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Ninety-one and a Half Trillion Falcon Chess Variants. Missing description[All Comments] [Add Comment or Rating]
Jared McComb wrote on 2006-08-14 UTCAverage ★★★
'Wow, let's use really big numbers to try to impress people!'

Andy wrote on 2006-08-14 UTCPoor ★
System with many CVs is not bad idea, but many rules here are arbitrary, many alternate pieces are ugly such as variant pawns that don't fit system. And tacking on warp points, switching chess, etc. is ugly afterthough to get bigger numbers.

Gary Gifford wrote on 2006-08-14 UTC
While I am impressed that a relatively large number of chess variants exist, I am not impressed about our ability to greatly increase that number just for the sake of doing so. The old saying, 'Quality, not Quantity' applies. Yes, it is true we can have a large quantity of quality games.... but to simply tweak a rule, add a new piece, change a board size, etc., just to create a large volume of games is rather pointless. However, it could be that the 91 and 1/2 Trillion FCV page is a satire (but if so, why wouldn't it be 91 and 1/2 Trillion Chess Variants instead of limited to Falcon Chess Variants? Anyway, if it is a satire it is so well crafted that I do not recognize it as such. If it is not a satire... well, I just can't take it seriously.

Andy wrote on 2006-08-14 UTC
I don't think it is satire, I don't think it is bad idea. Fisher random chess is 960 variants. Capablanca random chess is some number of variants. Other systems have been made that are some large number of variants. It is good way of eliminating prepared variations and reducing impact of computers. But I think many pieces and rules in 91.5 Trillion FCV are not good fit for system.

Sam Trenholme wrote on 2006-08-14 UTCExcellent ★★★★★
As it turns out, there are 9,820 opening setups for Carrera chess where the king is to the left of the queen and between the rooks, the bishops are not next to each other, and all pawns are defended in the opening array. (Read my recent post on the chess variants mailing list for details).

As I commented before, I like the idea of a variant that has many different possible permutations.

Jianying Ji wrote on 2006-08-14 UTC
It is the lack of rules not their addition that increases the variety of
opening positions. A quick look at sit-tu-yin would suffice. Other than
pawns, the other pieces has no fixed starting points and can be placed
anywhere. I generally like chess variants that has free placements at the
start. Anything that obliterate openings while at the same time decrease
number of rules is alright by me.

This page seems to address something different entirely, that of number of
variants given a set of mutators, a term explicated and promoted by João
Pedro Neto. Each of the 'rules' is actually a mutator. It is no surprise
the number of variants one can create by stacking mutators together.

What is missing here is an over-riding theme. By theme I mean a organizing
principal, not the story that the variant tell. Without a theme to guide
the relationship of the mutators, we just have the mutators themselves,
which though interesting seem haphazardly grouped together.

Andy wrote on 2006-08-14 UTC
This system makes possible game of: 10x10 Charging Rook, Reflecting
Ultima Pawn, Restricted Queen, Double Move, Knight Immobilizer, Falcon
Promoter, Strict Triangulation, Bishop Warp Point, Cylindrical Knight,
Switching, Double Black Hole, Alfil Jack, Bishop and Knight Altair
Jumping, Falcon, Bishop and Knight Dropping Falcon Chess

George Duke wrote on 2007-09-12 UTC
'1a2a3e4a5b6a7a8a9a10a11a12a12a13a14a15a16a17a18a19a20a' represents in our system on size 8x10, out of *91.5 Trillion* possible chess variates of Falcon, the one Gary Gifford is calling this week under his Preset 'Latrunculi duo milia et septum' on 8x8. On 8x8 it works without any extra Falcon piece, but the same enhanced Bishop and Rook. I.e., we use here the Crowned Rook (R+Ferz) and Crowned Bishop(Bishop+Wazir) with Falcon, so there is that difference. Yet Gifford says self-righteously in Comment below respecting some conceit of 'quantity and quality' that 'I am not impressed about out ability to greatly increase the number just for the sake of doing so'. We imagine then that Gifford has some technique to single out R-Ferz and B-Wazir on 8x8 as particularly of high quality, suitably screened for display separately. Instead, we represent that one single CV along with the other 91,499,999,999,999 without discrimination. On 8x8 board, what about the other trillion that can easily be derived the same way as here in '91.5 Trillion'? Just prefix [88] to represent that size, eliminate Rule Number 6 about Falcon alternatives, and somewhere on the order of 1 to 10 Trillion easily remain systematically described unambiguously with little effort. Well, clearly 100, or even as many as 500, of them are already enunciated by others within CVPage, DPritchard's ECV or elsewhere, so how easy to add one, two, three (uncreatively or self-servingly) from such still-very-extensive available sample.

Joe Joyce wrote on 2007-09-13 UTC
It's true that it's easy to offer a write-up of a game or games that can easily be permuted to produce 'zillions' of games. My 4th post, Two Large Shatranj Variants, is the biggest lie I've ever told. There are 2 board sizes, an 8x10 and a 10x10, and I offer a range of possibilities that extends into the zillions, with alternate pieces for each type of piece, alternate placements of pieces in the standard setups, a number of different promotion rules, and, with Atlantean Barroom, a new approach to 10x10 board setups that produced a new setup for Paulovit's 10x10 game. From that I've drawn 3 games, Great, Grand, and Barroom Shatranj. I think most of the other games would be poor, with an inappropriate mix of pieces. I consider 'Too Large' a game system, not a game, with a total of 3 current games [+ 2 variants using rooks] as its representatives. Only 3. Not zillions.

As far as Gary's game, with the RF and the BW, well, even though I am not a fan of the approach of making FIDE more powerful by adding shortrange moves to infinite sliders, it is obvious that I am in a very small minority. The chess world obviously prefers augmenting the current power pieces somewhat to actually replacing any of the current pieces. That being the case, there are only 3 good solutions currently that I've seen: Gary's, adding the 'sidestep' to the B&R; yours, adding the moa and mao to the B&R; and Carrera's, adding the N to the B&R. Only 3. [And not excellent, but that's me.]

[EDIT] When I posted this, I saw George had made another comment. Okay, I'd like more of a write-up from Gary, too, but it's been my experience that people don't like all that written stuff getting in the way of the game. I got complaints about my verbosity, and suggestions were made that any little stories I might want to add could be put in the back where they're very easily ignored. After Too Large and Atlantean Barroom, what do you think I'd wanted to write for Lemurian Shatranj? Look at the page: it's a bare-bones minimal piece and rules description with no background or flavor aside from the name, which is effectively meaningless without the background.

Gary Gifford wrote on 2007-09-13 UTC
Comment re-located to the Latrunculi duo milia et septum comments, where it belongs.

George Duke wrote on 2007-09-13 UTC
3e5b is one systematized CV. These Comments are supposed to be for this article '91.5 Trillion...' There is no evidence that JGifford or GJoyce have got past the title. Leaving out the defaults, which have 'a', simply '3e5b' describes a complete game here. To repeat, [3e5b] is one CV on 8x10 with a complete, unambiguous set of Rules. It has 'RNBFQKFBNR' array, Bishops enhanced by Wazir, and Rooks enhanced by Ferz. It should be a good playable game. The new Latrunculi Preset is a comparable game on 8x8 without Falcons and is no doubt very playable. However, it is Poor for having originally left out documentations. Probably still other games have already used (B+W) and (R+F) on 8x8 too; we expect that Ralph Betza did. It was the inventor's responsibility to research the prior art, or just not present the CV as own. The larger issue is not critique of one sloppy job of research, but Proliferation. We shall start a thread 'Proliferation' to reconnect to Comments made 2003-2005 on that issue. Thanks anyway to Gifford for adding the references, showing some inclination to do the right thing.

