Comments by GeorgeDuke

New piece in the argument is Ralph Betza's Rhino.  'P,p' are Berolina
Pawns--setting the stage for the next board immobilizing Black too.
8  ___E___P___ ___K___P___ ___T___P___P   E = Elbow Bishop; l = alfil
7 P___P___ ___C___W___H___ ___O___ ___P   S = Scorpion,5-sq. multipath
6 S___ ___C___ ___P___ ___ ___ ___ ___    O = Canon; C = Cannon
5  ___ ___ ___ ___ ___ ___P___P___ ___U   W = Wolf, double bent rider
4 a___p___a___b___p___ ___q___ ___p___    H = Rhino, Betza's directioned
3 p___ ___a___ ___m___ ___ ___p___ ___p   one-stepper o-d-o... knightlike
2 n___p___ ___ ___l___ ___ ___ ___p___   T = Priest, continual 90-degree-
1 p___ ___k___ ___ ___ ___n___ ___ ___p      change one-stepped pathways
  a   b   c   d   e   f   g   h   i   j   U = Quintessence(Knappen)Nrider 
If Archbishop-a4 or Berolina Pawn-b4 moves, Scorpion has a pathway.
If either Archbishop-c4 or -c3 moves, Cannon-c6 reaches King.
If Bishop at d4 moves, Wolf has path.
If Berolina Pawn-e4 moves, Rhino has path.
If Marshall-e3 moves, Elbow Bishop has path.
If Queen at g4 moves, Quintessence at  j5 has path.
If Knight at g1 moves, Priest has pathway h8-g7-h6-i7-j6-i5-j4-i3-j2-
    i1-h2-g1-f2-e1-d2-c1.
King cannot move because of Cannon at d7 and Canon at h7. (9)

A.J. Winkelspecht's Divergent Chess from 1999 gives 'Rook moves without
capturing as an orthodox Rook & captures by moving as an orthodox
Bishop.' The 'Dragon-type' here is the 'Passed Pawns, Scorpions and Dragon' piece extended from five squares to six squares, called Phoenix.
8  P___ ___ ___ ___P___K___ ___ ___A___V   
7  V___A___ ___A___ ___A___ ___ ___ ___F   V,v = Divergent Chess Rook
6  F___ ___ ___ ___P___ ___P___ ___P___X   
5   ___P___ ___P___ ___P___ ___P___ ___P   X,x = Phoenix, six-    
4  p___ ___p___ ___p___ ___p___ ___p___         square multipath 
3  x___f___ ___ ___ ___p___ ___ ___ ___f         
2  p___v___a___ ___a___ ___a___ ___a___v   A,a = Alfil;  F,f = Ferz
1   ___p___ ___ ___k___p___ ___ ___ ___p   
   a   b   c   d   e   f   g   h   i   j   P,p = Berolina Pawn

White: Actually only King can move! 'V' and 'X' have no pathway at first.
       If King e1-f2, Divergent Rook-a7 takes, illegal.
       If King e1-d2, Divergent Rook-j8 has the path, illegal.
       If King e1-d1, Phoenix has pathway j6-i5-h4-g3-f2-e1-d1, illegal.
Black: If King f8-g7, Divergent Rook-b2 has the path, illegal.
       If King f8-e7, Divergent Rook-j2 has the path, illegal.
       If King f8-g8, Phoenix has pathway a3-b4-c5-d6-e7-f8-g8, illegal.

New pieces in argument are Straight Wide Crooked Nightrider(Knappen's
Nachtmahr) and Beau Monde Countess from year 2000.(10)
8   ___ ___ ___P___K___ ___ ___P___P___   G = Flamingo,(2,7)leaper
7  C___P___P___G___P___N___P___U___W___F  C = Countess, in turn moves 
6   ___E___D___ ___ ___ ___B___ ___ ___      R then shoots as B; vv
5  P___ ___P___ ___ ___ ___ ___ ___ ___P  N = S.W.C. Nightrider
4  p___ ___ ___e___p___ ___r___ ___p___p  Wolf,Fox: doubly bent riders
3  p___ ___ ___m___ ___w___m___ ___ ___p  E = Elbow Rook; B = Elb. Bishop
2  p___ ___ ___ ___ ___ ___ ___ ___l___p  Dragon = 5-square multipath
1  p___a___ ___ ___ ___k___ ___l___w___p  U = Quintessence(Nachtmahr)
                                          q,queen; a,cardl.; m,marshall
   a   b   c   d   e   f   g   h   i   j   l, alfil;  w, wazir; e, camel

If Marshall-d3 moves, Countess moves a7-a6 and has path to shoot.
If Camel-d4 or Pawn-e4 moves, Dragon has (2) pathways.
If Cardinal-b1 moves, Elbow Rook has path.
If Wazir-f3 moves, S.W.Crooked Nightrider at f7 has path.
If Marshall-g3 moves, Fox at j7 has path.
If Rook at g4 moves, Quintessence at h7 has path.
If Pawn-i4 moves, Elbow Bishop at g6 has path.
King cannot move because of Flamingo at d7, Elbow Rook and Wolf at i7.

