   1-> ._. 
for what is called to right 8^8^8 in 64 cells.   234->        ._._. 
K50,64. Q51,63. R37,38,48,49.                  56789->       ._._._.    
The first are Black and second half White.  10 to 16->      ._._._._.
B26,27,35,36. N17,18,24,25.                 17 to 25->     ._._._._._.
Pawns in front 1 or 2 step, then 1 only.    26 to 36->    ._._._._._._.
Promotion zone Black is triangles           37 to 49->   ._._._._._._._.
4,9,16,25,36,49,64, and White across        50 to 64->  ._._._._._._._._.
correspondingly. All F.i.d.e. rules apply. Notice maximum Rook move is same 7 cells as in squares. Rook's path from corner 50 is 50-51-38-27-18-11-6-3. In these equilateral triangles, the return path is different, 3-2-5-10-17-26-37-50, with all the implications.  Jonathan was on the right track at Spratt's Chess for Three: 
http://www.chessvariants.org/index/displaycomment.php?commentid=18123.

.         6^6^6 is enough to look at Rook's movements in
  #  1->     ._.      I triangles. Starting at 26, -27-18-11-6-3 is five- 
 # 234->    ._._.    II stepper, ever fully being blockable. Returning is
56789->    ._._._.  III is 3-2-5-10-17-26 in different back-path to same 
10-16->   ._._._._.  IV cell. There are two Bishop bindings. Bishop has
17-25->  ._._._._._.  V pathway 26-17-10-5-2-1. This Bishop cannot reach 
26-36-> ._._._._._._.VI triangles with an odd sum of (Level + Cell). She
is the corner Bishop, and the other Bishop is the odd Bishop, as with the above six-sided and all equilaterals. Rook reaches eventually every triangle, and Bishop half of them. As n increases, the corner Bishop gains one each level. For example on 11^11^11, which is 121 triangles, the corner Bishop reaches 66 and the odd Bishop 55 for strategic planning. More primitive triangles are more normal than squares. [66 and 55 are now correct without other's comment.]

0       .          Boards need colouration ideally for clear two Bishop
  I      ._.         bindings. Each level adds 1 more corner binding 
 II     ._._. 2-4    than odd binding: 1-0; 3-1; 6-3 by Level III left.
III    ._._._. 5-9   By 11^11^11 there are 66 Black and 55 White cells,
 IV   ._._._._.10-16 correcting previous. In the event, the corner Bishop
  V  ._._.X._._.     has significant edge in piece-value vis-a-vis odd
 VI ._._._._._._.    Bishop. They could also be called exterior Bishop
VII._._._._._._._.   and interior Bishop.   Place Knight at 21 Level V,
which is a corner Bishop cell, marked X. Wherefrom Knight has 6 arrival
squares, one each through side or vertex to 7,10,16,28,34, and 43. To
Knight it makes no difference in the ''feel'' whether side or vertex.
To Falcon, however, there is slight difference, as should already be evident. That
covers Queen, Rook, Bishop and Knight in perfect equilateral triangles.
Rook, Bishop and Knight are mutually exclusive essentially by nature in any
worldly geometry. [''Geometry'' invokes Kepler who established Plato's that God geometrizes. Corresponding sixty-four Modern Queen Chess was already 100 years old when Tycho Brahe hired Kepler to work at Prague in 1600. Close: Tycho's model had Sun and Moon revolving Earth and the other planets revolving the Sun, but he did replace Ptolemy's sky chart, which everyone used all 1400 years. Also the same exact year of 1600, Bruno inquisitionally had jaws spiked shut through the palate and by cloaked priests known as the Order of Mercy and Pity was bound, stripped and burned at the stake in holy Rome. Afterword: Having refused to recant, ''He could say to himself something that Galileo should have said, but did not say -- 'Nevertheless it does move.''']

http://en.wikipedia.org/wiki/helpmate. Linked, the last sentence of history spells out Helpmate as next in prevalence after Direct Mates.
/// http://www.chessbase.com/newsdetail.asp?newsid=6768. Talk about off-topic is Nunn's Sagittarian Trifid Nebula.///
Now composers go to great lengths to author/create odd board positions in
constructed Helpmates out of the so many millions possibilities. Actually,
the starting point for the 100-year-old field should have been the
500-year-old array itself, RNBQKBNR, the thirty themselves.  Consider that the field has not really begun until this moment.  Helpmate operational definition: Black does utmost to assist White.  Long-known from initial position is that thus Black Queen mates in two. Now we formalize: White Queen mates in three from initial array.  White Bishop-f1 is Helpmate in 3, as is Black Bishop-f8. The latter could go: 1 f3 e6; 2 g4 B-e2; 3 (N-c3) B e2-h4 Checkmate. Bishop on h4, or g3 if h2 moves, is checkmate after f3 and g4 in either order without White King move, and there are many actual move sequences solving the condition.  White's particular '3 N-c3' is one such precluding the King step. Okay, Black Queen takes 2 to mate, White Queen 3 to mate, Bishop-f1 3 to mate, and Bishop-f8 3 to mate. That makes four solved cases of the 30 from array.  Next, in how few can Rook-h1 mate?
There are the two styles or cases, assisted and unassisted, in this further development of Orthodox Helpmates.  These are all going to be extreme unassisted, 
http://www.chessvariants.org/index/displaycomment.php?commentid=26767.