Comments by panther

Unless I'm mistaken, the various 5 levels of these 3D Hexagonal variants should have their hexes alternating different colour patterns at different levels. That's so that bishop moves between levels would stay on the same coloured hexes as the hex that the bishop would start on, and a rook would change the hex colour it's on if it's moving up or down one level (granted, it may take a significant amount of extra effort to show alternating colour patterns like that).

Note that a 5 level 3D Hexagonal variant that's a fairly close analogue of Raumschach (classic 3D chess variant that uses square cells) would be possible (such a variant might be called 'Hexagonal Raumschach'). Such could be with 12 pieces (K,Q,2Rs,2Ns, 3Bs and 3Us) and 15 pawns for each of the 2 players, having 5 small (with a peak width of 7 hexes, and 37 hexes) 2D hex-shaped board levels, with the two side's armies setup on 3 levels each, and Glinski's pawn rules (except no double-step) in effect for the possible pawns movements that are just on a single 2D board. Pawn moves between levels would be single step rook or forward direction bishop (or unicorn, to be truer to Glinski[?]) moves, the latter in case of capturing. That's with unicorns being seemingly superior pieces than in the case of Raumschach, in a way, since I believe just three of them on different colours would be able to eventually reach every cell on a such a 3D Hexagonal board, if empty. Also, a rook could move to a greater number of cells (than in the case of Raumschach) on an empty 3D Hexagonal board that has at least as many cells as a Raumschach board (yet having no more than 5 levels).

The chief (and major) drawbacks of such 3D Hexagonal variants (compared to Raumschach) might be that a number of piece types' moves between levels would be more difficult to visualize or concisely describe in detail for the players, perhaps more than is the case even for 4D variants that have square cells. Such 4D variants also have the positive features that a 4D movement piece type is possible besides the (3D) unicorn, i.e. the (4D) balloon, and that a single unicorn can eventually reach every cell on such an (empty) 4D board. [edit: I'd tentatively estimate the piece values for a variant 'Hexagonal Raumschach', with the general specifications for it as described above, to be: P=1; U=2; B=3; R=3; N=4; Q=10, and a K would have a fighting value of 4.5 (noting it can't be traded). Below is a diagram of one possible setup for such a variant; adding additional diagrams to illustrate piece movements for players, in a [preset] submission, seems a lot of extra work for something that may not be entirely viable {P.S.: I've since decided to make a submission based on the diagram}:]

I've also been thinking about possible 4D Hexagonal variants; perhaps it's a matter of taste, but for such 4D variants there seems no really positive points of comparison to 4D variants that use square cells (note again that, in either case, a single unicorn is able to reach every cell on an empty board eventually). For one thing, I think a minimum of 9 Balloons (these are exclusively 4D-moving pieces), instead of 8, would be needed to reach every cell on a 4D Hexagonal board. That's with, say, 37+ 2D boards arranged like a hex; each might be hex shaped with peak width 7 hexes, and 37 cells, easily allowing e.g. 2 armies of 36 pieces and 45 pawns each in the case of 37 2D boards. A more manageable configuration (in terms of diagramming, at least) would be 19 2D boards arranged like a hex, each hex shaped with peak width 5 hexes, and 19 cells, easily allowing e.g. 2 armies each of 36 pieces and 20 pawns (all within 4 or 5 moves of promoting on a last row 2D board). All of this is in the case of a 4D Raumschach analogue.

[edit: It appears to me now that pieces with a Balloon movement power would make infeasible variants based on such 4D Hexagonal games that include them, anyway, if also having multple pieces on the 2D boards in the players' camps. That's as such pieces' scope may way too soon reach too deep into the opposition's camp, on some 2D board(s). Any sort of Hexagonal analogue of TessChess (i.e. being 4D) seems infeasible, or at least unattractive, if only due to the possibility of a fast knight or bishop/queen balloon style check (or attack on an enemy queen) - or due to the use of an ugly and/or very large setup designed to try to avoid or minimize the effect of such. A Hexagonal analogue of Hyperchess4 (i.e. being 4D) may be feasible, however. A Hexagonal analogue of 4D Quasi-Alice Chess also might be viable, noting, however, that the pawns in front of each rook would be prone to immediate assault and loss if a Glinski's or McCooey's Hexagonal Chess setup for an 11x11 (2D) Hexagonal board is used (in addition, bear in mind the paragraph below). P.S.: I later submitted to CVP a 4D Hexagonal variant based on Hyperchess4.]

Similarly, it seems to me there aren't really any positive points of comparison between Alice Chess (classic 3D variant that uses square cells, on two 2D boards) and possible Hexagonal versions of it. That's except that a possible major plus is that knights are not colour-bound on either 2D Hexagonal board (though then knights as well as bishops ought to be worth more than 4 pawns, meaning that they seldom if ever can be equitably exchanged for a small number of pawns, which might be seen as a major minus; this applies to my own 4D Quasi-Alice Chess variant, too). A couple of such possible variants might be appropriately dubbed 'Glinski's Hexagonal Alice Chess' and 'McCooey's Hexagonal Alice Chess'. Note that in further comparison, standard Alice Chess has some possible early mating traps, which seems quite desirable, not to mention that all the basic mates available in standard chess are possible in Alice Chess (although, these things could be said when comparing any number of 2D Hexagonal variants to standard chess, but note for Alice Chess it's possible there might be significantly more early mating traps than for chess, which may well not similarly apply to an Alice Chess-style version of a given Hexagonal variant).