Gary Gifford wrote on 2007-09-13 UTC
Removed by Gifford... comment not needed.

George Duke wrote on 2007-09-13 UTC
Actually, in one thousand(1000) lines of Falcon poetry, there is already much material, Gifford, about real Falcons as living species, ancient Egyptian avatars as well as modern symbols. GGifford seems to resent that it will take more work all the time to present anything valuable in CVs, and that mathematical treatment of the subject matter is inevitable. Your spontaneous assemblage of (R+F) and (B+W) is nothing but two people's subjective opinion that a particular form is more valuable, and please, GGifford and JJoyce both, let's agree to continue to adhere to the style Joyce himself enunciates in which not the more vociferous, but the more conscientious or analytical, prevail.

Gary Gifford wrote on 2007-09-13 UTCPoor ★
I tried real hard not to comment here... but, I was very curious as to what the result would be if I rated this variant using George W. Duke's very own 6 Point rating standards (as were used in his rating of Latrunculi). So I borrowed his rating comment, read over his 90.5 Trillion rules and analyzed. I could only reach the conclusion that while it is a very good page for gaming theory and mathematics, it is poor as a chess variant, despite there being 91.5 Trillion games claimed. We begin: (1)The CV passes this first category, though I might have missed a reference to Shogi. Latrunculi referenced Shogi pieces, but G.Duke did not count that anyway. This first category is the effort to cite precedents of previous use. He passes, good so far. (2)Game analysis - oops I didn't see any games or game analysis (3) Justification - hmmm... no, can't say I saw any, other than to reach a big number, but as the song goes, 'That don't impress me much' (4) Game Scores - nope, no game scores. Out of 90.5 Trillon games you think there would be at least one game score (5) Starting a game to play - with 91.5 Trillion Games ... no, I did not see those started. (6)Putting up a Preset - saw none linked to from the page. Final score: 1 out of 6. Perhaps I misused Mr. Duke's rating system... but I tried to apply it the exact same way I saw it applied to Latrunculi (which also got a poor 1 out of 6).

George Duke wrote on 2007-09-14 UTC
Earlier today GGriffith had a sentence posted 'I am not one who considers this Poor' about this same essay, then he deleted it along with other strange sentences, so the poor man is really agonizing over this. If you would, think of '91.5 Trillion' as a model for what is inevitably to come. I feel honoured by this particular Rating, thank you for it, and please do not be hypersensitive when we get around to your 20 CVs. In advance, most of them we happen to Rate will likely get 'Good', but that actually divides into Excellent Art work and Average playability. None of them appear to be much to play at first blush by our standards, yet thus will be glad to give a string of 6s and 7s out of 10(with explanations) for Griffith's competent work as and when our Comments ready. Since there are 3000 CVs here to Rate, it takes a little humility to see one's contributions in perspective, and eventually it will take mathematical and statistical organization to find the Excellent ones, or potential Orthodox replacements.

Gary Gifford wrote on 2007-09-14 UTC
Please be sure to understand, the 'poor' rating is only due to using the 6-Point Rating Method you showed me. I actually do not agree with that method, i.e, that sample games be required, games be in progress, etc. If I were to come up with my own standard rating method I believe we would see higher scores for our two games here. Best regards, and take care.

George Duke wrote on 2007-09-14 UTC
Perfectly serious 732 TRILLION Falcon Chess Variants. The Model is fully extensible, both componentized and augmentable. Therefore, Rule Number 21 follows(new arrays): a-(default) standard RNBFQKFBNR, b-RBFNQKNFBR (Templar's), c-FBRNQKNRBF (Pyramids'), d-FRNBQKBNRF (Cheops'), e-BRNQFFKNRB (Horus'), f -RNBKFFQBNR (Osiris'), g RNBFQKFBNR (Sphinx), h FNRBQKBRNF (Nile). So, for example, simply '3e5b8c21d' is fully described as 8x10 Chess with medium Queen up to five spaces, Bishop-Wazir, Rook-Ferz positioned initially on second-choice array FRNBQKBNRF. Period. That's it. Complete game. No pretentious singling out one subjective form. All the supporting material, poetry, Mates in Two and Three, Presets entirely available through close links. This will be the last of the new arrays, because we eschewed that method as more for achieving quantity in the last couple paragraphs of our essay. Extensions 22 through 30(toward a GOOGOL variates, 10 to the 100th power) will be Rules changes continuing to be deemed the highlights of Chess Variant Page 1994-2008 incorporated to patented FC. We can do that and you cannot. Will we eventually use your pet Mutator or will your best-laid project be consigned to oblivion?

George Duke wrote on 2007-09-20 UTC
'20b22b' is one CV, specifically Falcon Chess RNBFQKFBNR with selective drop of any captured Falcon changing sides and conventional same-coloured Swap in lieu of a move. 5 Quadrillion 856 Trillion CVs defined plain as day. Rule Number 22: (a) no effect (b) In lieu of move, player may swap any Piece(s)/Pawn along one's line of attack with Pawn having the power along its one-square forward diagonal (c) King prohibited to initiate Swap (d) King dis-allowed to be swapped at either end (e) If Cylinder Rules(RN15) in effect, swap permitted across the sides Cylinder-like (f)Swap allows Cylinder-compability and also across any Warp Points(RN14)by Warp Point rules (g)Medium swaps only up to 4 squares (h) Short swaps only exactly 2 squares pieces so spaced. For ex., '7b15b20b22c' is standard with Falcon singled out for both Cylindrical power and selective drop capability as a move any time after one's having been captured, and also normal Swap(of any piece/pawn except King) as a move. 5,856,000,000,000,000.

Joe Joyce wrote on 2007-09-20 UTC
George, this makes you far and away the most prolific not merely chess variants but all games inventor of all time. ;-)

George Duke wrote on 2007-09-26 UTC
Easy as pie. or Pi. or Pi to 23 places, 3.14159265358979323846264... Rule Number 23(after RBetza's Wand one): a- no effect b- Queen has power, in lieu of a move, to teleport an adjacent piece to any empty square c- Falcon only has such capability d- Knight only has the power at option e- Q,F, and N may so teleport only an enemy piece f- King alone may so teleport any enemy piece within two squares g- Just Pawn may teleport any adjacent enemy piece to vacant square behind that Pawn's position any rank h- Pawn alone may teleport any adjacent friendly piece forwardly to any empty square of any rank. Resulting in 46 Quadrillion Eight Hundred Forty-Eight Trillion CVs. 46,848,000,000,000,000. For example, one as perfectly playable as any typical post-up is '2d7g21d23h'. 2d7g21d23h represents precisely Chess with Falcons starting 8x10 as RNFBQKBFNR with free castling, Berolina Pawns and said Pawns alone able to teleport any adjacent friendly piece forwardly to any available empty square in lieu of ordinary move.

