Comments by GeorgeDuke



Henri Poincare, Emanuel Lasker(chess), and Oswald Spengler were all early 20th-century mathematicians. Poincare said(tr.Fr.), 'In fact, what is mathematical creation? It does not consist in making new combinations with mathematical entities already known. Anyone could do that, but the combinations so made would be infinite in number and most of them absolutely without interest. To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice.' [Math and Chess starts in topic of Siam, or Thai, Chess.] The original starting-array symmetry question of this thread is only one variable to be dealt with mathematically in CV design.


A Chess Puzzle: to devise a game on 8x8 with no legal moves for White. All 8 Pawns(any kind) and 8 pieces(any mix of types)must start in own half of board, King only required to be within back-rank. Use already-invented pieces and Rules. Describe an initial set-up. Follow-up Puzzle Two is to contrive a starting array (also with full complement of 16 each side, 32 pieces and Pawns altogether), so that neither Black nor White can move, no legal first move at all either team, whoever goes first.Puzzle One Solution:
8 P____K____N____ ____ ____B____ ____P White small letters
7 P____ ____ ____ ____ ____C____ ____P Conventional Pawns
6 P____D____E____ ____ ____R____ ____P D = Dragon 5-square,5+way
5 P____I____ ____ ____ ____ ____ ____P C = Crooked Bishop
4 p____i____ ____w____w____ ____ ____p B = Ibis leaper
3 p____ ____ ____w____ ____ ____ ____p E = Elbow Chess Rook
2 p____ ____ ____ ____ ____f____w____p w = Wazir (1,2)
1 p____ ____ ____ ____f____k____ ____p f = Ferz (2,2)
I,i = Immobilizer
a b c d e f g h
There would be thousands of hard-to-find solutions CVPage-indexed pieces. One explanation: put all 16 standard Pawns in a-file and h-file. How about Immobilizers (Ultima) at b4 White and b5 Black. Black Dragon at b6 is after 'Falcons, Scorpions and Dragon.' E is Elbow Chess Rook in 'Multipath Chess Pieces,' after Pritchard ECV, having to make one 90-degree change of direction each move. Black Crooked Bishop at f7 is Betza's. Black Ibis(or Namel: 2,8) at f8 is Gilman concoction (hey let's find the things some use).
Justification: If Wazir at either d4 or d3 moves, Dragon-b6 has a pathway.
If Wazir-e4 moves or Wazir-g2 moves, Crooked Bishop at f7 has pathway.
If Ferz-f2 moves, Rook checks making it illegal.
If Ferz-e1 moves, Elbow-Rook-c6 has its pathway.
King cannot move because of Ibis-f8 and the Elbow Chess one again.
So, no White piece can move: beyond 'zugzwang,' half-the-board immobilization by all pre-existent pieces. QED. (More elegant may be upgrading one+ W/F to at least N because of relative strengths or some one-piece-type principle of economy. Puzzle Two remains more difficult)
When Carrera's was invented, Shakespeare was still writing plays and Newton was not yet born(1642). M. Winther writes, 'It is advantageous to the opponent should White threaten mate in the opening,' in Teutonic Chess, a new array of Carrera's Chess. There's hardly a large Chess without conceivable Fool's Mate in three, call it a threat or not. For example, Falcon Chess 8x10. There, if White moves Ni1-h3, then -i5, it threatens checkmate on the third move with the third move of that self-same Knight. However, Black's simple reply Ni8-j6 stops the attack and faces White with fork-mate threat in reverse, worsened by the i1-Knight's not being in place any more to thwart. So, exactly the same words of Winther apply, 'It is advantageous to the opponent...'
In Falcon Chess we call '1 Ni1-h3; 2 -i5; 3 -h7' Fool's Mate because Queen or Bishop cannot checkmate in three like that with full help of Black. 'Helpmates' are Chess problems, started it says in 1854 by Max Lange in Deutscheschachzeitung, and of course perfected by Sam Loyd 1860 on. Both sides cooperate to checkmate Black. That's what a trivial Foolsmate entails from the opening, called a Helpmate if pieces already developed, but any win in fewer than 6 moves is surely a blunder. CVariantists are already admonished to avoid channeling openings to just few lines, on account of there being no net disadvantage to making mating threat from Move 1, by one (or maybe two)specific moves, in some of the ridiculous or overused initial set-ups and piece mixes ever under consideration.
Brainking keeps its stats on games played there over years, (below somewhat inconsistent as to including a stray 0.1 or not) currently: Shogi Black 3320, 48.6% White 3446, 50.4% Draw 67, 1%. FIDE, W 47.5%, B 48.3%, Sample > 100,000. Chinese, Red 49.5, Black 47.6, Sample > 5000. Maharajah, W 32%, B 60%, Sample > 3000. Janus, W 50.4%, B 47.4%, Sample > 4000. Cylinder, W 48.6, B 47.1, > 3000. Amazon, W 50.4, B 43.9, > 2500. Fischer Random Chess, W 48.7%, B 46.4%, > 3000. Knight Relay, W 50.0, B 48.5%, > 1500. Grand, W 50.3%, B 47.0%, approx. = 2000. Capablanca, W 50.8, B 46.0%, approx. = 2000. Los Alamos, W 49.0, B 45.0, approx. 5000. That's about half their Chess games. Maharajah needs 10x10 to win, so fares badly at Brainking. FIDE Black > White also stands out. [Never heard of Chieftain, not in the alphabet, but imagine it will be found, since we like to tear them apart]

