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Ninety-one and a Half Trillion Falcon Chess Variants. Missing description[All Comments] [Add Comment or Rating]
George Duke wrote on 2008-01-12 UTC
RN212 Wolf & Shepherd. (a) no effect (b) Specifiy some one piece-type as Wolf for both Black and White, another as Shepherd, lasting the duration. Wolf (NBFR or Q) may capture a Pawn with immunity for one turn except from Shepherd. Of course by the second turn, Wolf may be captured anywhere by any unit unless just having captured another Pawn. (c) 'b', King can always capture Wolf. (d) 'c' King and Queen, and also exception whenever Wolf gives check in Pawn-capturing. (e) 'c' King, Queen and (another) Pawn (f) 'b', Wolf can thus capture and immediately self-immolate (rare advantage to establish a check). (g) 'b', Wolf can additionally capture Shepherd with one-turn immunity. (h) 'b', Shepherd may always capture Wolf in the manner of the Wolf (piece-specific inverse capture). (i) 'h', also Wolf may capture Shepherd by inverse capture. (j) 'b', any Pawn doubly protected voids the effect. (k) 'b', Pawn triply protected nullifies the Wolf's special power. (l) 'e' and 'i' (m) 'e', 'f', 'i' (n) 'e', 'f', 'i' and 'j' (m) After capturing Pawn, Wolf can unmask as a 'Werewolf' by sacrificing any one own individual piece, immediately removed from board, thereby conferring two-turn immunity -- void upon Wolf's moving again. (p) 'o' three-turn. Cumulative: 1.89498130 x 10^40 Chess Variates. Lesson: e to the power of (pi times i) plus one = ? Despite infinite possible answers, only one can be correct, under many names: zero(0), Null, zilch, naught, cipher.

George Duke wrote on 2008-01-11 UTC
RN211 Localization. Localization of the World 'Economy' is opposite of Globalization, eventually to reverse the experiment's damages. Each turn player must search for the local area required to move, as follows. (a) no effect (b) Only pieces or Pawns within one's own most crowded rank may move, loosely called 'dispersal'. Initially, back rank and Pawn rank have 10/10 (=100% occupancy) on ten-rank sizes, so the first move is normal. In case of tie, any of the tied ranks' pieces/Pawns may move. (c) 'b', player must move from own most crowded rank or file, with 8/8 superceded by 10/10, or 4/8 by 5/10, 5/10 by 5/8. (d) 'b' Both players' pieces count in determination of most-crowded rank. (e) 'c' both players' units (f) 'b' excludes King (so Pawn must move first). (g) 'c' excludes King. (h) 'b' Any square subset of squares figures in calculation of local group required to move piece or Pawn. For example, 10/10 (rank) supercedes any 4/4 (of given 2x2), and 7/9 (of 3x3) supercedes 7/10 (rank). (i)'c' and 'h' (j) 'd' excludes Kings. (k) 'h' and any same piece-types adjacent, mixing either side's units, have highest priority of all. (l) 'h' excludes Kings. (m) 'h' excludes Kings and Falcons. (n) 'k' and 'm' (o) 'c', 'h' and 'k', with both rank and file as 'c' not 'b' (p) 'o' with condition 'k' actually in effect on board permitting double move of the involved piece-type without capturing or checking on second leg. Cumulative: 1.1843633152 x 10^39 Chess Variations in combination. Beginning to see the approach of one distinct Chess Variate for each atom in Earth, the next 11 Mutators are already worked out in principle: Over the Edge, The Sea Is Rough, Hot Potato, Dispersal, Shepherd and Wolf, Cat & Mouse, Pedestal, British Bulldog, Sinkhole, Ali Baba & Forty Thieves, and Fibonacci Numbers. We always start with the name like that for two reasons. Many CVs stand on their name alone. Second, if each and every number had a name, mathematics would be lots easier for the masses not to mention programmers.