George Duke wrote on 2007-10-11 UTC
Each and all are perfectly serious CVs, not ballyhooed one by one by one by one, but presenting themselves collectively. It saves time, a lot of time. Rule Number 24 [after Ralph Betza's Wand Chess wand 4] : a) No effect. b) Instead of ordinary move, Knight or Falcon may 'Stone' an adjacent piece or itself, effecting its immobilization and immunity from capture for 10 moves, whereupon the piece returns to normal. c) Any piece has the power of stoning. d) Only Knight has the capability. e) Any piece has the stoning ability along its line of attack instead. f) Pieces and Pawns both have the power along their line of attack(capture) effective for 5 moves. g) The effect of choice 'f' is good(mandatory) for a full 10 turns. h) Only same-coloured pieces may be stoned by the manner of option 'g'. Thus reaching 374 Quadrillion 784 Trillion separate Rules sets, perfectly playable CVs. For example, with the other provisos registering their defaults, '3b8b20c24e' represents Falcon Chess RNBFQKFBNR with free castling and no Queen promotion, utilizing Charging Rooks (that move backwards only like King), Queen up to 4 spaces and the rest standard pieces and pawns; with also captured Knights changing sides for drop in lieu of a move, and finally this new Mutator choice allowing any piece to stone along line of attack for 10 moves(see above). 374,784,000,000,000,000 CVs.

George Duke wrote on 2007-10-26 UTC
Rule Number 25. Reaching the Quintillions. 2,998,272,000,000,000,000. No rounding up to 3 Quintillion either, leave it that way. A logical thread too. Here we ask the age-old problem, how can Knight or Bishop be further strengthened on 10x10? Answer in part, Selective Inverse Capture. (a) No effect (b) In addition to regular move and capture, Knight attacked by any piece or pawn may capture it by its manner (c) Bishop only has the power of Inverse Capture[Ralph Betza's ICC] (d) Both N and B have the capability (e) Falcon only adds this inverse capture provision to her repertoire (f) Knight, Bishop and Falcon (g) The provision of 'b' excludes Pawns attacking (h) The sub-rule 25d excludes only Falcons, never able to be captured inversely. For example, '1c4b25d' strengthens Knights and Bishops on 10x10 to the extent that Knight can also move as Camel at option, and Knight and Bishop both may capture inversely. Period. Fully described. No need for separate Chess Variant Page write-up #3501, nor politics.

George Duke wrote on 2007-11-09 UTC
OrthoChess apologists like to say religiously there are more possible chess games than atoms in the Universe. We have all read that in Chess columns when they get defensive. [Continued below] Rule Number 26, Selective Immobilization: a) No effect (The following differ from RN 24 'Stoning' in that this Immobilization persists.) b) In addition to normal power, Knight immobilizes adjacent enemy piece or pawn. c) Both Knight and Falcon have the Immobilization effect. d) The power for Knight only is Betza's Basilisk-like along line of attack. e) The capability for Knight is Betza's Medusa-like only if opposing piece/pawn (along its line of attack) can 'see' the Knight. f) Version 26d applies to Knight and Falcon. g) Version 26e applies to N & F. h) The immobilizing ability of 26b excludes Pawns. Cumulative: 23,986,176,000,000,000,000. //[Continued] As far as Chess games exceeding number of atoms, they mean of course game scores of 64-square (32-piece) Chess. What they do not tell you is that includes millions of ridiculous games computer-generated like moving White Bishop repeatedly e4-d5-e4-d5-e4-d5-e4 (because Black is moving too, so no 3-fold repetition). The next '91.5 Trillion...' Comment we will develop how the potential number of game scores compares to atoms (and number of elementary particles) in Universe, considerably fewer than a Googol (10 to 100th). Also whether even the number of CVs, let alone scores, is a Cantorian continuum or merely infinity of the Natural numbers, Aleph-naught. What Cardinality has the number of Chess Variations? Which of the two infinities are CVs, countable or otherwise(C)?

Joe Joyce wrote on 2007-11-14 UTC
Hi, George. While I'm not up on my math, I think the numbers of chess variants are limited. Instead of building up from the bottom, taking games like Falcon Chess and showing how each variant can be modified in all sorts of ways, giving zillions of games, let's look at it the other way, from the outside rather than the inside, so to speak. What are the hard limits of chess? There are 3 components to a game, the board, the pieces, and the rules. 
Board size: it can't get much smaller than 1 or 2 squares, nor can a game of chess go much larger than a 100x100 2D board. Even the 'infinite board' variants really don't need more than maybe 1000x1000, and realistically, can be pretty much played out on 100x100 without too much trouble. Let's take 100x100 as our top size, then, for a board; 10,000 squares should be enough room for most games of chess. And we can deal with the rest later, should that be necessary.
Numbers of pieces: If you assume 50% board coverage, then 5000 pieces is about the maximum number you'd want on the board. That seems a bit much for me. Without some tricky movement rules, I've found that 100 pieces per side is a bit much. And without some tricky piece design, 25 different pieces per side is also a bit much. Even if you go with 1000 pieces per side, and 100 different pieces [a team chess game if I ever saw one], that's still a  number we're familiar with. And running all the permutations through just gives you a very big number. And only potential, not actual, games.
Rules: here's where we get crazy. This is where we think all the infinities come in. And we all too often design game systems instead of games, adding to the mess. And what else we often do is mistake the potentialities of the system for the actualities of games. The map is not the territory. Further, while we're into the gadjillions of potential games through permutations, all these games still, in principle, are countable - we're doing it ourselves as we go along. So let's say that the total number of permutations to any starting game is [on the order of] one bazillion, with the specific value of bazillion to be determined [by actual count] in the future. 
Number of chess variants: Currently, there's about 1000 - 10,000 CVs, giving somewhere between 1 and 10,000 bazillion known total potential CVs. Since they're made by people, one way to look at it is that unless there are people and chess forever, the number of variants cannot be infinite. Current theories of the universe favor the less than infinite position.
How many ways can a piece move? On a board of 1 - 10,000 squares, how many different ways can a piece move? ... ... ... Now, dump the really stupid ways. Does that add up to infinite? [Even putting the really stupid ways back in doesn't; heck, people with computers'll play and do darn near anything. And, judging by the spam I get, they think I will, too!] 
How many different boards are there? Well, this has gotta be a very big number, but it has to contain between 1 and 10,000 or so squares that have to be connected in some sorts of ways for the pieces to interact. If you dump the turkeys, it becomes a somewhat manageable number, at least conceptually.
Each new game is going to add either a new bazillion to the total number of CVs, or is going to increase the size of a bazillion for all the other games [at least; truly innovative games may do both, more than once]; in either case, it's countable. 
Chess occupies a limited area in 'game space', that conceptual area where all games are found and [somehow] categorized. And it is a game of discrete parts, digital in nature rather than analog. Pieces and board positions come in units: in chess, the number of squares on the board is set in the rules [even if the rules allow changes, these are determined by the rules] and the number of pieces on the board is there for all to see [and count]. Changes in this number of pieces are again determined by the rules and the actions of the players as allowed by the rules. But all changes are in discrete units, going up or down some whole number, of the limited number of pieces or squares we can have in a game that can be called 'chess'.
Given that humans play these games, either on boards or on computers, I think a case has been made for a very large but countable number of realizeable games. And even playable games. And given the limitations of humans [and you can interpret that broadly to include until-now hypothetical intelligences if you wish], I think it's more reasonable to assume there is a limit to the number of decent chess variants, and, by extension, all chess variants. And while the former number may well be a question of taste, the latter number is easily seen even without calculation to be a number far huger than the total number of chess games ever played or, most likely, to be played. 
So, the number of variants is effectively, if far from actually, infinite, but most of the best pickings are near the top. While many weird and complex games may gain great stature in the future, I think that the percentage of 'hits' will be higher in the smaller and simpler games, and spread out in the larger number of more complex games in a pattern much like that of prime numbers. 