Puzzle One Solution: 8 P____K____N____ ____ ____B____ ____P White small letters 7 P____ ____ ____ ____ ____C____ ____P Conventional Pawns 6 P____D____E____ ____ ____R____ ____P D = Dragon 5-square,5+way 5 P____I____ ____ ____ ____ ____ ____P C = Crooked Bishop 4 p____i____ ____w____w____ ____ ____p B = Ibis leaper 3 p____ ____ ____w____ ____ ____ ____p E = Elbow Chess Rook 2 p____ ____ ____ ____ ____f____w____p w = Wazir (1,2) 1 p____ ____ ____ ____f____k____ ____p f = Ferz (2,2) I,i = Immobilizer a b c d e f g h There would be thousands of hard-to-find solutions CVPage-indexed pieces. One explanation: put all 16 standard Pawns in a-file and h-file. How about Immobilizers (Ultima) at b4 White and b5 Black. Black Dragon at b6 is after 'Falcons, Scorpions and Dragon.' E is Elbow Chess Rook in 'Multipath Chess Pieces,' after Pritchard ECV, having to make one 90-degree change of direction each move. Black Crooked Bishop at f7 is Betza's. Black Ibis(or Namel: 2,8) at f8 is Gilman concoction (hey let's find the things some use). Justification: If Wazir at either d4 or d3 moves, Dragon-b6 has a pathway. If Wazir-e4 moves or Wazir-g2 moves, Crooked Bishop at f7 has pathway. If Ferz-f2 moves, Rook checks making it illegal. If Ferz-e1 moves, Elbow-Rook-c6 has its pathway. King cannot move because of Ibis-f8 and the Elbow Chess one again. So, no White piece can move: beyond 'zugzwang,' half-the-board immobilization by all pre-existent pieces. QED. (More elegant may be upgrading one+ W/F to at least N because of relative strengths or some one-piece-type principle of economy. Puzzle Two remains more difficult)

Rating 7 out of 10 for Berkeleian Chess(1984): 'When a piece is unobserved it disappears from the board. An observed piece is one that is defended or notionally defended (in the case of a pinned piece) by another man.' --full write-up in 1994 Pritcard's ECV. Notes: 1) Nice idea 'Berkeleian' could apply widely, including to any of the 3000 CVPage games in general. 2) Presumptively classifiable here as 'modest cv', Berkeley theme is actually genuine mutator, unlike way-overworked sterile mixing-around or randomizing back rank of pre-existing games. (A fortiori, slight majority of CVPage games are propietarily at best half-creative new combinations of known elements, but the 100-member Carrera-Capablanca family fails even rising to that) 3) Tactically in real play, Berkeleian forces, whatever particular embodiment thereof, tend to group effectively together, like present games being played of Elephant Chess in CVPage Game Courier. 4) If we missed someone's using partly the Berkeley theme already, Berkeleian was not cited, or we would have noticed, so anyway this points to origination.
Dave's Silly Chess Game suggests a new group of chess problem themes, namely, initial positions' fulfilling certain conditions. Puzzle One at DSCG Comment shows one array where White cannot move on 8x8, Kings being in back rank and 'full complement' meaning 50 percent piece density altogether with half of them Pawns. The greater the board size, the more solutions, so 8x8 has thousands using CVPage-indexed pieces. Here is second, albeit similar solution: 8 P____ ____ ____K____N____ ____ ____P Black capital letters 7 P____ ____ ____ ____C____Z____ ____P C Crooked B; N Namel(2.8); 6 P____E____D____ ____R____ ____ ____P Z Zemel(2,6)leaper 5 P____ ____ ____ ____ ____ ____I____P E Elbow-Chess Rook that must 4 p____ ____ ____w____n____ ____i____p turn once only 90 degrees 3 p____ ____ ____w____ ____ ____ ____p Immobilizers(Rococo) 2 p____ ____ ____w____ ____n____ ____p Dragon 5-sq. 5+way multi-path 1 p____n____ ____ ____k____ ____ ____p w wazir a b c d e f g h White cannot move because: If Knight-b1 moves, Elbow-Chess Rook has pathway. If w-d2, w-d3 or w-d4 moves, Dragon-c6 has a pathway(each one different). If n-e4 moves, Rook has its pathway. If n-f2 moves, Crooked Bishop has pathway. King cannot move because of leapers Namel(2,8) and Zemel(2,6). See 'Passed Pawns, Scorpions and Dragon', Betza's 'Crooked Bishop', and Gilman's 'From Ungulates Outward'.