Also related to possible Hexagonal variants, I recently thought of using a ring board (as in the square board variant Rococo that's popular on CVP/Game Courier) on a 91 cell hex-shaped board with hex cells, to try to invent some sort of fresh variant. The concept seems worthless, however, as an attempted 2 hex diagonal jump by a piece over a diagonally adjacent opposing piece on the edge of the inner cells can sometimes go past the ring of outer cells. Nevertheless, such total failures are reassuring in a way, in that they show that there can be limits that otherwise plausible variant ideas may exceed (otherwise all of the many variant ideas I've come up with to date might be viable to some extent).

Raumschach

Hexagonal Raumschach

Glinski's Hexagonal Chess

McCooey's Hexagonal Chess

Alice Chess

TessChess

Hyperchess4

4D Hexagonal Chess

4D Quasi-Alice Chess

Rococo

I'm curious whether there is a precident (or another source's advocacy) for the promotion rules for this preset (i.e. that pawns promote only on the upper- or lower- most levels, depending if they are White or Black pawns respectively). It was noted on the page for Raumschach that there are two differing versions of the pawn capture rules, at least.

I'd tentatively estimate the relative piece values in Raumschach as follows:

P=1; U=1.75; R=3; B=3.25; N=5; Q=10, and a K has a fighting value =6.66 (noting it can't be traded).

I'm posting another diagram, for my study at leisure, which might form the basis of a variant:

Not attempting to harp on the subject of computer or statistical studies of piece values, my thoughts on margin of error in these cases has been the same for a long time now. They're threefold: firstly, I'm thinking it's possible in such studies margin of error might have been estimated as at best half of what it should be. That is, say piece X is assumed to be superior to piece Y, then it's superiority might be thought to be manifested as 50%+superiority%+margin of error[assumed no greater than 100/2 or 50]% out of 100% total of n games in a sample. In calculating the margin of error, I think it should be double that [i.e. no greater than 100%], since in THEORY (however unlikely it seems) there could be a sample where piece X scores less than 50%. This is unlikely (though not impossible, given sufficiently weak players or a weak computer program) if X is a rook and Y is a bishop, but suppose X is a knight instead. Another possible problem in estimating the margin of error in such studies is that if one uses a pawn as a kind of standard candle, a pawn is a much greater fraction of a minor piece (e.g. bishop or knight, i.e. about 1/3rd of either of these) than it is a fraction of a senior major piece (e.g. archbishop, chancellor or queen, i.e. a pawn is worth roughly 1/9th [or more] of any of these), which may deserve to be taken into consideration when calculating any sort of margin.

[edit: If the above does deserve to be taken into consideration, after one calculates any 'initial' margin of error for a study, however one approves of doing it, I can suggest it be multiplied by a 'Fudge Factor' to reach a final margin of error. This Fudge Factor could be (as a crude example guess of mine) = ([Assumed total value {in pawns} of the assumed superior or equivalent piece[s] being measured] Squared) Divided by (Assumed total value {in pawns} of the assumed inferior or equivalent piece[s] being measured + 1). Now for example cases: if one side has an extra pawn, Fudge Factor = (1x1)/(0+1) = 1. If one side has a bishop for a knight, Fudge Factor = (3x3)/(3+1) = 9/4. If one side has a rook for 5 pawns, Fudge Factor = (5x5)/(5+1) = 25/6. If one side has a queen and the other side has an Archbishop (or Chancellor), if we say for the sake of argument that they're equivalent then Fudge Factor = (9x9)/(9+1) = 81/10. If one side has two bishops and the other has a knight and bishop, Fudge Factor = (6x6)/(6+1) = 36/7. If one side has 3 queens and the other side has 7 knights (which should actually beat the 3 queens [which are superior on paper in value], with no pawns involved anyway) then Fudge Factor = (9x3x9x3)/(3x7+1) = 27x27/22, i.e. very large. In coming up with Fudge Factor, I tried initially to take into account the total value of each side's Army (not counting kings) for a given setup. That is, the setup being studied in order to measure a [sub-]set of piece[s]. However, this complicated my attempts at finding a plausibly suitable formula (IMHO) too much, in spite of it seeming otherwise very desirable to take the value of the Armies into account somehow.]

Also, I still believe strength of the playing sides (even if they are one and the same player, such as a computer program) can significantly affect the results of such studies (enlarging the margin of error, to put it one way). A link I gave elsewhere notes that knight odds are compensated for by a difference of 600 rating points in chess, so even a pawn difference can be less significant in games between weaker players or computers than in games between stronger players. An analogy I'd make is that if you let kids play games in a sandbox, you'd be lucky if you'd see a somewhat competently designed sand castle at some point, while if a master sculptor played in a sandbox, we'd receive masterpieces that made the best use of the material available.