George Duke wrote on 2007-11-14 UTC
Clearly JJ misses the mixture of irony and analysis involved in developing '91.5 Trillion..' toward a Googol variations. Joyce in starting, ''While I'm not up on my math...'', is certainly correct. The unifying theme by the way is 'the best Mutators of CVPage 1995 through 2008'. Nice try at understanding, Joe, but the point of an 'infinite' number of CVs is the real fact that Chess columnists often write that there are more possible chess game scores than atoms in the universe, not really infinite at all of course. Have you read that before? We have read that dozens of times from Larry Evans to Mike Henroid only last month. One message likely would be the utter pointlessness of a Googol (or even 1000 actually) separate CVs(FCVs really are 1 only), becoming even more pointless than [tens of] millions of game scores of one particular form. A second challenge, Joe, would also be how to state a position succinctly as part of your system, or philosophy, not too hard on readers in literal length of text. With thanks for interest, is JJoyce taking offense at drawing attention to reality of so many CVs and thinks to try, however ineptly, to be ironic in turn? [Well, 'ironic' is too nuanced adjective for this case; we guess the attempt by JJ's lengthy Comment is trying to be 'humorous', by use offensive words like 'bazillions', 'gajillions'.]

Joe Joyce wrote on 2007-11-14 UTC
George, I've been enjoying your leg-pulling for quite a while now. 

Senorita Simpatica wrote on 2007-11-14 UTC
A speck of dust can contain 3x10 to the twelfth power (3 trillion) atoms. So, that is just for one piece of dust. Now, imagine how many pieces of dust it would take to make up your game pieces and board for just 1 copy of a variant. So, some might argue, that variants can be conceptualized and require no consumption of atoms. But there are quite a few atoms involved with conceptualization, which requires an electro-chemical thought process. Just something to think about before one runs off to try making more variants than there are atoms.

George Duke wrote on 2007-11-15 UTC
Remember OrthoChess experts are always saying their game-scores potential is greater than this huge number, therefore, their Rules must never change. We are seeking 4x10^79, the number of hydrogen atoms in Universe. That is considerably fewer than so-called 'Googol', 10^100. It will take some 60 or 80 more Mutators to the 25 already, not so difficult. No one has much wanted to address Proliferation seriously, except to tout their own inclusions, so the experiment is illustrative. Actually, we could achieve the same 4x10^79 in myriad ways, and it could be interesting to do for 20-40 other worthwhile CVs. Appreciate the speck of dust factoid-Comment, because we were going to establish a sort of 'midpoint' which is not much greater, [maybe only encompassing the Solar System. (*Later, not very accurate, only less than Earth, remarkably, Earth having 8x10^49 atoms or so*)]: 'midpoint' in terms of number of zeroes. We actually prefer either 3, or 4, or 5 CVs altogether, no more than 6 or 10, even if it means 'consigning to oblivion' (David Pritchard's words in Intro 'Encyclopedia of Chess Variants') all of the rest.

Pierre wrote on 2007-11-15 UTC
George Duke, who is 'we'?  Why do you repeatedly refer to yourself in the
first person plural??  Delusions of grandeur???

George Duke wrote on 2007-11-17 UTC
To humour, Joe Joyce is correct some are better than others and they could surely be Centennial Chess etc. instead only by tweaking. Yet with RN27(Philosopher's Chess) making 1.91889408 x 10^20 CVs, they line up for fun like billiard balls, and appear well into visible range of masses having equivalent number of atoms(as CVs). Approaching 10^21(sextillion) means within order of magnitude or two of Howlet's wing or Elephant's trunk. One CV for every atom -- Atom! -- in the tail of a Dolphin. Separately delineated as '1c6e27d', representing one exclusive game, Falcon Chess on 10x10 RNBF..., with Falcon enhanced by Knight leap, and four(4) Philosophers pre-placed in front Pawns, to move 1 orthogonal in lieu of a regular piece move, or 'converting' to either of two other modes of four total (w,x,y,z)always applicable to both sides at once. // End of Rules for '1c6e27d' // Explanation: Philosophers are pre-positioned before Move 1 by agreement in the rank before each side's Pawn row. Philosopher moves conceptually 1 diagonal only(w), or 2 diagonal leaping(x), or 1 orthogonal only(y) default, or 2 orthogonal leaping(z). For conversion (like Philosopher's 2x2), (w,z) and (x,y) are pairwise non-adjacent. (a) no effect; (b)Two Philosophers preplaced. In lieu of a normal move, player may move 2 Phils. or 'convert' adjacently '1o' to (2o or 1d), '2o' to (2d or 1o), '2d' to (2o or 1d), '1d' to (2d or 1o); (c) 3 Philosophers after 27b; (d) 4 Philosophers following 27b; (e) 5 Philosophers 27b; (f) 6 Philosophers 27b; (g) 5 Philosophers 27b, and player may move two (mandatory) or move only one and 'convert adjacently' the same way, in either order. (h) 5 Philosophers according to 27g with three Philosophers moving (mandatory) or two(mandatory) and conversion in any order, in lieu of normal piece move.

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'?

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 2007-11-19 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

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.

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
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
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 2007-11-21 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 2007-11-24 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 2007-11-26 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 2007-11-29 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 2007-11-30 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 2007-12-04 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 2007-12-31 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]

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

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.

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 2008-01-05 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.]

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:

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

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.

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 2008-01-09 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 2008-01-10 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 2008-01-11 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 2008-01-12 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 2008-01-14 UTC
RN213 The Sea Is Rough. One or more squares skew line pieces exclusively and systematically. [48 variates, one theme: see also Betza's Earthquake and Sibahi's Quake Chess for relatedness.] (a) no effect (b) Whenever Kings are on opposite-colour squares, the Sea is Rough. So, standard 8x10 and 10x10 the Sea is Calm initially. When Sea is Rough, line pieces (RBQ) travel one, two or three steps normally, then shift 45 degrees one square, after which continuing in original direction. Where the shift actually begins (at the third square) determines whether it is right or left. For this 'RN213b', any square left side of board effects shift 45 left, and right side 45 degrees right. (On such as 15x15, RN301, either shift may be employed at option along the center line.) (c) 'b', shift occurs square two. (d) 'b', shift-effect takes place square four. (e) 'b', shift begins at square one, i.e., after one normal step. (f) 'c', Knights also shift by moving to (2,4) or (3,4) at option but no further. (g) 'e' and 'f' (h) 'b', right side and left side reverse, called 'Southern Hemisphere effect' (i) 'b' except Sea is Rough iff defined shift-square is same colour as King's present square (j) 'b' except the determinant is the combined Kings' ranks being odd (k) 'b' except the determinant is the combined Kings files being odd (a=1,b=2...) (l) 'b' with the determinant(odd) the combined number of pieces and Pawns adjacent to own King (m) 'l' only pieces (n) 'l' only Pawns (o) 'l' opposite King's pieces (p) 'l' opposite King's Pawns (q) 'l' enemy King's pieces & Pawns (r) 'c'&'j' (s) 'd'&'j' (t) 'e','f','j' (u)'e','f','k' (v)'e','f','l' (w)'d','f','k' (x)'d','f','l' (y)'d','f','n' (z)'d','f','o' (aa)'h','k' (bb)'h','l' (cc)'h','m' (dd)'h','n' (ee)'h','i' (ff)'h','j' (gg) 'h','k' (hh)'h','l' (ii) 'h','m' (jj) 'h','n' (kk) 'h','j' (ll) 'c','f','q' (mm) 'd','f','q' (nn) 'd','h' (oo) 'e', with Pawns also shifting on double step. (pp) 'e', 'f' 'oo'. Cumulative: 9.009591024 x 10^41, as many games as water molecules in notional cylinder upon, or within, the Atlantic Ocean 3.0 kilometers in diameter and 0.5 kilometer deep.

