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Ninety-one and a Half Trillion Falcon Chess Variants. Missing description[All Comments] [Add Comment or Rating]
George Duke wrote on 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
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 2007-11-09 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)?

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 2007-10-11 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 2007-09-26 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.

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 2007-09-20 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.

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?

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

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
Comment re-located to the Latrunculi duo milia et septum comments, where it belongs.

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.

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.

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

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.

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.

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.

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 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.

Jared McComb wrote on 2006-08-14 UTCAverage ★★★
'Wow, let's use really big numbers to try to impress people!'

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