This time Ranks 4 and 5 have only one Pawn each. Yet White's every move is frozen illegal-- notwithstanding 3 Queens, 2 Archbishops(BN) and Marshall.(7) 8 ___ ___P___K___P___P___P___O___P___ W = Wolf, doubly bent rider 7 P___P___S___P___R___E___ ___P___D___D S = Sissa: so many as Bishop, 6 W___ ___C___ ___ ___ ___ ___O___ ___ as many as Rook; and v.v. 5 ___ ___ ___ ___ ___ ___ ___ ___ ___P R = Reflecting Bishop 4 ___ ___ ___ ___ ___ ___ ___ ___ ___p E = Elbow Rook 3 p___a___a___q___p___b___m___ ___ ___p O - Canon; C = Cannon 2 p___ ___p___q___q___ ___p___ ___i___p D = Diagonal Narrow Crooked 1 p___n___k___ ___ ___ ___ ___ ___ ___p Nightrider(Knappen) i = Ibis(2,9)leaper a b c d e f g h i j If Pawn at a3 moves, Reflecting Bishop has path. If Archbishop at b3 moves, Wolf has path. If Archbishop-c3 moves, Cannon threatens King, illegal. If either Queen-d3 or -e2 moves, D.N.C. Nightrider at i7 has pathway. If either Queen-d2 or Pawn-e3 moves, Canon-h6 has path to King. If Bishop at f3 moves, Elbow Rook has path. If Marshall-g3 moves, Sissa-c2 has path. King cannot move because of Canon-h8 and D.N.C. Nightrider at j7.


ProblemThemeTwo here is reserved for the more extreme subset where neither White nor Black can move. In Dave's Silly Chess Game(2x2) we pose difficult Puzzle Two whether an initial position exists where there is no legal move for either side on 8x8(or 8x10 okay). Required are 50% piece density all on own board-half, half being Pawns, Kings positioned in back-rank, and use of CVPage-indexed pieces. Of course it must be 'legal' position where Kings are not initially checked(unlike David Howe's spoof). One solution 8x10 will be posted later today.

New pieces in the argument are Rose(Betza), Ship(BachDangChess) and Priest(Fantasy Grand Chess). No White piece or pawn can move; try it. 8 ___ ___P___K___N ___ ___S___ ___ ___ 7 ___P___W___P___C___ ___P___P___P___O Ship = 5 diagonal,then 3-o, 6 P___ ___R___ ___ ___ ___R___T___E___ then 2-o; o=orthogonal 5 P___ ___ ___ ___P___ ___ ___ ___ ___P W = Wolf, doubly bent rider 4 p___m___ ___ ___a___ ___ ___ ___ ___p C = Cannon; O = Canon 3 w___n___ ___ ___ ___ ___ ___ ___ ___p R = Rose, Betza-type nightrider 2 p___p___ ___a___ ___m___q___ ___ ___p T = Priest, any continual 90- 1 p___p___f___p___k___a___ ___ ___ ___p degree diagonal one-step path m = Marshall; a = Cardinal a b c d e f g h i j w = wazir; f = ferz If Knight at b3 moves, Ship has path. If Marshall at b4 moves,Rose-c6 has path. If Cardinal-d2 moves, Wolf has path. If Cardinal-e4 moves, Cannon reaches King. If Cardinal-f1 moves, Elbow Rook has path. If Marshall-f2 moves, Priest moves h6-g5-h4-g3-f4-e3-f2-e1. If Queen moves, Rose-g6 has path. King cannot move because of canon-j7. (8)
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