George Duke wrote on 2008-01-10 UTC
RN210 Hard-Boiled Eggs. (a) no effect (b) Queens are Hard-Boiled Eggs and cannot be captured when adjacent to any own Pawn. (c) 'b', required Queen's being adjacent to two Pawns at once for the effect (d) 'b', Queens are Hard-Boiled adjacent to any two own pieces and/or Pawns. (e) 'b' except a Falcon can always capture a Queen (f) 'c' except Queen always vulnerable to Falcon (g) 'd' except Falcon (h) 'b', such immune Queen moves only up to 3 spaces. (i) 'c', the Queen immunity from capture means restricted Queen up to 3 spaces. (j) 'd', such Queen is restricted up to 3 squares. (k) 'f' and 'i' (l) 'g' and 'j' (m) 'j' one or two spaces only (n) 'i' one or two spaces only (o) 'h' up to the two squares only (p) 'e' and 'o'. Cumulative: 7.40227072 x 10^37 Chess Rules-Sets in logical ordered combinations of these well-defined Mutators.

George Duke wrote on 2008-01-09 UTC
There are about 1.33 x 10^50 atoms in the Earth and 10^80 atoms in Universe. Given the goal to expand to googol, 10^100, Chess Variants. At this juncture en route, is radical notion that, 10^80 being established roughly by current consensus, the approximately 10^40 atoms(to be refined) in Great Pyramid, mark some ''logarithmic halfway point'' from the very small, one atom, to the very large, all atoms, of any moment? (2.4 million blocks: 6 million tonnes.) RN209 Green Light. (a) no effect (b) Player specifies one piece-type of opponent that can, at option, move twice moves 6-8, called the 'Rally' or 'in the Rally' or 'Rush', then again moves 16-18... (c) 'b' moves 3-4 then 13-14... (d) 'b' 4-6 then 14-16... (e) 'b' 5-8, then 15-18... (f) 'b' odd-numbered turns (g) 'b' even-numbered turns (h) 'b' no capturing with one of that piece-type whilst provision is holding (i) 'b' no checking under the provision (j) 'c' no captures (k) 'c' no checks (l) 'f' no capturing by the involved piece-type (m) 'f' no checking (n) 'b' thrice, no captures or checks (o) 'b' thrice, no capturing (p) thrice, no checking. Cumulative: 4.6264192 x 10^36 Chess Rules-Set alternatives.

George Duke wrote on 2008-01-08 UTC
RN208 Blue Queen. So there appear to be about 200 billion Shakespearean atoms per sentient being. Parallelly, both sides alternately possess the one Blue Queen. Blue Queen belongs to player on move. Since BQ is always the player's moving, BQ can never be captured. (a) no effect (b) BQ initially positioned by agreement at one of central four-square or two-square (9x10), player's turn consists of moving Blue Queen and then one's piece or Pawn normally. Only differences from moving a Queen is that Blue Queen can only capture a Pawn if (hypothetically) attacking her and Blue Queen cannot exactly reverse the last move. Also, only for check or checkmate, Blue Queen belongs to both teams at once. I.e., when there is any check at all, player on turn may move Blue Queen, possibly removing one check, only to be still checkmated, after completion of step-two of move, with even the very Blue Queen figuring in a checkmate by the other player. No prohibition on error of self-checkmate. (c) 'b' the BQ actually so checking can only move up to 2 spaces. (d) 'c' 3 spaces (e) 'c' 4 spaces (f) 'c' 5 spaces (g) 'b' After (compulsory) move of BQ player may move at option an opponent's piece/Pawn adjacent to BQ in place of own. (h)'g' only N, F (i) 'g' only B, N, F (j) 'g' B, N, R, F (k) 'g' only Pawns so adjacent (l) 'g' Pawns, N or F (m) 'g' Pawns, B, N, F (n) Pawns, B, N, R, F (o) 'h', also Blue Queen adjacent to own N or F may move as that one at option. (p) 'j' BQ adjacent to own Falcon may optionally move as Falcon. Cumulative: 2.89151221765 x 10^35 Chess Variations. Provisionally that covers entire lowest level of Great Pyramid blocks of stone in equality of molecules, or atoms -- visual comparison-description soon slightly to be re-calibrated by studying similar calculations elsewhere, given estimates herein being fairly close to other specialists', within reasonable definitional margins of error.