George Duke wrote on 2008-01-15 UTC
RN214 Hot Potato. Capture more widely than particular square a piece rests. (a) no effect (b) Player designates opponent's Hot Potato, one piece-type for the duration. Hot Potato, being either RNBF or Q any of which, can be captured only on 8 adjacent squares that are vacant, not present standing square. (c) 'b', Hot Potato can be captured only on such adjacent Black squares. (d) 'c' White squares for Black side and Black for White (e) 'c', King and Pawn may additionally capture H.P. on standing square. (f) 'd', 'e' (g) 'b' H.P. captured only on orthogonally adjacent square (h) 'b' as 'g' except diagonally adjacent (i) 'c', 'e', 'g' (j) 'c', 'e', 'h' (k) 'c', 'f', 'g' (l) 'd', 'f', 'h' (m) 'b', 'e' (n) 'd', 'f' (o) 'b', 'c', 'g' (p) 'b', 'c', 'h' (q) 'b', 'd', 'g' (r) 'b', 'd', 'h' (s) 'b', Player may relay Hot-Potato designation to any adjacent own piece-type by sacrificing one Pawn, immediately removed, in lieu of turn. The chosen piece-type becomes the side's H-P. (t) 'e', 's' (u) 'd', 'e', 's' (v) 'f', 's' (w) 'f', 'g', 's' (x) 'f', 'h', 's' (y) 's', the relay, or change, requires two-Pawn sacrifice. (z) 'e', 'y', (aa) 'd', 'e', 'y' (bb) 'f', 'y' (cc) 'f', 'g', 'y' (dd) 'f', 'h', 'y' (ee) 's' three Pawns (ff) 'e', 'ee' (gg) 'd', 'e', 'ee' (hh) 'f', 'ee' (ii) 'f', 'g', 'ee' (jj) 'f', 'h', 'ee' (kk) 'b', capture of any H. P. voids the effect for remaining duration. (ll) 'c', 'kk' (mm) 'b', capture of any H.P. removes any other H.P., meaning same piece-type of the side. (nn) 'c', 'mm' (oo) 'd', 'e', 'mm' (pp) 'f', 'mm' (qq) 'f', 'g', 'mm' (rr) 'f', 'h', 's', 'mm' (ss) 'd', 'e', 'y', 'kk' (tt) 'd', 'e', 'y', 'mm' (uu) 'g', capture of H.P. with no more of that piece-type on board relays the H.-P. effect in the sequence NBRFQN, so there is always Hot Potato whilst any piece at all on board by side. (vv) 'uu' except reversing as NQFRBN. Cumulative: 4.32460325 x 10^43 playable Chess Rules-Sets in combination.

George Duke wrote on 2008-01-16 UTC
RN215 British Bulldog. Capture is by tackling. [See Winther's Bifurcation pieces for relatedness.] (a) no effect (b) When tackling, the victim is taken in normal move of the piece by replacement, but the tackler's momentum carries on systematically. Rook, Bishop, Queen tackle-capturing end up forward of the target square one step 45 degrees offset. (Rook at c1 takes c4 and Rook's arrival square becomes d5 or b5 at option.) Knight tackles to Falcon squares, Falcon to Scorpion squares. No King or Pawn tackling. If no arrival square is available those ways beyond the victim, tackle (and capture) is illegal. (c) 'b', Pawns tackle like RBQ one step 45 degrees forwardly only (two spaces altogether from Pawn departure square). (d) 'b', Kings tackle by direct one-step counter the victim's position. (King e2-d3 takes either e3 or d2, or both.) (e) 'd', No King double capturing means choice of victim. (f) c,d (g) c,e (h) d,e (i) 'c', En passant tackling to the logical forward one-step 45-degree-angled (j) c,d,i (k) c,e,i (l) 'b', Knights alone may double tackle-capture (Nightrider-like), useful on 10x10 empowering Knight. (m) c,l (n) c,d,e,l (o) b, no tackling on the adjacent square (p) b,d, no tackling on the adjacent square except that performed by King (q) b, If a protected piece is tackle-captured, the protector (player and piece) immediately may 'untackle'. To untackle means moving onto the square just vacated by the captured piece normally, and ending in a legal tackle position just beyond; finally in third step, the just-captured piece reappears on its selfsame square. (r) q, untackling permitted up to two following turns (s) c, q (t) d,q (u) c,d,q (v) c, d, e, q (w) d, r (x) c,d,r (y) c,d,e,r (z) d,o,q (aa) c,d,i,q (bb) c,d,e,i,q (cc) d,i,r (dd) c,d,i,r (ee) c,d,e,i,r (ff) d,i,r (gg) d,q,l (hh) c,d,l,q (ii) c,d,e,l,q (jj) d,l,r (kk)c,d,l,r (ll) c,d,e,l,r (mm) d,i,l,q (nn) c,d,e,i,l,q (oo) d,i,l,r (pp) c,d,l,r (qq) d,i,l,r (rr) d,o,q (ss) c,d,e,o,q (tt) d,o,r (uu) d,e,o,r (vv) d,i,o,r (ww) d,i,o,r. Cumulative: 2.07580956 x 10^45 separately-playable Chess Rules-sets, now within four or five orders of magnitude how many atoms exist throughout planet Earth.

George Duke wrote on 2008-01-17 UTC
RN216 Sinkhole. Player moves piece and also the Sinkhole. The Sinkhole has neither Warp Point Chess nor Jacks & Witches Teleporter-square modalities, but has some similarity. Strategic move to Sinkhole and loss of piece thereby may rarely open lines of attack. (a) no effect (b) Player moves piece/Pawn and then the Sinkhole mandatorily one square King-like. (c) b, Sinkhole moves Dabbabah-like. (d) b, Sinkhole moves Alfil-like. (e) b, Two symmetrically-placed Sinkholes by agreement (f) c,e (g) d,e (h) The piece (not Pawn) lost into Sinkhole immediately effects an upgrade of any chosen remaining piece with that one's moving ability, usually creating a compound. (E.g., Bishop moves to Sinkhole, disappears, and immediately a Knight by choice becomes Carrera Centaur (BN), a.k.a. Cardinal. (i) c,h (j) e,h (k) f,h (l) g,h (m) h, Pawn lost (deliberately or forcedly) to a Sinkhole upgrades King right away to promotable royal compound. In other words, that empowered King reaching the last rank promotes, as usual for Pawn, to royal NBRF (typical case, RN1) at option. (n) b, As alternate win condition, seven(7) pieces/Pawns lost into Sinkhole(s) win the game. (o) n, 6 pieces/Pawns (p) n, 5 pieces/Pawns. Cumulative: 3.321295296 x 10^46 distinct Chess games.

