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George Duke wrote on Sat, Mar 3, 2012 04:51 PM UTC:
TABLE OF SOVEREIGN VALUES (XI) (reformatted 25.11.13, all earlier still to redo)
P/T         P/V    Mate#
STAG        3.0    2
EAGLE       3.5    2
PEGASUS     6.0    1
UNICORN(ii) 7.0    1
PRIEST      2.5    4
OGRE        4.0    2
ASSASSIN    7.0    1
BALROG      9.0    1
SEERESS     4.5    1
CROOKED BSP 3.5    2
When is the board too small to mate?
  Some long-range leapers will be inhibited by 8x8
   to the point of banishment.  Since only one piece-
   type is featured at a time for worthwhile cal-
   culation of p/v and mate number, one's King sort
   of alone has to keep the other King from staying    at the centre.  Basically, that will not work if
    the leaper itself cannot reach d4, d5, e4, e5 on 
   8x8.  Take Gilman-named Rector who leaps distance   of '4,5', an obvious p/t unexpected to use much
   except maybe compounded. Just as with Flamingo the
  1,6 leaper and several others, there are central
squares unreachable -- in case of Rector conveniently exactly those four.
It is methodologically unfair to assume Black King does not start there,
and White King cannot keep such-positioned Black from going back and forth
some two available ''orthogonally'' adjacent squares. Control of tempo
does no good here because however many Rectors, Black stays out of reach.
So Rector the 4,5 leaper cannot be Sovereign Piece-type without any
reliable mate on 64 squares.  In the Sovereign System, the boards are important inclusively 8x8 to 12x12, including 8x10 and all other rectangles in between.  If a p/t fails a Mating test that range, no Sovereignty. For follow-up, what are the 28 Sovereign Boards?  Or really 51 with the Pawns reversed?  
Also for eventual follow-up with another Table construction are cases of separate Sovereignty, where one or two additional units of a Sovereign piece-type may be necessary the larger boards, for which Paulowich links the 12x12 thread,  
Http://www.chessvariants.org/index/displaycomment.php?commentid=20099.

George Duke wrote on Sat, Feb 25, 2012 04:30 PM UTC:
TABLE OF SOVEREIGN VALUES (X) Chemical valence numbers, indicating
P/T             P/V MATE#   reactivity by how many electrons in the
OVERTAKER       2.0  3      outer orbit, vary 1,2,3,4,5,6 to 7, and
DIAMOND WARRIOR 2.75 2   predominate at 1, 2, 3 and 4.  Carbon has
LION MAN        4.50 1   '4' valence, the basis of organic chemistry.
GRAND BISHOP    4.0  2   Likewise Mate Numbers in component squares
MAGE            5.5  1   forming rectangles over 7x7 have the same
CARDINAL(i)     4.5  1   double breakdown into 7 and 4.  Part of the
FORT            6.5  1   reason is the same eight possibilities 
FROG            4.25 1   towards completion, of either orbitals or
ROC(i)          8.0  1   diagonals/orthogonals, and that any occupied 
MOONRIDER       8.0  1   state has had already to choose one and only one.
That is, insofar as a stationary piece or atomic species' energy level has
''chosen.'' This paragraph at this point should be taken metaphorically
for viable exploratory channel. There is potential to reduce atomic orbital
theory from three- and higher-dimensionality to just the two- by
equivalence to empowered chessic movements confining resolution.  Each
numeric pair ought always to be unique in ToSVs for one exclusive type
being elucidated.  Ganymede and Altair featured have not preponderance
conventional p/ts. There is neither effort to get standard or popular name throughout ToSVs.  Whatever first naming occasions stays with the p/t defined by its two refinable values here, or across disciplines as well. So also tolerating such as Ganymede Cardinal(i), there being other Cardinals, but not Bishop-Knight compound who will appear staying as Carrera's Centaur.