George Duke wrote on 2008-01-07 UTC
RN207 Hobbler. (a) no effect (b) Player designates at Move One a piece-type that can only move forwardly. (c) 'b' and the Hobbler piece-type changes for Moves 11-20... There must be at least one on board at transition to new Hobbler. The old 'Hobbler' (QFRB or N) regains full move. (d) 'b' and Hobbler promotes at final rank in the strict order one step upwards: Knight to Bishop to Rook to Falcon to Queen to Knight. (e) 'c' and 'd' (f) 'b', the precise handicap for Hobbler is to move alternately forward, then back, then forward successively within the appointed piece-type. (g) 'c' and 'f' (h) 'd' and 'f' (i) 'c', 'd' and 'f' (j) 'd' except reverse promotion obtains: Q to F to R to B to N to Q (k) 'f' and 'j' (l) 'c', 'f' and 'j' (m) 'c' and 'j' (n) 'b' and King can be designated Hobbler too. (o) 'c' and King can be Hobbler per that ten-move interval. (p) 'f' King inclusive. Cumulative: 1.807195136 x 10^34 Chess Rules-Sets. If that number as molecules, turned to stone, were rock comprising Great Pyramid (granite, basalt, limestone, variously Turah limestone), it would encompass a hundred(100) roughly 2m. x 2m. x 2m. casing stones on the lowest level.

Senorita Simpatica wrote on 2008-01-06 UTC
Hola Senor Duke: You seem to enjoy mentioning atoms in many of your writings. Do you know how many of Shakespeare's atoms are in your body? You may enjoy this article (see link). There is a calculation for that number:

http://jupiterscientific.org/review/shnecal.html

It seems that each of us here likely have atoms that were once in each other. Adios


George Duke wrote on 2008-01-05 UTC
OrthoChess fundamentalists say religiously that there are able to be more game scores on the perfected 8x8 than atoms in Universe, which is 10^80. RN206 Pawn Islands. Pawns must always form one continuous line, orthogonally or diagonally adjacent, or there are consequences. (a) no effect (b) Any smallest Pawn island of a side is removed from the board at its appearance immediately before that player's turn. If player causes the condition by own move, the offending Pawns are removed upon completion of that turn. If two smaller Pawn islands are equal, player chooses which one to remove. (c) 'b' except no removal of any island of five (d) 'c' except 4 or greater are exempt from removal (e) 'c' except 3 or greater are okay to remain (f) 'c' with however Knights and Falcons able to 'bridge' a Pawn chain, taken as 'continuity' and obviating any need for removal (g) 'f' Falcons, Knights and King (h) 'c' and Pawns can move one step laterally. (i) 'd', Pawns can move one step laterally. (j) 'e', Pawns can move one step laterally. (k) 'd' and 'h' (l) 'f' and 'h' (m) 'e', and Pawn islands so removed individually go back to any Pawn array square or, if they exhaust, any square in back rank. (n) 'f' and 'm' (o) 'e', 'g' and 'm' (p) 'g', 'h' and 'm'. Ongoing Cumulative # of individually-distinct 'CVs': 1.12949696 x 10^33. At over 230 tonnes if that number of molecules were living tissue, it exceeds the largest Blue Whale and largest ever dinosaur, probably Argentinasaurus, a sauropod, both by factor of 2 or 3. So, we leave living forms behind finally and can compare in volumes of astronomical bodies and chemical species inanimate with generally fewer atoms per molecule. [We get back on track by Earth's inclusive 10^49 or 10^50 atoms ahead; for what it is worth, here we already are exceeding life forms by factors of 20 or even 100. The comparisons visual do not affect the game-rules and their totals in combination.]

George Duke wrote on 2008-01-04 UTC
RN205 Kick the Can. The King is a Can, positioned at centermost b-file square in White, i-file in Black, and cannot move. In lieu of checkmate, Kicking the Can wins, as per each modality below. (a) no effect (b) King so set up cannot move or capture. King, fully surrounded adjacently 8 ways, orthogonally and diagonally, by either side's pieces and Pawns is ipso facto 'kicked' for Checkmate. Player can self-Checkmate but it is stupid. Enemy units adjacent to King are uncapturable at all. (c) 'b' except King is able to move and capture but only in direction of the Cauldron, files e and f, whence King cannot further move (d) 'b' with 7 surrounding units able to Kick the Can (e) 'b' with 6 units effecting Kicking the King(Can) (f) 'c' and 'd' (g) 'b' with Pawns able to move, not capture, laterally one step (h) 'c' and 'g' (i) 'c', 'd' and 'g' (j) 'c' with Pawns being full Quadra-Pawns(Centennial-like) having crossed the center line once (k) 'c', 'd' and 'j' (l) 'b' and 'j' (m) 'j' these mutated quadra-Pawns cannot capture backwards. (n) 'g' and King can Kick back three times per game, meaning displacing any piece one square in the direction of the King's 'attack', with however King not moving, but the defensive maneuvre itself constituting a full turn (o) 'n', King can Kick back twice only. (p) King has the right to Kick back once only. Cumulative: 7.01843456 x 10^31 Chess Rules-sets Variations. In molecular equivalence, the largest ever Tyrannasaurus Rex improbably ever reached in weight the approximately 15 tonnes entailed.