To sum up my position as it stands now, I believe we'd have piece values from such studies that could be trusted with a high degree of confidence (at least by myself) if margin of error is convincingly accurate and (more importantly, perhaps) computer programs with (widely accepted) very high chess ratings were used as the playing sides in such studies (which are intended, at least for now, for chess and rather chess-like games).

I once wrote on CVP about more manufacters of chess-like pieces manufacturing [more] popular fairy chess pieces. I had dug up an old Comment thread started by CVP editor Joe Joyce on the idea of using what he called Universal Pieces (i.e. an assortment of the most popular types, if I recall correctly). I was unaware webmaster Fergus Duniho wrote an article on popular types of fairy chess pieces (it seems tough to highly organize such a massive website as CVP, so that anything relevant to a topic can be brought to one's fingertips, even if one was unaware of that thing or article's existence).. Anyway, one point I made is that there is going to be some quasi-duplication of piece types if manufacturers ever do start to produce fairy chess pieces en mass. That's since some pieces go by different names, and thus different piece figurines might need to be produced for those who preferred them by a certain name. Such would be the case for the Archbishop, for example, which is also known as a Princess, etc. This is a quirk of chess variants that can be kept in mind, such as when compiling lists of popular piece types.

P.S.: Note to CVP editors: I submitted a variant I invented, for your review, about the 9th of January.

I'd tentatively estimate the relative piece values in Modern Shatranj (current version) as: Pawn=1, Knight=3.5, Rook=5.5, King's fighting value (noting it cannot be traded)=4, General=4 (noting it can be traded or put what be 'in check', unlike a K, but I've judged their value in action to be similar enough), with the Elephant=3.125.

Greg Strong wrote:  "I find it hard to believe that the knight enhancement is worth less than half a pawn..."

My own primative way of estimating the value of Aurelian's enhanced knight (i.e. a 'knightwa') would be to add the value of a knight (on an 8x8 board) to the value of a wazir, plus a pawn, to get my estimate for such a compound piece. On an 8x8 board I'd say a knight is worth 3.5 and a wazir is worth about half a king's fighting value (thought to be 4 pawns, by chess theoreticians) minus half a pawn, i.e. I think a wazir worth about (4-1)/2 or 1.5 (since a king's fighting value [or equivalently, a man's value] itself is worth a wazir + a ferz + 1 pawn, in my way of estimating, noting a wazir and a ferz are worth about the same numerically in pawns in spite of the ferz' handicap of being colour-bound, IMHO, since we're dealing with such small values). Thus Aurelian's enhanced knight (i.e. 'knightwa') I'd put tentatively at 3.5 + 1.5 +1 , or 6 pawns. Quite a difference in value assigned to the enhanced knight. Perhaps the true value of the enhanced knight is somewhere in between?

P.S.: My own estimate for a N and Man compound piece (known by at least some as a Centaur, i.e. which has both wazir AND ferz movement capability, besides a N's) on an 8x8 board would be N+Man+P = 3.5 + 4 + 1 = 8.5, which may or may not be fully in line with Dr. Muller's previously expressed (on CVP, I seem to recall) opinion to the effect that a Centaur is quite a strong piece.

P.P.S.: Fwiw, Ralph Betza once gave the value of a N and wazir compound piece (i.e. Aurelian's enhanced knight) as worth about a rook (which I think is 5.5 pawns, on an 8x8 board): http://www.chessvariants.com/piececlopedia.dir/ideal-and-practical-values.html

I've made corrections to my piece value estimates for some of this game's piece types; I've also made corrections for some of the piece values I gave in my Carrousel Chess game page, and in my 4*Chess (four dimensional chess) game page (and in pages for a couple of 4D spinoff games that I subsequently invented) I rather downgraded the value(s) I gave to Balloon pieces, to take into account their forms of binding better, IMHO.

Sometimes I've wished to see what a specific individual Chess Variant Pages member has currently selected for their CVP Favorite Games (besides seeing other information that is allowed to be public). I don't have a problem eventually finding someone's personal CVP info in this regard if they have ever been a Contributer (i.e. game page inventor and/or author), or if they make Comments now and then, but so far I haven't found a way to look up someone's CVP personal info if they have not done either of these. Perhaps someone can tell me if there is already a way to do this; if there is not, perhaps there could be a way created at some point in time, if this is deemed to be desirable (such as for facilitating Game Courier invitation choices; maybe the number of Favorite Games someone can have should have a bigger limit, for this purpose, too). [edit: I see how to do so now, but it is quite a long list, and not really in alphabetical order, like the Authors & Inventors lists are.]

I've edited my previous comment in this thread somewhat substantially.

On an 8x8 board, according to chess theroticians a chess king has a fighting value of 4 pawns (though noting it cannot be exchanged). Since a mann moves exactly like a king, even though (or especially as) it is a non-royal piece, I see no reason not to put a mann at 4 pawns in value as well.