George Duke wrote on Tue, Feb 21, 2012 04:46 PM UTC:
TABLE OF SOVEREIGN VALUES (IX) Take a really Meshuga compound of duals,
P/T        P/V Mate#   meaning any such bi-compound beyond Gnu and
WOLF-RIDER 5.0   1     and Man, the first two.  Add Knight to it,
WARRIOR    2.25  4     say the third dual-compound Zebu is chosen to
JAGUAR     2.25  4     get (Zebra + Zemel + Knight), who is Knighted
PANTHER    2.25  4     Zebu, a tri-compound more practical than awkward
COYOTE     2.25  4     Zebu bi-compound.  Because of the spacing of 
WOLF(ii)   2.25  4     three supposedly cooperating legs, it still 
LION       2.25  4     takes the three of the Knight to describe 
TIGER      2.25  4     SOVEREIGN Knighted Zebu(8.0, 3), tested by 
BEAR       5.5   1     mobility. Sovereign Boards are 64-144, and this
CHEETAH    2,25  4    tri-compound of (N+Z+Zemel) all-leaping really
practically needs 121-256, so will not be tabled formally.
How about plain vanilla Zebu?  Squared and squired on 100-256 is Sovereign Zebu(6.0, 4).  To justify the piece-values, Knighted Zebu on 100 centralized reaches 24 squares matched to Rook's 18 there; and Zebu leaps to 16. Yet Rook Mate# is 1 and the higher piece-value ones have Mate#s 3 and 4.  So piece values can be high, or higher, over 5.9, and accompanying Mate#s over 2.  
    Looking at examples upsets somewhat the first impression of some kind of reciprocal, or inverse, relationship P/V to Mate#. As piece value rises Mate Number often or usually falls as generality, but there is no simple relationship that always holds. Mate# is positive integer and piece value rational number.      
Another example from the only five at most significant compounds of duals follows.  Antelope has dual Namel, and the bi-compound Namu looks like Sovereign Namu(5.0, 4) suiting boards 100-256; the leapers involved are (3,4) and (1,7) for squares they reach.
Eventually after several hundred p/ts, M&Bxxs themselves beginning with the Ungulates chapter p/ts the afore are representative of, can be computed for sovereign tables. ''Lions and Tigers and Bears'' above are Fantasy Grand Druids as well as 'The Wizard of Oz'.*
Many, many questions are raised for follow-up how V piece value, M mate number, and Z board size interrelate, with opposing King inviolably eight-directional. For all we know, there may be a relationship to chemical valence numbers, where 1,2,3,4,5,6,7 are the values, 7 maximum the main groups, and 1 to 4 predominating -- exactly like these Mating Numbers.
*Caution: cozy(?) 'tWoO' author Baum's virulent racism towards genocide, http://en.wikipedia.org/wiki/L_Frank_Baum.
Http://www.wendyswizardofoz.com/script8.htm.

George Duke wrote on Tue, Feb 14, 2012 08:37 PM UTC:
TABLE OF SOVEREIGN VALUES (VIII)The Mate# is accompanied by Piece Value,
P/T            P/V  Mate#  neither stand-alone.  Of course in most embod-
GIANT          3.0  3      iments, there will not be so many as three or
CYCLOPS        4.5  1      four of a piece-type at once.  That indicates
COLOSSUS       5.5  1      Mate# of 3 or '4' or more conveys something
2-HEADED CYCPS 7.5  1      of an abstraction.  Piece-value and Mate# 
BEHEMOTH RIDER 5.5  1      mutually refine each other in the Tables
TITAN          5.0  1      towards more complete understanding over-all 
WARLOCK        4.0  2      value.  Not to design more, or the most, of 
OGRE           3.75 2      one or the other value, but to uncover intrin-
ASSASSIN       7.0  1      sic mechanisms of differing conjugal types,
BALROG         9.0  1      and even randomly-related types. Actually,
Mate# of 1, and also Piece Value greater than 6.0 -- those two as separated
attributes in general for the moment -- are harder for designer to
implement successfully.  Examples of Mate# '1': both Queen and Rook tend
to dictate their own effective counterparts and environment.  They of Mate
Number '1' require compatible rules and other p/ts, and seem to enlist
those p/ts of order '2' and '3'. '4' and 5, to revolve around them. At their extreme, '1',
able to Mate with just King, they channel to the point of delimiting, what else belongs the given CV rules-set, whether conscious to designer or not.  Exclusively Fantasy Grand in Table 8 has numerous 'Mate#1's; Mate# 1 can be expected to accord with range in value from 4.0 to 12.0.