George Duke wrote on 2008-01-04 UTC
There will be no atoms left for Presets. RN204 Relinquishment. (a) no effect (b) After Move 5, effective for Moves 6-10, player announces one own piece-type, with at least one on board, unable to move the duration. Then after Move 10 that piece-type is 'reinstated' and a different own one piece-type announced for relinquishment for turns 11-15, and so on 16-20... (c) 'b' except the relinquishment-reinstatement interval is 4 Moves (d) 'b' 3 Moves (e) 'b' 6 Moves (f) 'b' 7 Moves (g) 'b' 8 Moves (h) 'b'-mode may 'rejuvenate' the piece-type at start of any turn by sacrificing any one piece, immediately removed from board, then proceeding to move normally, including one just reinstated at option, and subject to new 'immobilization' of type only at required interval, here five(5). (i) 'c' and 'h' (j) 'd' and 'h' (k) 'e' and 'h' (l) 'f' and 'h' (m) 'g' and 'h' (n) 'h' with also two Pawns permitted to be sacrificed for such rejuvenation (o) 'n' three Pawns (p) 'n' four Pawns. Cumulative: 4.3865216 x 10^30 Alternative Chess Rules-sets. Thinking of so many molecules instead: related familially to Horses, young adult Rhinoceros (myotis lucifugus) would correspond to the about 877 kilograms that entails. Evolved 50 million years ago, venerable African Rhinos are down to 2500 individuals from recent one million. Astronomer Fred Hoyle, before he died in 2001, spoke of ''the unrealized potential of animals.'' If only, suppose instead, someone or something had just nipped Australopithecus in the bud, we would taken all together probably be better off.

Anonymous wrote on 2007-12-31 UTC
When are you coming out with the presets?

George Duke wrote on 2007-12-31 UTC
RN 203 Flying Dutchman. Let's see, leaving off a month ago, before the Solstice, at CVs in number roughly equivalent to number molecules in the head of ordinary individual adult member of the superfamily Hominidae(be one chimpanzee or homo sapiens). The Comment 24.November.2007 proves by typical case explained, being so many in combination, that these are one and all viable, playable CVs. (a) no effect (b) Prior, each player designates one own piece-type as the Flying Dutchman and one square in the opposite back rank as the Port. Instead of checkmate, the winning condition requires one of this pre-designated piece-type to reach Port, called Weathering the Gale. Any captured F.D. returns immediately to 'Sea', namely its array square. (c) 'b' subject to F.D. being uncapturable every odd-numbered turn (d) 'b' with only F,N,B or R as F.D. (e) 'c' with only F,N,B or R as F.D. (f) 'b' subject to only R,F,Q being F.D. (g) 'c' with only R,F or Q being F.D. (h) 'b' only F or N being F.D. (i) 'b', except that, rather than a piece-type, player designates a specific piece, to be marked as Flying Dutchman. (j) 'c' as 'RN203i' (k) 'b', and the designated Port can only be in the back-rank Wide Cauldron, e.g. d1,e1,f1, & g1. (l) 'b', and the specific piece-type(F.D.) can never move backwards (laterally okay). (m) 'd' with the Flying D. unable ever to move backwards (laterally okay) (n) 'f' with 'Port-directed movements' as equivalently in both 'l' and 'm' (o) 'i', and the Flying Dutchman moves according to 'n'. (p) 'c' and 'o'. Cumulative: 2.7415776 x 10^29 CVs, approximately 48 kilograms of living tissue having that many molecules, as may be guessed, about the same as smallish human being, say the young Napoleon or Pocahontas. Later, we compare to Hydrogen atoms exclusively, which predominate 100:1, rather than these molecular aberrations -- in order eventually to achieve CVs in number greater than actual atoms in The Universe. [Would need revision in that one human has between 10^27 and 10^28 molecules not so many as 10^29, as the previous Comment begins to correct]