George Duke wrote on 2008-01-23 UTC
RN217 Dual Capture. Capture is more deadly, always able to remove two units. (a) no effect (b) Capture by standard replacement removes, in addition, one more piece or Pawn of opponent's side. The criterion for the second unit lost, immediately upon completing any normal capture, is 'closest' or 'nearest' Pawn/piece. One away diagonally equals one away orthogonally. To distinguish the two-phase capture, the first phase is 'capture' and the second is compulsory 'removal'. If two or more are equidistant from that arrival square, where the regular capture takes place, the capturer then chooses. Squares blocked, even for Knights, do not count in figuring distance away. (For ex., White Pawn-c4 x Pawn-d5 captures Pawn-d5 and, if Black Bishop at d4 and Black Knight at e4, White picks between the latter two for removal.) (c) 'b', the dual-capture effect excludes capture by Pawn. (d) 'b', effect excludes capture by or of Pawn. (e) 'b', effect excludes capture by or of Pawn and excludes Pawn removal in second phase. (f) 'b' requires only Pawn, not piece, in the second 'removal' phase. (g) 'c', 'f' (h) 'd', 'f' (i) 'b', only capturing with Knight and Falcon implement effect. (j) 'b', 'd', 'i' (k) 'b', 'e', 'i' (l) 'b', 'f', 'i' (m) 'b', capturing with Knight only activates. (n) 'b', capturing with Knight, King (o) 'b', capturing with Knight, King, Falcon (p) 'b', only with Falcon, King (q) 'b', Instead the 'dual-capturing' of this RN removes another of the piece-type regardless of position, proximity not being the factor in this modality. (r) 'q', If none exist, one of that piece-type of own side must be removed upon the normal capture. (s) 'c', 'q' (t) 'd', 'q' (u) 'e', 'q' (v) 'f', 'q' (w) 'i', 'q' (x) 'i', 'q', 'r' (y) 'j', 'q', 'r' (z) 'k','q','r' (aa) 'l', 'q', 'r' (bb) 'm', 'q','r' (cc) 'n','q','r' (dd) 'o','q','r' (ee) 'p', 'q', 'r' (ff) 'b', 'q', 'r'. Cumulative: 1.0281472 x 10^48 distinct Chess Rules-sets. Remember: Earth has 10^50 atoms. We shall need criteria to evaluate so many examples and somehow reduce the sample set. One start might be to key off Western Chess. It would mean forgetting about admittedly-great Xiangqi, which warrants its own millions of variations somewhere. Xiangqi sites do not get preoccupied with multiplicity of form, possibly because we do it for them. Just ignoring Shogi, with its about average playability to most, as regional form, is far easier.

George Duke wrote on 2008-02-16 UTC
EnjoyLolHeyFarOutPuddingheads. Trial-and-error birds-of-a-feather, one size fits all? No way. Working towards one CV per atom in the Universe, no light-weight matter finding entities approving each of incipient 10^80 rules-set, on account of strict self-evaluation and autonomy. RN218 Mutual Annihilation. [The Swapper in Rococo has option to do this adjacently only; otherwise inferior CVs -- with huge armies or overdone piece differentiation -- have similar effect, that we recall offhand.] (a) no effect (b) Capture removes both pieces involved. IOW, capture by replacement is normal, except for both being taken off the board. HEY, they are on the same square! It has no bearing on check as such or checkmate. This Mutator works best with enhanced-piece Mutators like RNs 4,5,6,7 in the article and follow-up Comments. That way checkmate by even one piece alone may be very plausible, according to specific design. (c) 'b' excludes Pawns capturing. (d) 'b' excludes Pawns captured -- making Pawn capture rare. (e) 'b' excludes Pawns capturing or captured. (f) 'b' applies only to Falcons capturing. (g) 'b' applies only to Falcon & Knight capturing. (h) 'b' Falcon, Knight, Queen (i) 'b', instead the capture returns the capturer to any own starting array same-rank square by choice. (j) 'i' only Queen & Falcon (k) 'b' returns Pawns alone capturing to any Pawn second-rank array square. (l) 'd' and 'k' (m) 'f' and 'i' (n) 'g' and 'i' (o) 'h' and 'i' (p) 'i', the opponent chooses the initial array square. Cumulative: 1.64503552 x 10^49 separately-distinguishable and respectable Chess Rules compendiums. Earth has near 10^50 atoms, so almost the CVs now for that milestone. The '24.November.2007' Comment establishes that the individual CVs are easy enough to call up for one given complete Rules-set, limited to realistic 32 Mutators activated for playable game to taste.

George Duke wrote on 2008-03-22 UTC
RN219 Northern Exposure [after 'Northern Exposure *TM*, see Disclaimer] (a) no effect (b) Joel Fleischman is misfit M.D., transplant from Flushing and Columbia, so Bishops move is normal, except last step requires one final step orthogonal 45 degrees right or left, as in half of Rennaissance Chess Cavalier pattern. (c) Maggie O'Connor the flyer is Falcon, altered to jump one only at option along pattern, not capturing the one jumped. (d) Ed Chigliak is Pawn (see also 'n') and Native Pawns mimic at option the nearest same-side piece's method, provided no friendly Pawn as close or closer. (e) Knight Chris Stevens at options retracts last move and moves from either square-location as bona fide present move. (f) Maurice Minnifield astranaut-King may jettison any check by 'invoking authority', meaning any friendly Pawn, protected by Pawn, may upon any check, interpose to any square thwarting said Check, in lieu of other move. (g)  Holling Vincoeur Rook, being French, operates from a pedestal. Rook cannot reach adjacent squares, but starts at Dabbabah square and moves onward. Additionally no castling, but anytime once-per-game switch(exchange of places) of King and Rook, provided King unchecked, regardless other disposition of pieces or prior movements. (h) Shelly Tambo Queen Northern Lights goes as Queen only up to 4 squares, jumping one permitted, as Falcon in 'c', with no permitted capturing the (first) unit overtaken. (i) b,c,d,e,f,g,h (j) 'i' with 'f' any protected piece also (k) 'j' with 'h' 5 squares (l) 'j' with 'c' up to two (m) 'k','l' (n) 'i' except 'e' has right-side Pawns(Marilyn Whirlwind) empowered with all-orthogonal-direction capture (no diagonal at all) only (o) j,n (p) k,n.   Cumulative 2.64856  x 10^49 CVs crosswise allowing up to 32 Mutators activated.
[The above one-paragraph chess quasi-parody, and self-parody, in yet serious untheatrical exposition, respecting copyright of USA television series 1990-1995, intends no commercial use or other publication whatsoever.]