George Duke wrote on Fri, Feb 10, 2012 04:43 PM UTC:
TABLE OF SOVEREIGN VALUES (VII)  Sovereignty is considerably inclusive.
P/T        P/V    Mate#  There has to be the effort to get the crucial
CHIEFTAIN  12.0    1*    connecting values.  Usually dutiful play-
DWAR        3.25   2     testing uncovers the preliminary approximations.
FLIER       3.0    2     For inventive/aesthetic artisty to actualize
PADWAR      2.0    3     in the real world, the numbers have to be
WARRIOR     2.25   3     generated and assigned under scrutiny.  What
UNICORN     9.0    1     purported pieces are found not to be SOVEREIGN
BENT SHAMAN 3.0    2     PIECE-TYPES? Medusa, Promoter, Coordinator,
JESTER      2.5    3     Warp Point, Black Ghost, Bulldozer, Medical
WARRIOR(ii) 3.0    2     Service Unit, Ghast -- moveable all without 
LOREMASTER 12.0    1*     Sovereignty.  However many each, they cannot
Mate.  They and their ilk are all something else, call them Effectors,
more so into the Board-complex they be, as shifting environment. 
     The such exclusions tend to be demonstrably 10% of manifest units.
The preponderance 75% piece-types in consideration are subdividable between Pawn and Piece.  If array-factor advantages are necessary to get Mate, the however-multiply-coordinated unit is no Sovereign Piece-Type, rather Pawn-type.   
Each pair out of Pawn/Piece/Effector creates topological interface for three all together.  There inhabit remaining over-10% moveable-types debatable what they represent. In those present regions of indeterminacy, for advanced consideration is Black Hole effector or Piece?  Perimetre Rook arguably Sovereign?  General Staff a piece or enabled-Pawn requiring back-ranking?  
Tabled, this Sovereign Jester(2.5, 3) is King's Court, Warrior(ii) Fantasy Grand, which will have up to twenty more p-ts, two tables unto itself.

George Duke wrote on Wed, Feb 8, 2012 04:42 PM UTC:
TABLE OF SOVEREIGN VALUES (VI) There are not so incidental variant Kings
P/T          P/V      Mate#  and win conditions among thousands of
DIMAECHAER   3.5      5      presentations by the modern CV artists.
HOPLIT       3.5      5      King, however, is remarkably stable across
HOPLOMACH    3.5      5      all forms, Xiangqi to current f.i.d.e.
RETIOR       3.5      5      OrthoChess.  It figures that 'Mate#' is
PEGNIOR      3.5      5      mandatorily one of the two numbers com-
SAGITTAR     3.5      5      prising the complete SOVEREIGN VALUE. Each
THRAEX       4.0      4      SOVEREIGN PIECE-TYPE has both its piece
VELES        4.0      4      value V and Mating Number M. One-stepping
RANGER       3.5      2       King, the four directions become eight, 
SPEARSMAN     3.75     2       power and vulnerability -- eternal 
attributes.  From first conception in East/South Asia two millenniums
ago, one King per side and how to run Him down, emulating own's own; today more scientifically
the question exactly how many attackers sufficient, expressed in the
Mate#. Mate# is generally stable across boards 64 to 144: 1,2,3,4,5,6, or 7, or interesting cases to come findably higher, legitimately Sovereign. However, that should not be read as *always* the same between extremes 64 and 144 for a given specific piece-type, just usually so, and convenient to begin assigning values. Two numbers then complete definition a p-t, V and M, without which name and definition by themselves represent mere art for art's sake.  Bifurcators above again, the eight more, attain clarity
attacking/capturing/mating first leg; the challenging other half of them
capture second leg and may all have Mate# '5'(provisional).
'Provisional' in that subject to determining for sure whether fixed checkmate set-ups each bifurcator are attainable in practice against Black best play. This Spearsman and Ranger are Outback Chess.