George Duke wrote on 2007-12-04 UTC
Only 34 Mutators in combination make over 10^27 CVs. Any CV may readily be 'dismantled', or 'deconstructed', into typical 5 to 50 constituent, 'originating' Mutators without ambiguity. Too many Mutators on one CV create awkward play. (In separate problem, too many CVs themselves existing are inherently humanly impossible to play.) Started '200-series' are new Mutators above and beyond RNs 1-32. Next starting here, '300' series ('301', '302'...) extends modes of RNs 1-32 themselves over their mere 3 to 10(usually 8) previously up to a consistent 32 ('a' to 'ff') in all cases. In other words, the corresponding 300-series Mutator 'calls' one of RNs 1-32 in order to advance modalities eventually to achieve fully thirty-two each. RN 301, Sizing, generally calls 'RN1' building on it. In furtherance of modalities, piece-arrays are set up as symmetrically as possible by agreement, with defined board sizes' rank preceding file. (d) 10x11 (e) 11x10 (f) 11x11 (g) 11x12 (h)12x11 (i)12x12 (j) 12x13 (k) 13x12 (l)13x13 [rare] (m) 13x14 (n) 14x13 (o) 14x14 (p) 14x15 (q) 15x14 (r) 15x15 (s) 15x16 (t) 16x15 (u) 16x16 (v) 'RN1a' with four corner squares(Omega-like), total 84 sqs. (w) 'RN1b' four corner squares, 94 sqs. (x) '1c' four corner squares, 104 sqs. (y) '1a' with 20 wrap-around squares (FalconChess100-like), 100 sqs. (z) '1b' with 20 wrap-around sqs., 110 sqs. (aa)'1a' with 24 'Reshevsky-Zonal-Chess' flank extensions, 104 sqs. (bb) '1b' with R-Z-C 24, 114 sqs. (cc) 'RN1c' with R-Z-C 24, 124 sqs. (dd) '1c' with 4 squares removed centrally, as Jacks & Witches(2003) and The Pit(2002) remove instead 16 squares; 96 sqs. (ee) '301i' with 4 sqs. so removed, 140 sqs. (ff) '301u' with 4 sqs. so removed, 252 sqs. Cum.: 1.7169973579 x 10^28, about equivalent to number molecules in any one human being, for example.

George Duke wrote on 2007-11-30 UTC
RN202 Passed Pawns. Passed Pawn means no enemy Pawn in front of same or adjacent file. (a) no effect (b) At option, a passed Pawn promotes to any piece regardless Pawn's present rank. This promotion is either upon completion of moving the Pawn or in lieu of full turn without any piece or Pawn move at all. (c) '202b' excludes Queen. (d) '202b' excludes Queen and Falcon. (e) '202b' applies from Rank 5 on. (f) '202b' from Rank 6 on (g) '202b' at Rank 7 (h) '202e' excludes Queen and Falcon. (i) '202e' allows promotion to Knight or Bishop only. (j) '202b' applies only to passed Pawns within the Cauldron, files e & f. (k) '202b' applies only to passed Pawns within the Wide Cauldron, files d,e,f,g. (l) '202j' excludes Queen. (m) '202e' stipulating also that once player's move establishes a Passed Pawn promotion, the opponent immediately designates the piece to which said passed Pawn promotes (n) '202m' excludes Queen & Falcon. (o) '202m' excluding Queen (p) '202o' applies to passed Pawns only within the Wide Cauldron. Provisional Cumulative: 1.609685023x10^27 (>octillion). Equivalent number of molecules in head of a Baboon (Genera Papio, Theropithecus, and Mandrillus)