George Duke wrote on 2008-03-28 UTC
RN220 Northern Exposure[TM] Pawns -- disclaimer at 219. Each of 7 piece-types individually deserve fuller treatment. Six of them are Holling Vincouer Rooks, Chris Stevens Knights, Joel Fleischman Bishops, Maggie O'Connor Falcons, Maurice Minnifield Kings, Shelly Tambo Queens. Ed Chigliak Pawns(ECP) and Marilyn Whirlwind Pawns(MWP) follow. The case 'RN220b' right below represents one of first couple instances so far we have had of a RN 'calling' another RN. The real over-all development trends toward #CVs exceeding # elementary particles in this known Universe (a) no effect (b) Call 'RN219n', but instead, ECP and MWP are alternately a-file Pawn, b-file Pawn, c-file... (The largest board size 16x16 under 'RN301 Sizing' thus has MWP as p-Pawn.) (c) 'b' except ECP cannot move as the nearest piece of choice from an array position (d) 'b' except ECP only so move within far half of board (Recall that under RN 219 throughout, any friendly Pawn close by negates the empowerment: so ECP are most often ordinary Western Pawn.) (e) 'b' for ECP takes effect only after Move 15. (f) 'b' for MWP dis-allows capture orthogonally backwards. (g) 'b' for MWP captures orthogonally backwards only. (h) 'b', MWP promote immediately upon crossing center line. (i) 'b' except the distribution in initial set-up requires players pre-select and -place any chosen mix of ECP and MWP before Move One. (j) 'c', 'i' (k) 'd', 'i' (l) 'd', 'g', 'i' (m) 'd', 'h, 'i' (n) 'h', 'i (o) 'g', 'h', 'i' (p) 'c', 'g', 'h', 'i'. Cumulative 5.16849473 x 10^50 now actualizes more-than-remotely-playable CVs of greater number than atoms in the Earth [Calculations show Earth to have 10^50 atoms], the running total so far.

George Duke wrote on 2008-04-07 UTC
Next RNs 221-225 are to be Northern-Exposure R,N,B,Q and K in turn. We also have a 300-series of Mutators. Plausible future Mutators include Move-Turn Order, because so far only RN10 has used that idea very minimally. Actually, there is never shortage of material whatsoever. Ralph Betza's work alone suggests 50 or 100 additional Mutators not yet implemented here. Incidentally will #CVs exceed # elementary particles in Universe? Easily only the next 50 or so Mutators achieve that. Theoretical infinity of CVs, totally different concept, would be separate demonstration in mathematical mode.

Rich Hutnik wrote on 2008-04-07 UTC
The next challenge, get this up to be infinite.  You could also go with drops and gating that even add more pieces to it, and change when they come in, and create a reserve.  One could also go with the idea of mutators that enter the game at different times.

Did we even begin to discuss the board that it could be played on?  We could even vary the boards here.  So, he idea is mutators, shuffle, drops and gating, different pieces, etc... to end up with a different game.  

So, what else can be added to make it infinite?  I believe to have this, is that ONE element that is infinite get added to the mix.  This should be a practical element that can be implemented.

May I suggest people also take this discussion to the Chess of Tomorrow project Wiki discussion to discuss going infinite?

This would fit under the Calvinball/Hericlitian Chess idea that it is possible for humanity, given endless time, to never play chess with the same rules twice.

Rich Hutnik wrote on 2008-04-10 UTC
Hey, let's also go with an 8x8 board, a 8x9 and an 8x10 board.  Shoot, you could also go all the way up to 8x14 or 8x16, giving the starting positions a larger back row space (as is seen in Skirmish Chess and Near Chess).  You could also push the pieces forward or back more.

Gary Gifford wrote on 2008-04-10 UTC
I like 10 x 10 boards. With side frames the same 10 x 10 board can become other boards, for example: 9x10 (uncommon) 9x9, 8x8, 9x8, 8x10.

George Duke wrote on 2008-04-11 UTC
'Sizing' Rule Number 301 has many larger ones, as options, already up to 16x16. After ongoing '9x9' theme and finishing 'The Turk' up to Kasparov, we will add boards below 8x10 also. Thanks for the suggestion.

George Duke wrote on 2008-06-18 UTC
We have made our serious whack at proliferation, and one legitimate CV, in combination, per atom within the inner Solar System has been no small task. Moreover, we are doing it with respect by not taxing people in over-length or every separate write-up per humble idea. They are all right here. This is purely organizational reference for upcoming Mutators, ours so far having been:  11> Immobilizer 12> Promoter 13> Triangular Transference 14> Warp Points 15> Cylindrical 16> Switching 17> Black Hole 18> Jack 19> Altair ranks 20> Selective Drop 21> Arrays 22> Capture & Drop 23> WandI 24> WandII 25> Selective Inverse Capture 26> Selective Immobilization 27> Philosopher's 28> Coordination 29> Hegemony 30> Reduction 31> Acid-Base 32> Strong Acid-Base; RN201> Fixed Pawns 202> Passed Pawns; RN301> Sizing; 203> Flying Dutchman 204> Relinquishment 205> Kick the Can 206> Pawn Islands 207> Hobbler 208> Blue Queen 209> Green Light 210> Hard-Boiled Eggs 211> Localization 212> Wolf & Shepherd 213> The Sea Is Rough 214> Hot Potato 215> British Bulldog 216> Sinkhole 217> Dual Capture 218> Mutual Annihilation 219> Northern Exposure[TM] 220> Northern Exposure(Pawns)  /// Intended Mutators are more Northern Exposures and ''Nuclear Particle Physics'' as ongoing theme.

Rich Hutnik wrote on 2008-06-19 UTC
Let me know when this hits a Heraclitian-Calvinball state.

George Duke wrote on 2008-09-19 UTC
Joe, for Track One sizes we have 8x10, 9x10 and 10x10. For Track Two ''Sizing'' Mutator 301 4.December.2007, we have choices: 10x11, 11x10, 11x11, 11x12, 12x11, 12x12, 12x13, 13x12, 13x13, 13x14, 14x13, 14x14, 14x15, 15x14, 15x15, 15x16, 16x15, 16x16. Under Passed Pawns and related articles there are 6x6, 7x7, and 8x8.

Rich Hutnik wrote on 2008-09-19 UTC
Let me know if you have gone multiple dimensions and different space shapes. Also, how about point to point configurations?

Joe Joyce wrote on 2008-09-20 UTC
For track 1, I lean toward the 10x10. Hadn't considered the 9x10 size; it could give some interesting games. Again, here I'd be inclined to put the pawns on the 3rd rank, and make them only 1-steppers. But then the pawns could not meet in the middle on turn 1. This alone may disqualify any such game from serious consideration. So we're left with 8x10 and 10x10, both of which can easily and naturally give 4 squares between pawn rows, maintaining a key aspect of western pawn formations, as well as the little wrinkles of the double first step and en passant. This should keep the orthodox players happy. 

For a serious first pass at 'the next chess', I strongly suggest grabbing an old idea, and dropping the standard 8x8 setup in the middle of a 10x10 board. By the way, understand I don't believe there is such a thing as the next chess, but the concept of a game sufficiently like chess to grab the attention, and playing time, of FIDE players is a truly excellent design challenge. Back to the 8x8 setup on the 10x10 board. Here we have the basic design of chess and Christian Freeling's Grand Chess. Now the important question becomes: what minimalist changes can we do to this setup to create a game that appeals to a wide range of chessplayers? 

Break the question into steps. Do we add 2 pawns to cover the front? What pieces might we slide back to the last row? Then maybe we might look at new pieces, as it doesn't feel right to increase the number of any particular piece, unlike with pawns, where adding 2 is not only natural but obvious. What sorts of piece[s]? Since there are no more simple infinite sliders, it's going to be either a complex infinite slider, or shortrange pieces. Here, my personal preference says shortrange.