George Duke wrote on Tue, Feb 7, 2012 04:44 PM UTC:
TABLE OF SOVEREIGN VALUES (V) Bifurcators have clearer mates when capture
P/T           P/V  Mate#     is on the first leg.  Whether bouncing,
DoubleBarrel  3.5  5         colliding, or hopping, they benefit from
DoubleCannon  3.5  5         boards larger than 64 squares.  There are 
Laquear       4.0  4         more opportunities for needed adjacencies
Essedar       4.0  4         on 10x10 than 8x8, and Pawns become more
Helmsman      3.5  5         important factor to enable Bifurcator
Buccaneer     3.5  5         line of move or attack.  Like Cannon 
Murmillo      3.5  5         capture-mode and Contrahopper dual-mode,
Meridian      4.0  4         bifurcators need such enabler en route,
Samnis        4.0  4         not limited as a group to hopping modality.
Gaul          4.0  4         As the board clears, the second-leg-capture
bifurcators, like Cannon, fall in value. Above, hopping is considered the same as leaping or jumping in the Bifurcator page; the three are synonymous with Bifurcators. Deflecting is the fourth modality not yet in the main list there but one example. All four cases, needed screen trasitions first to second leg.

George Duke wrote on Mon, Feb 6, 2012 10:34 PM UTC:
Rigorous analysis may not be necessary if someone already knows what the
value is. Each p/v is targeted +/- 0.25 as stated. I have played over 200
live games at Brainking and over 200 at Game Courier excluding FRC and
OrthoChess. One gets to know whether to trade a Half-Duck for a Rook, a
Kangaroo for a Platypus etc. That trade-off method alone is a solitary test. Then
there are 25 more or less rigorous tests, separate from experience and
short of Computer runs. Jeremy L. should please start a separate thread on
his way of getting to 'For the Crown' values. Here I intend to list the 25
tests of value, just some few Betzan. 
This thread is going to be long enough by the time there are 2000 Sovereign
piece-types without side-topics.  Soon to add to Tables are 40 more
Bifurcators, rest of Martian Chess p-ts, all the Nightriders, Problem-Theme
threads compound leapers, rest of Outback Chess p-ts. If 'For the Crown'
has some suitable for regular rectangles 64-144, they should be added here with Sovereign values or
attributed if borrowed from pre-existing CV. Back-ups more comprehensive
will be Truelove's and Gilman's compendiums.  Three or four Tables a week
yield 50 p-ts a week, that will be the 2000 piece-types undergoing
Sovereign analysis this year, or over 2012-13 anyway.  These last few
comments are filler of background and basis, for the main emphasis will be
pure Tables.  If anyone sees a value out of line, please call to attention. Obviously it is easy to study one particular embodiment, such as 6-piece-type OrthoChess and settle confidently on values less than 0.1 off useful practice. They of OrthoChess ridiculously do not even re-compute yet for different Fischer Random line-ups. The Sovereign p-t development is more rigorous both for being more extendable and for being bi-partite with Mate#s to go with the refinable Piece Values.

Jeremy Lennert wrote on Mon, Feb 6, 2012 09:58 PM UTC:

The FIDE laws of Chess do not forbid threefold repetition; rather, law 10.10 allows either player to claim a draw in the event a threefold repetition occurs.

In the absence of such a rule, the game would presumably go on forever, with neither player willing to break the cycle. The threefold repetition rule is simply an observation of the fact that if both players find an endless loop preferable to other options, then they have both implicitly consented to a draw. It doesn't change whether any position is theoretically won, lost, or drawn, it just cuts short the infinite loop.

For the Crown has many unorthodox pieces, and is adding more with each expansion. However, material values are quite different than they would be in a FIDE-like context, due to differences in piece density, deployment (dropping) rules, and various other factors. And mate #s are completely irrelevant, since both players have the ability to bring new pieces into play as the game goes on, and therefore bare king endgames do not arise.

I have composed rules and recommended piece values for using the For the Crown pieces in a point-buy chess variant, which are available on the publisher's product page. I believe I have subjected these values to rather more rigorous analysis than George has used in this thread, but I still consider them to be educated guesses, at best; I haven't tried to get more precise than nearest-pawn, and it wouldn't surprise me if several were wrong, even by that loose standard.