George Duke wrote on 2007-11-29 UTC
RN201 Fixed Pawns. Required three(3) opposite-side Pawns fixed(such as W a4,c4,i4;B a5,c5,i5), including here pairs in adjacent files. (a) no effect (b) Any three pairs of opposite Pawns so facing off cause the effect for following player, requiring one extra move per turn each side(no exact move retracing allowed). A capture of Pawn that ends the condition also immediately terminates the player's turn. (c) 201b required four pawn-pairs fixed, or 'faced off', instead for the effect (d) 201b with the extra move given optional (e) 201b prohibits capture of any piece. (g) 201b dis-allows other than Pawn captures for the duration. (h) 201b requires one normal move and one King move. (i) Anticipating Limit[M] 201i through 201p: '201i' applies 201h for maximum three turns only. (j,k,l,m,n,o,p) Respectively, as '201i' is limiting 'RN201h' to three full turns, so 201j four turns...201p 10 turns(20-ply). (After J.P.Neto's ''Mutators'' Limit[Mutator]) Provisional Cumulative: 1.00605313952x10^26, over 100 Septillion. In water molecules instead of hydrogen atoms, 2.7 kilograms H2O have number molecules equal to this many CVs.

George Duke wrote on 2007-11-26 UTC
As a practical matter, we shall not exceed 32 Mutators operational at a time(example 24.Nov.07). Hence the standard is 'X Mutators taken 32 at a time'. Goal of course is attaining one-to-one #CVs to #Atoms(in universe). For convenience, new Mutators after RN1-RN32 are 200-series, designated 201, 202... The 'Cumulative totals' go on as before because of the following. Doug Chathan 18.Nov.07 links J.P.Neto's year 2000 article 'Mutators'. By principles and notations there, we can expand RN1-32 themselves in tandem with restricting new Mutators at most 32 activated. Examples available are such as Neto's Inverse, if any, of a Mutator and applying a Mutator repeatedly until fixed point etc. These will be spelled out when used. Mostly, we shall add to the number of modes periodically beyond the customary eight(8) so far, 'a' through 'h', of already-established RNs 1-32(RN 7 for Pawns has ten 'a' to 'j') themselves. Deliberately, the two currents can keep the running 'Cumulative' closely equivalent to our technique(usually having been just to multiply by 8 each step of the way). In other words, reductions from requiring only up to 32 active are offset at will by additional modalities of pre-existing Mutators. Thus, the very same over-all method essentially holds and continues, viz., more and more good Mutators serially onto the same Basis -- thereby making more and more games. Occasional adjustment and re-calculation in keeping with that standard 'nCr', namely nC32, 'X Mutators 32 at a time', will be tolerated; and anyway, in the end, we should be able far to exceed 10^80, in workable and well-defined CVs, to compensate for any slight inaccuracies; which may also arise from occasional contradictions not easy to reconcile(among some unusual RNs, in combination, by their very wordings and effects). So, next one is 'RN200' rather than RN33.

George Duke wrote on 2007-11-24 UTC
Objectors should be disabused of any notion that fully 33 Mutators are impractical and cannot be employed serially. The following notation, being perfectly playable with perhaps ready crib sheet, has all Mutators, or descriptors, activated (no Mutator at all registering default 'a' mode), and admittedly defines the most complex yet still illustrative type of prospective CV -- showing that such extremity as this(that one would not ordinarily want to play) nonetheless legimately counts in the mounting tabulation. To wit, '1c2b3c4b5b6c7d8b9b10e11c12c13b14b15b16b17b18b19b20c21d22b23b24d25b26d27b28b29e30f31b32c' represents Falcon Chess 10x10 array FRNBQKBNRF, each piece-type enhanced or limited in turn: Chaturanga (one-step) Pawns able to move two pawns at a time for any turn optionally(RN10) and promoting to Queen too, and said Pawn 'reducing' opponents (to one step) adjacently after having crossed center line(RN30); Rook and Queen both only able to go up to 4 squares, and Queen alone able to 'teleport' any adjacent piece(RN23), and opposite Queens only that attack each other thereby immobilizing Kings(RN32); Knight having Camel leap able to 'stone' adjacent piece(lasting 10 moves, RN24) and also to capture inversely(RN25), and also exclusively immobilizing along own line of attack, and further when captured changing sides for later drop, and finally also adjacent opposite-side Knights negating each other's capture ability (RN31); Bishop (plus Wazir) able to rank-jump (RN19) alternatively and also able to swap places along line of attack [there would be priority of first actual mover creating a condition for any conflicting effects from ''overlapping'' 'adjacencies' and 'lines of atack'] and said Bishop having 'hegemony drop' ability(RN29) upon reaching last rank; Falcon (as Ferz too) able to move cylindrically(RN15) and capture coordinately(RN28); and King having Knight leap once per game. Pre-placed sequentially before Move One in front of Pawns are: both Knight-moving Immobilizer(RN11) and Promoter(RN12); two one-step Warp Points(RN14); and two Philosophers(RN27). Also permitted are triangular transference(RN13) and switching any adjacent pieces(prohibited when already 'reduced' by that adjacent enemy Pawn), both these factors in lieu of a regular piece or Pawn move(s).