This board achieves two long-travelling Priests(Fantasy Grand Chess, 2000)
one from the very opposite corner. Berolina Pawns.(11)
8  T___P___ ___K___ ___N___ ___P___ ___P  T = Priest, all-90-degree one-
7   ___ ___P___ ___P___ ___P___ ___N___       step diagonal pathways
6   ___P___ ___P___ ___ ___ ___R___ ___   I = Nightrider; N = Crooked NR
5  P___I___P___T___ ___F___ ___S___O___   F = Fox, doubly bent rider
4   ___d___ ___q___ ___n___q___ ___ ___p  R = Rose(Betza Nightrider)
3  p___ ___p___m___p___ ___ ___p___q___n  d = Dragon, 5-square multipath
2   ___p___ ___p___ ___ ___ ___ ___ ___p  S = Sissa, so many as B(R)as 
1  p___w___p___ ___ ___ ___a___ ___ ___k      many as R(B)
   a   b   c   d   e   f   g   h   i   j  m, marshall; a, alfil; w, wazir
If Queen-d4 moves, Nightrider-b5 has path.   
If Marshall-d3 moves Priest has pathway d5-c4-d3-c2-d1-e2-f1-g2-h1-i2-j1.
If Knight-f4 moves, Fox-f5 has path.
If Queen-g4 moves, Rose-h6 has path.
If Pawn-h3 moves, Sissa has path.
If Queen-i3 moves, Crooked Nightrider has path.
If Knight-j3 moves, Priest-a1 has pathway a8-b7-c8-d7-e8-f7-g8-h7-i8-j7-i6-j5-i4-j3-i2-j1.
King cannot move because of Cannon at i5.

Scrabble(TM) has greater SE quadrant 8x8. For convenience a-h and 1-8 differ from professional Scrabble(TM) notation. Only * (=Double or Triple Word) corresponds to actual official bonus squares. ~ is (Quadruple Word), - is (Quadruple Letter). There are seven(renewable) tiles and two chess pieces in hand each player: White b&n, 
8  *H___E___D___G___E___R___ ___*   Black r&n. Pieces are blockers and     
7    ___ ___ ___ ___ ___O___ ___    no tile or piece may stand             
6    __- ___ ___ ___ ___O___ ___    on same square. Each turn has
5    ___ ___b___ ___ __-K___ ___    two mandatory legs in order:
4    ___ __~ ___ ___ ___ ___ ___    either dropping or moving any
3    ___ ___ ___ ___ ___ ___ ___    chess piece on board and
2    ___ ___ ___ __- ___ ___ ___    playing lettered tiles normally.
1   *___ ___ ___ ___ ___ ___ ___*  1)White plays: b-f8; a8 HEDGE,20 pts. 
    a   b   c   d   e   f   g   h  1)...Black: b f8-c5;
                                     f8 HEDGER ROOK,             34 pts.

New pieces in argument are DoubleCannon(X) and DoubleBarrel(Z), having
optional second leg. X moves as Rook, Z as Bishop. If and only if to
capture, each turns 45 degrees, jumps one adjacent piece & moves on.
8  ___P___P___ ___P___K___ ___ ___P___P  G = Diagonal Narrow Crked NN
7 G___ ___X___ ___Z___P___P___I___ ___   I = Crooked Nightrider(Betza)
6  ___T___ ___D___ ___ ___ ___P___R___O  Z = (above)moves Bishop, iff
5 P___ ___ ___P___ ___ ___ ___ ___ ___O   to capture 45 degrees, jumps
4 p___ ___ ___ ___b___ ___ ___ ___ ___q  X = (above)moves Rook, iff
3 p___ ___ ___p___ ___b___p___q___ ___p   to capture 45 degrees, jumps
2 p___ ___ ___ ___q___ ___ ___p___ ___p  T = Priest(F.Grand)90-degree
1 p___l___n___ ___ ___l___k___p___l___       continual diagonal one-step
  a   b   c   d   e   f   g   h   i   j  R = Rose(Betza); l = Alfil
If Pawn-d3 moves, DoubleCannon(Winther 2006)c7-c6-c5(pc.d4)-e3-f2-g1.
If Pawn-g3 moves, DoubleBarrel(Winther 2006)e7-f6-g5(pc.g4)-g3-g2-g1.
If Queen-e2 moves, D.N.Crooked Nightrider(Knappen)moves a7-b5-d4-e2-g1.
If Queen-h3 moves, Crooked NN moves h7-g5-h3-g1.  
If Queen-j4 moves, Rose moves i6-j4-i2-g1.
If Knight-c1 moves, Priest moves b6-c5-b4-c3-b2-c1-d2-e1-f2-g1.
If Bishop-f3 or -e4 moves, Dragon-d6(5-square multipath) has one(or two) pathway(s). King cannot move because of Canons-g5 and -g6.  (17)