George Duke wrote on Mon, Feb 6, 2012 07:19 PM UTC:
Nonsense. That is strange, incorrect comment off the mark in entirety. The demonstration shows under 50 moves White wins with 6 Rotating Spearmen
against Black's best play. That is the whole point or the main point. A Computer or longer trials
can more emphatically confirm it now. This Spearman example should complete way under 50 moves with Black best effort. It may well not even be a 20-mover. Mentioning no Pawn Promotion and over 50 moves for other p-ts as interesting studies is conservative adherence to principle. They do not apply here to Spearman anyway. Cannot Jeremy L. follow the unflawed demonstration? It is not final proof but strong evidence that Mate# is '6' or possibly only '5'. Or is he perceiving an error, which would be welcome input to address? Put it into words regarding Moves 1 through 7 below. The continuation to Moves 8,9, 10 is somewhat obvious by the position of the other Spearmen. The object is to keep Spearman in the piece-type camp with no special favours like given OrthoPawn.

 Also, I will be happy to subject 'For the Crown' to similar scrutiny. I have not really looked at it yet beyond noticing the rules seem well-written. Are there any variant chess pieces there for calculation of these Sovereign Values, the subject of this new thread? Or are they all Orthodox in 'For the Crown'?
Repetition in the Rotating Spearman example is illegal for Black because Black has the two other Moves by common CV rules as well as early history/regional Chess rules. Black cannot absurdly claim a Draw, she must proceed with one of the two legal moves at her disposal Move 7 below. The prospective 3-fold repetition is not forced and play proceeds by equally standard practice to current f.i.d.e dogma. It happens to redound to White's advantage and toward completion of inevitable Mate, establishing Rotating Spearman as Sovereign. That interpretation of 3-fold is century-long problemist strict compliance, as otherwise interpreted inelegant. 
Thanks for the opportunity to extend this summary of the analysis respecting the 12-year-old Centennial Chess p-t, now legitimately Sovereign Rotating Spearman(2.0, 6).

Jeremy Lennert wrote on Mon, Feb 6, 2012 06:59 PM UTC:
If you're calculating mate #s based on your own variant chess laws instead
of the orthodox ones, you should have stated that up front.

And if your variant laws include removing the 50-move draw and making
repetition illegal instead of a draw, then the numbers you are calculating
are likely much closer to helpmate numbers than forced mate numbers. 
Eventually, ALL non-mate positions will be exhausted, and black will be
forced to collude in his own checkmate by process of elimination.

George Duke wrote on Mon, Feb 6, 2012 04:12 PM UTC:
Black's goal is to Draw, and we are in ground become-superficial gms of
OrthoChess do not venture. The invocation of three-fold repetition is
precisely for White to get Black moving upward for White to win and for us
to get a Mate#. Jorg, I recreated now what I did to get the puzzling '6'.
Some Sovereign values were taking seconds, this one 1/2 hour and another
1/2 hour now.  Here is the argument.
 Black King gravitates to Rank One and especially the two corners, one or the other. Pick it up from there with start position: White: King-d1, Spearmen a1, a7, a8, b7, b8, h8; Black: King-g1. Then
1 K d1-e1; K g1-h1.
2 K e1-f1; K h1-h2.
3 Spearman b7-h1; K h2-h1 (takes Spearman)
That Black move is initializing a position.
4 K f1-f2; K h1-h2.
5 K f2-f1; K h2-h1.
6 K f1-f2; K h1-h2
7 K f2-f1...
Now Black cannot return to h1. She has to go 7. ...K h2-h3 or else 
7. ...K h2-g3.  Out of there! Black is flushed away, where clearly at least 4 Spearmen are necessary, it would seem a full six Spearmen. Regardless, on the safe side, it becomes Mate# of '6', both to secure the start of the endgame itself and to have the same effect readily at the other corner 'a1' if necessary.  Hopefully fine and dandy if Computer knocks it down to the '5' or even '4'. Rotating Spearman is SOVEREIGN PIECE-TYPE, having no Mate# of zero.________________________________________________________
In these CV studies I prefer no 50-move rule. What's the difference whether it takes 49 or 199 moves?
Also anyone thown for a loop by (unofficial) Sovereign Pawn(1.0, 12), obviously aesthetically no Promotion allowed. Dealt with here is raw piece-type power minimally contexted, maximally diversifiable as to piece mixes and board ranges 64-144.
A Zeitgeist bland and banal OrthoChessists lost generations ago.