George Duke wrote on 2007-11-21 UTC
OrthoChess fundamentalists say there are being more game scores than atoms in universe, which would be 10^80. RN32, Strong Acid-Base. (a) no effect (b) Pairwise same-type opposite-side pieces (not Pawns) attacking each other immobilize the Kings and all pieces and Pawns adjacent to Kings. So long as condition holds, even King checked cannot move, ergo(likely) Checkmate. (c) Only Queens create the effect. (d) Only opposite-colour Queens and Rooks (d) Only Queens, Rooks and Bishops (f) 32b excluding Falcons (g) 32b excluding Queens (h) 32b excluding Queens and Falcons. Cumulative: 6.287832122 x 10^24(over 6 septillion). Notionally one CV for every single molecule in rare south Russian tube-nosed Bat Murina ussurrensis. Additional tribute to ''Orange Band'' the name of the last individual Dusky Seaside Sparrow, who died 1987 at Walt Disney World, Florida USA, species Ammodramus maritimus nigrescens, now extinct having survived 6 million years. Killed off by DDT and Kennedy Space Center development, declared extinct 1990. Survival of the Dimwittest.

George Duke wrote on 2007-11-19 UTC
RN31 Acid-Base: Pairwise same-type adjacent opposite-side pieces mutually lose their capturing ability. (a) no effect (b) Opposite-number Knights adjacent, diagonal or orthogonal, have their capture ability 'neutralized', negated. They can only move away without capturing. (c) Opposite Falcons so adjacent cannot capture, called the Acid-Base effect. (d) Acid-Base applies to Knight and Falcon. (e) A-B extends to all paired same-type opposite-side pieces adjacent. (f) Any opposite-side piece (not pawn) adjacency neutralizes each other's capture capability, irrespective of piece-type. (g) 31f applies only to pieces wholly in the two central files (e&f), the Cauldron. (h) 31f applies centrally to opposite pairs(any mix of types) within files d,e,f,g, the Wide Cauldron. 7.859790152 x 10^23, approx. 786 sextillion, exceeds Avogadro's number. Early hominid Australopithecus' companion: ''Nose in the mud and the bend of the neck of a thing to the ground, as a convenience in eating grass. The all-day gnaw of the fields. But the eater of meat is released from the munch. One way to broaden horizons is to climb a tree. Another way is to stand on one's own hind legs, away from the grass.''

George Duke wrote on 2007-11-19 UTC
RN30 Reduction, similarity to Lavieri's Reducer in Altair etc. 9.82473769 x 10^22 CVs (approx. 98 sextillion). (a) no effect (b) Pawns 'reduce', so that any piece adjacent to enemy Pawn can move/capture one square only. 'Reduced' B, R, Q go one square only along their regular paths, whereas Knight thus reduced becomes Wazir + Ferz and Falcon becomes Squirrel(N+Dabbabah+Alfil) all leaping components with no two-path necessary. (c) 30b Pawn reduction does not extend to Falcons. (d) 30b Pawn's reducing ability covers only Knights and Falcons. (e) 30b Pawns reduce only if on dark-square half of board. (f) 30b Pawns reduce (all enemy others adjacent) only once having crossed the center line. (g) 30b Pawns reduce only by lateral or forward one-square adjacencies. (h) 30b Pawns reducing (not isolated) next to last rank, one step from promotion, are themselves immune to capture at all. In tribute to the size range we pass through currently>  Elephants and Sunflowers: long stems;  Camels and Peanuts: humps.