By more tools to work with, there exist more solutions. Winkelspecht's
1999 Divergent Chess Rook, Winther's 2006 bifurcation piece Murmillo, and
Falcon extension (1996 copyright) Dragon all three key for 2-player immobilization. 8x8 solution shows all White & Black pieces' having no legal moves, whoever first, in legal initial set-up, Kings back-ranked.
8   ____F____W____L____K____ ____ ____L   P,p = Berolina Pawn
7  P____ ____P____ ____P____ ____P____    D,d = Dragon, required 5-square
6  V____P____ ____P____ ____P____V____P         multipath
5  M____ ____P____ ____P____ ____M____D   V,v = Divergent Ch. Rook moves
4  d____p____ ____p____ ____p____ ____m         as R, captures as Bishop
3  p____v____p____ ____p____ ____p____v   M,m = Murmillo, moves Bishop,
2   ____l____ ____p____ ____p____ ____p      only if capturing turns
1  f____ ____ ____k____l____ ____l____w      45-degrees for 'bounce-
   a    b    c    d    e    f    g    h      capture' second leg
                                           F,f = Ferz; L,l = Alfil
                                                 W,w = Wazir
White:   If King d1-c2, then V-g6 has path, illegal.
         If King d1-e2, then V-a6 has path, illegal.
         If King d1-c1, then Dragon has pathway h5-g4-f3-e2-d1-c1.
Black:   If King e8-f7, then v-b3 has path, illegal.
         If King e8-d7, then v-h3 has path, illegal.
(2)      If King e8-f8, then Dragon has pathway a4-b5-c6-d7-e8-f8.

World's first binary computer? Chessboard 64-square uses Rook and Bishop
moves. [Addition algorithm: depict each number to add across a rank by
'R' counters, then use Rook moves to slide all the representations to
Rank 1; right to left, replace any and all 'doubles' by one to left, 
  ___ ___ ___ ___ ___ ___ ___    continuing until each first-rank square
  ___ ___ ___ ___ ___ ___ ___    is binary 1 or 0, where a 'Rook' is 
  ___ ___ ___ ___ ___ ___ ___    '1']  Bishop-like multiplication to
  ___ ___ ___ ___ ___ ___ ___    left shows chess-computer-abacus' 19x13
  ___ ___ ___b___ ___ ___b___b 1  operation (differing procedure than for
  ___ ___ ___b___ ___ ___b___b 1  Addition).  After placement, Bishop-
  ___ ___ ___ ___ ___ ___ ___  0  counters are to move diagonally left
  ___ ___ ___B___ ___ ___B___B 1  downward. Moves become b d4-a1,
128  64  32  16  8   4   2   1     b d3-b1, b g4-d1, b g3-e1, 
 a   b   c   d   e   f   g   h     b h4-e1 and b h3-f1, making first Rank now:   B___B___ ___BB__BB___B___B___B  and again replacing the 'doubles' with  just one to each pair's adjacent left:
           B___B___B___B___ ___B___B___B  =   11110111  = 247(base 10)
          --Method of John Napier in 1617 'Rabdologia', including also
Subtraction, Division and Extracting Square Roots on chessboard, improves
Middle Age calculating methods: 'bank' deriving from German counting
board, Rechenbank.  Scientific American 1985

Thanks a lot, Jeremy, for analysis of highlights of the Falcon model of coherent piece development. Remarkable the co-equality of Knight and Bishop on 8x8! Yet it breaks down by 9x8 or 8x9 where B>N, and smaller would be N>B. So, probably it is coincidental (like Sun-Earth-Moon 400 factor?). Competing philosophy is expressed by Larry Smith 22.March.04 under 'Game Design' thread: 'If a game was populated with pieces of near equal value, the advantage of exchange might not be significant. But if the pieces were of various degrees of value, enough to clearly differentiate them, exchanges would hold the potential of an advantage. Then a player can make sacrifices to obtain positional advantage.'  There we developed formula M = 3.5Zt/(P(1-G)), where P = Power Density(Betza), G = Smith's Exchange Gradient[quantified by myself], t = piece-type density, and Z = Board Size in number of squares, used to calculate M, game length(number of moves expected average).  [Mike Nelson named what Betza defined 'Power Density']

Nalls just says here that 'Hex Chess SS is my personal favorite invented
game.' On 1.October.2006 here (scroll back)he says in a Piece Value
Thread: 'Hexagon & Triangle spaced games are inferior compared to square spaced games. Games based upon hexagonal spaces have no special interest to me personally.'--Derek Nalls