Jeremy Lennert wrote on Mon, Feb 6, 2012 07:47 AM UTC:
If you suppose your king will always maintain opposition to the enemy king,
then it can block the rank with no help at all.  But if you don't maintain
opposition, then the enemy king necessarily has a head start towards one
side or the other, and can break your line there before your king can get
close enough to defend, since you are vulnerable on both sides.  And since
maintaining opposition at all times will require all of your moves, it
cannot be part of any plan to force mate.

But a pair of DD (with leaping power) plus a king CAN force the enemy king
back using zugzwang, unless I am much mistaken.  For example, suppose white
DD on a2 and b2, king on c3, black king f3.

1. Kd3 Kg3 (black tries to stay on rank 3)
2. Ke3 Kh3
3. Kf3 Kh4 (black is forced back a rank; only legal move)
4. Kg2 Kg4
5. DDb4 Kg5 (King threatens f3, g3, and h3, DD threatens h4 and f4)
6. DDa4

For thoroughness, we should also advance our own king to rank 5 without
breaking the line, so we can repeat the process...

6. ... Kf5
7. Kg3 Kg5 (black tries to maintain opposition)
8. DDc4 Kf5 (white loses a tempo to break opposition)
9. Kh4 Kg5
10. Kh5

The final mate is only slightly more complex.  Suppose white DD a6 & b6,
white king c7, black king f7.

1. Kd7 Kg7
2. Ke7 Kh7
3. Kf7 Kh8
4. Kg6 Kg8
5. DDf6 Kh8 (f8 is threatened; black confined to corner)
6. DDa4 Kh7 (white loses a tempo)
7. DDa8+ Kh8
8. DDf8# (or DDh6#)

I trust it's easy to see why this doesn't work if the DDs block each
other.

Charles Gilman wrote on Mon, Feb 6, 2012 07:08 AM UTC:
'Lame' also carries pejorative connotations that portray, for example, Xiang Qi as an intrinsically poor game, which it is not. Stepping is a more politically correct term.

Returning to the main topic, obviously the attacking player's King would have to get close to the bare King soon enough to avoid the risk of such captures. What is more pertinent is that the crucial step of pushing the bare King back a rank or file would be impossible, as neither piece could even move to the rank or file along which the bare King was moving. A pair of Stepping pieces that moving odd numbers of ranks but even numbers of files, or a pair moving odd numbers of files but even numbers of ranks, could not force mate either, at least in a game where players strictly alternated moves. A game where players could make two moves at a time, but not with the same piece, is a different matter for such pieces, but that is not the kind of game on which this thread's 'number required to mate'.

The two kinds of piece that I invented in this comment (unless anyone knows better) are bound to alternate files and alternate ranks respectively, but their compound is the unbound full Rook. This is reminiscent of amphibian pieces, but as I understand it the term amphibian is reserved for where both component are symmetric.

Jeremy Lennert wrote on Mon, Feb 6, 2012 05:07 AM UTC:

Black's goal is to draw. He doesn't have to avoid threefold repetition; white does.


George Duke wrote on Sun, Feb 5, 2012 08:23 PM UTC:
Now Sovereign OrthoPawn(1.0, 12) may be correctly evaluated there by
numbers but it is not in a Table yet.  
For OrthoPawn(1.0, 12), allowance must be made for array, whereas Spearman
can be treated as full-fledge piece.  The array consideration being unnecessary for Spearman, that means only the routine selected bindings to advantage and no unfair-to-White proximity of Black King to piece-unit of White. No other stipulation to begin to grind out a Mate#, as for all legitimate p-ts, then what is the Mate# each piece-type on the level playing field described? In all, treat Rotating Spearman the same way as regular p-t it is. 
As Jorg Knappen points out King wants to get behind the 
Spearmen. If staying in front beyond the second rank, there are shorter Mates with smaller forces. Arrive at position: White King-d1; Spearmen h1, h4, a1, a8. Black King-f1, where Black is supposedly safely behind the lines. 
1. Spearman h4-e1; King f1-g1.
2. King d1-e2; King g1-h1 (takes Spearman).
3. King e2-f1; King h1-h2. A reason this is stopped here for now, is 'e2-f2' the better move? The object is to tie Black up in 3-fold problem.
For follow-up, above in first three moves
one Spearman is captured and three remain, and 2 more in problemists' reserve if necessary.  Are more than four necessary to achieve Mate within set number of moves?  Does the original position need some 1 or 2 additional Spearmen to get there, despite the Black tropism to Rank One? The above moves up to three only are incomplete and need to continue to 8 or 10 in follow-up, re-checking the pattern and whether the Black King can indeed be flushed from Rank One.  
Thanks for calling to attention, the argument for Spearman values would be among few the 50 p-ts so far having less certainty. Hey sovereign Spearman(2.0, 6) is no sovereign Rook(5.0, 1).