Joe Joyce wrote on 2008-09-20 UTC
For track 2, since it is for fun, and not for serious chess replacement games, I'd like to add another board size/shape, the 16x12, 16 squares wide, and 12 deep. At 176 squares, this is 3 standard boards in area. I've found that reducing the starting piece density [from FIDE's 50%] helps manageability and playability. A 33% density to start gives 32 pieces & pawns/side, noticeably easier to deal with than 50%'s 48 pieces/side. At this size, I also advocate multi-move turns to speed things up. This combination of larger board and several moves/turn allows a whole range of new games - just where they'd fit in the 91.5 trillion, I don't know. ;-) But it's a convenient size to try out new effects. And now, I bid you good night [and probably should have before I wrote this]. Enjoy.

Charles Daniel wrote on 2008-09-20 UTC
In Pick the Piece Big Chess, I started out with this premise. And taking it one step forward - Chess players will probably like a 'natural' start position, not one with the pieces in the middle of the board. 
Thus you have two empty slots in the wings after you fill in the holes with pawns. 

Further design considerations: Bigger board weakens the knights and the pawns. Stepping knights seem an interesting solution. 
Dropping extra pawns (stronger pawns) help with the pawns as well.  

Net result - similar to chess but still different.  

The lesson from 80 square chess variants applies - change one parameter and the game is radically different. 
The only possible 'next' chess is something like Fischer Random or perhaps just an alternate setup - something like Displacement Chess, and even these are doubtful - we are talking the next 100+ years or so. 

Trying to 'convert' chess players to this new variant reminds me of Communism -- it will only work under a dictatorship in the end ...LOL. 

I mean, come on, we will all be long dead before Chess 'dies' - lets not get too obsessed with the 'next' chess since there is a good chance that this next chess never happens!

Joe Joyce wrote on 2008-09-20 UTC
Charles, you're absolutely right about chess outlasting us, but the *concept* of a 'next chess' is fascinating, precisely because it cannot/will not occur. Is there a game sufficiently close to FIDE that chessplayers will play it? FRC/960, bughouse, blitz, shogi, Xiang Qi, all these get played by serious chessplayers. Is there a game that we could add to those? More than one game? Note that what you've got for 'different' games are: chess; chess; chess; Japanese chess; Chinese chess. There is one noticeable trend here. The first 3 games are the same game. The next 2 pose hope that 'the next chess' won't be something like this: Set up all pieces except queens. The black player gets his choice of queen, chancellor[minister], or archbishop. White then picks one of the remaining two. I believe this would give black a slight edge in games won. It's practically chess, only 1 piece different, and allows a bit of handicapping, too. [Heh, my guess is Betza did this already.] But what else is there that is chess, but different? That's the question I'm playing with, Charles. The 'next chess' bit is just an extreme way of asking the question. 

A related question: what is the 'half-life' of a chess game? In other words, how long before half of the various forms of chess played in the world get a significant rules change, new piece, different board... ?

George Duke wrote on 2008-11-25 UTC
Proliferating happily, we left off here in June 2008 with one CV per atom within the solar system out to Saturn. That is, by correspondence one-to-one. We never exceed 32 Mutators active at once, fewer than more complicated games like Nemeroth. Joyce has asked about sizes of boards. Under RN301 we have, other than 8x10, only square sizes up to 16x16 and those where number of ranks and files differ by just one like 10x11. That needs to be remedied, as there is a popular one today that appears 17x9. One upcoming Rule-Numbered mutator will accommodate unusual size boards systematically by mathematical notation, not one after another in dreary specificities. It is tricky because changing the number of files must also add or subtract appropriate corresponding pieces, singly or paired, in the starting array. So we need to hierarchize the pieces to use beyond Rook, Knight, Bishop. (We have no intention to shrink the board -- leave that for others -- so RNB will always be there.)

George Duke wrote on 2009-05-08 UTC
Here are a core 91.5 Trillion CVs 3 years ago. Comments below extend them to Billions of 91.5 Trillion and beyond. I would not fob any one off on others, or for preset, or advertisement without incredible winnowing, sifting and sorting of the inner core to 50 or 100, counting FRC array-mixing. I may need to get going on the play itself, because we left off at CVs equal number of atoms (not too afield really from elementary particles) out from and including Sol to Jupiter. We discovered serendipitously somewhere between Earth and Jupiter is the ''halfway point'' -- I can't think of a better name but suspect there is one --in powers of ten, from one quark to number of atoms in Universe(we're just talking about 10^40 and 10^80); and we only need about fifty more Mutators to reach # atoms absolutely everywhere, in combinations for CVs, stipulating not exceeding ever 32 Mutators per artistic item. Betza's Nemeroth and Short's Schizophrenic are examples rational and comprehensible employing fully 32, 36 Mutators interpretably. My personal favourites? Why, Northern Exposure and KICK THE CAN and The Sea Is Rough and Hot Potato and Sinkhole and Strong Acid-Base, to name a few.

George Duke wrote on 2016-09-17 UTC

Ten years ago this month went up 91.5 Trillion. Similar development could apply to any great CV: Great Shatranj, Mastodon, Eurasian, Schoolbook, Unicorn Great. That is, taking an original CV and multiplying the possible subvariants to billions and trillions by innocent changes rules and pieces.

Just using the first page of this article, let's get some of the 91 trillion from word association -- a new twist not tried before.

(1) Barack Obama Falcon Chess translates to 21313152131. The method is to lop the letters back to 1 to 5 sequence each time they reach five, so for example k equals 1(one) cyclically. The stoppage at five is because most of the first twelve rule numbers list five alternatives. One learns it makes better CV to have several 'A' that is '1', if possible, since that is the default, meaning no rule change the given category. In sum, Barack Obama Chess is common Falcon Chess on 9 deep 10 wide with fixed Castling, Rook as Betza's Short Rook up to 4, and Bishop as Bede (Bishop plus Dabbabah), and the rest of the pieces unchanged. However, RN10 as '3' makes this Progressive with White one move, then Black two, White three and so on.

(2) How about Aanca? That is 11431, and Aanca Falcon Chess is 8x10 Chess with Knight having added Wazir and Rook as Half-Duck. (No Aanca at all, think of it as 11431 only.)

(3) Arimaa Falcon Chess among these 91.5 trillion possibilities is 134311, and that is the regular game on 8x10 with Rook Half-Duck again and fixed Castling and Queen promotion (the standard when A/1 is designated is promotion to only rnbf).

(4) Syzygy? 412121, and that adds to standard Chess two things, Charging Rook having backwards as King and Bishop plus Wazir in place of the Bishops. All other rules the same.

George Duke wrote on 2016-09-20 UTC

Three errors have been corrected in games (1) to (4) of last comment.

(5) VLADIMIR PUTIN Falcon Chess? That is 22149393-11544, same as 22144343-11544. Vladimir Putin Chess is on 10x10 therefore, following each RN (Rule Number) of first two pages of article. Pawns move like Chaturanga one-step Pawns, but promote to any piece including Queen. Knight adds Wazir option, Falcon adds Ferz option. Bishop is Crooked Bishop or "Boy Scout," and Queen is medium up to five spaces only. The above is pretty clear game, but RNs 11, 12 and 13 add two new pieces and a board effect. King-one-stepping Immobilizer sits on Queen-front e2 with Pawn on e3. Promoter (see namesake CV) moves like Falcon and starts on King-front f2 with Pawn on f3. Finally any Pawn has triangular effect where own two pieces/pawn forming right angle at the Pawn transfer strictly their moves powers one to the other (the hypotenuse pair where 90 angle exists).

Well, Russia is complicated.

All other rules the same.

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