George Duke wrote on 2007-11-19 UTC
RN 29 Hegemony, newly-devised Mutator. (Differently Japanese medieval 25x25 Tai Shogi has Emperor that can always move to any square on the board, except opposite Emperor's if protected.) (a) no effect (b) Any Knight upon reaching the last rank is immediately placed on any square (to capture too) other than one of that same last rank's squares and either King's square. (c) Instead, any Falcon reaching final rank (opposite its initial Pawns's row) has the 'hegemony drop' that one move. (d) Knights and Falcons have 'hegemony'. (e) Only Bishop has hegemony (always immediate mandatory one-turn implementation upon reaching last rank). (f) Hegemony of 29b (Knight) permits 'capturing' (checkmating) unguarded King. (g) Hegemony of 29c (Falcon) can thus 'checkmate' unguarded King. (h) In a twist, hegemony applies only to Kings themselves. Note throughout this Mutator permits up to two captures in one move. 1.22809221 x 10^22(over 12 sextillion). Present range in about RN23 to RN38 closely match and follow number of atoms or instead H2O molecules, progressively in Virus(interface inanimate), Prokaryotic cell, Eukaryotic cell, Argentinasuarus(largest), and all the gizmos 'twixt.

George Duke wrote on 2007-11-19 UTC
RN28 Coordination makes 1.535115264 x 10^21, approx. 1.5 sextillion CVs, in molecular equivalence approx. 2.5 milligram water medium (JJoyce). Frogs, fishes, worms: hops, flops, squirms. Coordinator captures piece by its move that discovers the captive on the intersection(perpendicular) of rank or file of the Coordinator and its King. More logical is paired same-type's coordinating that way to capture. (a) no effect (b) In addition to normal moves, same-side Knights capture also by mutually coordinating along one's arrival-square orthogonal lines perpendicular to the other Knight's, in the manner of Ultima/Maxima. (b) Upon completion of move Falcons only additionally capture coordinately. (c) Knight and Falcon are able to do so (these all enable capturing 1, 2, or even 3 at once). (d) Bishop, Knight, and Falcons capture mutually coordinating (only same piece-types effecting it). (e) Bishop and Knight only (f) Rooks only capture by mutual coordination. (g) The coordination-capture effect of 28c extends maximally 3 squares both rank and file (h) The capture (Knights) of 28b extends 4 squares at most orthogonally.

Joe Joyce wrote on 2007-11-19 UTC
Doug, thank you for the reference on mutators. With a little work, it was understandable. [I think/hope!] While JPNeto's specific examples of mutators are limited as to types, the write-up clearly indicates that any one chess variant can mutate into any other. So 'Mutator' really is another name for 'Rule or Board'. And, no matter how many new mutators we come up with, the total number of all variants will always and forever be exactly '1 Bazillion'. Joe

Doug Chatham wrote on 2007-11-18 UTC
Joe Joyce,
See this page for a description of what a 'mutator' is.

Joe Joyce wrote on 2007-11-17 UTC
Hi, George. Might I point out that Avogadro's Number, currently measured at 6.022 141 99 x 10^23 per mol, is the gram molecular/atomic weight of a substance; for hydrogen gas, 2 atoms of hydrogen, each containing 1 proton and 1 electron, combine to form a molecule with a molecular weight of 2, so Avogadro's Number [A] of hydrogen atoms weighs 1 gram, and of hydrogen molecules weighs 2 grams. Flesh is mostly water, molecular weight 18.  The number A [6.02x10^23] is almost 3 orders of magnitude larger than the current total number of your games, 'approaching 10^21', or, to consider this another way, it would represent about 30 milligrams of actual flesh. I won't be crass and point out this ain't exactly an elephant, but it is true you have about 5 orders of magnitude to go before your 'game mass' is visible at ranges longer than 'up close'. You're going to need more mutators; have you used 'fluid' and 'facing' yet? ;-) 

There are, however, some serious questions raised here, at least by implication. By the use of the numbers 'bazillion' and 'gadjillion', I was trying to indicate 2 very huge numbers that were noticeably different sizes. And I would like to examine the concept behind the bazillion number. Bazillion is the total number of games you will get, starting with Falcon, and ending with however many games that one game multiplies out to when *all* the mutators are applied. Does the number 'One Bazillion [derived from Falcon]' games include every other possible CV, some but not all CVs, or few to no other CVs? Are there games that fall outside the 'permutatability' of any, or some, or every other game, or do mutators rule supreme? What *are* mutators? Are they a specific class of things, limited in their applications, or are they another name for 'rules'?
Enjoy,
Joe

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