George Duke wrote on Sun, Feb 5, 2012 08:06 PM UTC:
Thanks Jorg, Spearman becomes interesting, I knew I had thought through 3-fold repetition but no saved work. Here'e re-creation and rationale by way of partial proof. As of now, I still see a full 6 as necessary Sovereign Spearman(2.0, 6). Realize Spearman is one of projected 2000 p-ts for here course of 2012, and only a possible million p-ts creatable.  Gilman's being self-described ''comprehensive'' is extremely optimistic. So what's important is the process of either p-vs or in this case Mate#, which may or may not need later computer correction, usually downward, in unlikely event interest develops for some specific embodiment having cheap-piece Spearman right on the piece/Pawn interface; or need to refine Centennial value itself.   Computer being necessary for fixed-form cv, Sovereign Piece-type values are for more generality in different piece mixes and boards at once.

George Duke wrote on Sat, Feb 4, 2012 04:20 PM UTC:
TABLE OF SOVEREIGN VALUES (IV) There is no reason not to extend the table
P/T        P/V   Mate#        to hundreds or 2000 on a par with M%Bxxs
SCORPION   5.0   2            as it were supplement to it. Then like that
DRAGON     5.0   2            one, corrections unlikely more than 10% the
MASTODON   4.0   1            values, can be periodically entered. Notice
ARCHER     9.0   1            all the p-ts are for squares, because 
LARGE TANK 4.0   1            Square would be over 99% the interest
SECUTOR    3.5   5            among the world's Chess players numbering
FOX        3.5   2            a billion or two.
DUKE       4.0   2            The first test is usually Mobility, and the
CAVALIER   5.0   1            other 20 or 25 tests can be listed not too
MOTOR UNIT 4.0   2            time-consumingly.  
CAVALRY    3.75  3            Archer is Fugue. Once patented, Large Tank
         is Betzan 'Q3', two p-ts are from Rennaissance Chess, Motor Unit Novo, Cavalry Chess-Battle. Some few of these Mate#s are board-dependent between 8x8 to 12x12 including all of 8x10, 10x8, 9x9, and 10x10, not limited to them, but requiring majority of both ranks and files 8-deep or more each chosen board.  That allows boards such as Omagan 104 and Zig Zag and others so long as the squares all hold 64 to 144.
[Obviously 'Table II' Water Rook should read what is intended 'Water/Land Rook'. The first correction was the Mate# of Quintessence at 'I'.  This Errata can be ongoing until the bullets number about ten, there being only the two so far, then to put them in one comment's revised Table of ten revision/typos/corrections.]

Jeremy Lennert wrote on Sat, Feb 4, 2012 08:15 AM UTC:
'Lame' is Betza's technical term for a piece that can be blocked on a
square that it cannot land on.

Say you've got a DD on a6 and another on h6.  What do you do when the
enemy king moves to b7?

If they're full Dababba-riders, the one on a6 just moves to g6, and you
still cover the whole rank.

But if they block each other, you're stuck.  If he moves anywhere on the
same rank, he blocks the attack from h6 to b6, and the king slips through. 
If he moves anywhere on the same file, he is no longer covering c6, and the
king slips through.  If he doesn't move, the king captures him.

Charles Gilman wrote on Sat, Feb 4, 2012 07:22 AM UTC:
'...but the Water/Land Rooks are lame [Jeremy Lennert's word]
Dababba-riders, and therefore cannot control an entire rank/file even when
working together.'

What about if they were at opposite ends of a rank/file? Surely then they
would threaten every square on it, as neither would block the other.

Jeremy Lennert wrote on Fri, Feb 3, 2012 05:10 PM UTC:

As far as I can tell, George gets all of his piece stats from about 95% sheer intuition and 5% wildly unrepresentative examples. If you actually went through his numbers rigorously and systematically, I suspect you'd discover that many of them are total fabrications.

He even gives a mate # of 2 for Water Rook, a piece that George himself defined as specifically only moving on light-colored squares (the piece that moves in exactly the same pattern on dark squares has a different name), which therefore obviously cannot force a mate with any number! That's like giving a mate # for Bishops that are all on the same color.

...and even if he hadn't defined them in this bizarre way, two is definitely not enough of them to force a mate in general. I believe two Dababba-riders can sometimes force mate, if they are on different colors and can cut the enemy king off from the 'safe' edge of the board, but the Water/Land Rooks are lame Dababba-riders, and therefore cannot control an entire rank/file even when working together.

Incidentally, if we're playing fox-and-geese with rotating spearmen, I think you'll find that 3 spearmen + king is sufficient to win most reasonable starting positions (use two spearmen pointing forward to confine the enemy king to a corridor and then just chase him down).


Jörg Knappen wrote on Fri, Feb 3, 2012 10:43 AM UTC:
I don't understand how you derived the number 6 for the Spearman. In fact,
it has no backwards capture move and once the opposing King has broken the
line of Spearmen, no number of them can mate.

Maybe you want to say that a fox-and-geese style game with 6 Spearmen and a
King vs. a lone King from some initial position is won, but this something
very different.

George Duke wrote on Thu, Feb 2, 2012 05:48 PM UTC:
Thanks Michael. Let's identify sovereign Amazon(12.0,1*) for unaided. 
TABLE OF SOVEREIGN VALUES (III)  Another positive value p-t, sovereign
P/T          P/V  Mate#     Coordinator(3.5, 0) has Mate# equal zero, as
THOAT        4.25 2      however many of them, they and King cannot
SPEARMAN     2.0  6      Mate.  Still to process is Paulowich/Muller-
WYVERN       4.0  3      contributed thread '12x12 Checkmates'.  
PROVOCATOR   3.5  5      Sovereign Piece-type values actualize the
WIZARD       3.0  3      abstract philosophical definitions.  Otherwise
ELBOW BISHOP 3.5  2      the rules-set places a great burden on the
WINDMILL     4.0  1      player/reader and remains cv-artwork.  Values
ADVANCER     8.0  1      are relational and Pawn should normalize from
KANGAROO     4.5  2      1.0 to 2.0 setting itself. '2.0' for like of
PLATYPUS     3.75 1      Cannon Pawn pronounces the Pawn/piece interface
CAMBLAN N    4.0  2      is reached or overstepped; then too familiar
BACH D. SHIP 2.0  7      '8.0' for Long Leaper and Advancer, both about
ALFIL        1.5  5      Queen value, keeps. Thoat is Martian Chess, Wizard Omega Chess, Wyvern Beastmaster, and two p-ts are from Outback. Centennial's Spearman is first uncovered '6' Mating Number.  While there are over 25 piece-value tests, there is much resolution by the time of applying four or five or six of them, even though some tests can be contradictory.  Usually tests reinforce and without Computer, piece-value work-up +/- 0.25 settled on, further refinable if indicated. In 2000 Centennial has table of values that 95% of CVs since negligently omit even the attempt.

Michael Nelson wrote on Thu, Feb 2, 2012 03:51 AM UTC:
George,is the mate# also one for pieces such as the Amazon which can force
mate without the assistance of the friendly King? Is there a need to
distinguish these pieces from mate number 1 pieces such as the Rook which
can easily force mate with the help of the friendly King but not without
it?

David Paulowich wrote on Wed, Feb 1, 2012 01:01 AM UTC:

The question of sufficient mating force becomes more complex on larger boards. See the thread 12x12_checkmate for some interesting results obtained by H. G. Muller. In particular, both the Commoner (FW) and the Half-Duck (HFD) may fail to force mate against a lone King on a 16x16 board. A 12x12 board can be 'too large' for the Woody Rook (WD) or even the (WAD) piece.


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