@Bruce:

I converted my 4-men EGT generator to doing the Omega Chess board. (I mapped the board into an 11x12, and then it effectively only needs 122 elements, as neighboring boards can be partly interleaved.)

Oddly enough this confirms the numbers you gave for Bishop+Knight and Wizard+Knight!

What I had not realized is that these end-games are not generally won at all, but are mosty fortress draws: you can only deliver mate in the corner of the Bishop's/Wizard's shade, as you need to cover both the corner and the Wizard square, or the King will simply escape to the latter. And if the bare King takes shelter in the other corner there is no way to smoke him out of the Wizard square there. So you have to go through excessive trouble to prevent the bare King fleeing into that corner, which apparently causes an enormous slowdown. On a normal board it is easy to drive the King along the edge from one corner to the other, so trying to reach whatever corner is not a good defensive strategy there.

As a consequence, only 38.3% of the KBNK positions are won (22.3% lost), and 33.7% of the KWNK positions (17.9% lost). Against 99.8%won / 81% lost on regular 10x10.

Your 3-men generator seems buggy, though; as the checkmating applet here shows, WD is a quite easy win on 8x8.

And WD on 8x8 can be tried here. It doesn't seem to have much difficulty forcing checkmate against any play, even though it starts in a generally unfavorable position (with the strong side crammed in a corner.) For a piece like WD it could be worse if it starts in the corner opposite from its own King; then there are positions where it is 'dynamically trapped', when it is on the same diagonal as the bare King.

and if you'll allow the humble 8x8, you can test out that endgame:
https://www.chessvariants.com/membergraphics/MSinteractive-diagrams/EGT.html?betza=WAD&name=Champion&img=champion
(I really like this thing; thanks H.G.!)

I noticed that the Champion's Piececlopedia page has an incorrect diagram (due to the new marker code).  I'll fix that and add a link to the 8x8 checkmating practice after work today.

Are you sure about those numbers? I cannot do the Omega Chess board, but my EGT generator for a plain 10x10 board says KBNK maximally takes 47 moves (average 39.4), and Knight + Wizard maximally 48 moves (average 40.1). I can imagine that having the Wizard squares could take 2 or 3 moves extra, but not nearly as much as what you mention. The hard part is usually to get the bare King in the desired corner. For Bishop + Knight it might not take any extra moves, as in the standard mating patterns the Bishop would automatically attack the Wizard square as well.

I agree that 50 moves does not leave much room for errors, and in general it can take longer to make progress in large games.

[Edit] Oh, I now also see your previous comment. And no, Kevin did not misunderstand me; for maximum DTM with a WD on 10x10 I get 52 moves, while 95.7% of the positions with the strong side to move are forced wins (see table below). On the Omega board this is of course no longer true; not even a Rook can force mate there. The WAD probably doesn't fare any better.

$ ./3men10x10 KwK
allocate 1010064 at 6d0040
        mated    mate
King captures 129224
mates      16         ( 0.01 sec)
in-1       40      64 ( 0.01 sec)
in-2      208     248 ( 0.01 sec)
in-3       88     916 ( 0.01 sec)
in-4      300     624 ( 0.01 sec)
in-5      224    1428 ( 0.02 sec)
in-6      468     768 ( 0.02 sec)
in-7      528    1696 ( 0.02 sec)
in-8      468    1728 ( 0.02 sec)
in-9      400    1836 ( 0.02 sec)
in-10     480    1080 ( 0.03 sec)
in-11     396    1328 ( 0.03 sec)
in-12     312    1416 ( 0.03 sec)
in-13     512    1192 ( 0.03 sec)
in-14     304    1656 ( 0.03 sec)
in-15      72     812 ( 0.04 sec)
in-16      56     304 ( 0.04 sec)
in-17      80     280 ( 0.04 sec)
in-18     168     392 ( 0.04 sec)
in-19     468     712 ( 0.04 sec)
in-20     768    1408 ( 0.04 sec)
in-21     768    2096 ( 0.04 sec)
in-22     708    2152 ( 0.05 sec)
in-23    1056    2080 ( 0.05 sec)
in-24     908    2812 ( 0.05 sec)
in-25    1640    2620 ( 0.05 sec)
in-26    1376    4128 ( 0.06 sec)
in-27    1516    3720 ( 0.06 sec)
in-28    3944    4524 ( 0.06 sec)
in-29    4536   10044 ( 0.06 sec)
in-30    6588   11060 ( 0.07 sec)
in-31    9456   15224 ( 0.07 sec)
in-32   15880   20516 ( 0.08 sec)
in-33   27248   32184 ( 0.09 sec)
in-34   33956   48452 ( 0.10 sec)
in-35   45448   56908 ( 0.12 sec)
in-36   60972   71044 ( 0.13 sec)
in-37   77556   89008 ( 0.15 sec)
in-38   88852  100212 ( 0.17 sec)
in-39   86540   90180 ( 0.19 sec)
in-40   81708   71664 ( 0.21 sec)
in-41   57772   46460 ( 0.22 sec)
in-42   40900   31352 ( 0.23 sec)
in-43   25296   20336 ( 0.24 sec)
in-44   19160   15656 ( 0.25 sec)
in-45   12944   11152 ( 0.25 sec)
in-46    8928    6976 ( 0.25 sec)
in-47    5456    4136 ( 0.26 sec)
in-48    2520    1968 ( 0.26 sec)
in-49     912     696 ( 0.26 sec)
in-50     224     200 ( 0.26 sec)
in-51      72      56 ( 0.26 sec)
in-52      32      16 ( 0.26 sec)
in-53       0       0 ( 0.27 sec)
won:     928744 ( 95.7%)
lost:    731228 ( 75.4%)
avg:       37.9 moves

I think that using the 50 move rule for this and several other large Chess variants is probably not appropriate. For example, my Chess engine computes the maximum number of moves to mate in this variant for Bishop+Knight vs King to be 69 moves, for Queen+King vs Rook+King to be 72 moves, and for Knight+Wizard vs King to be 85 moves! Perhaps for this and other large Chess variants it should be a 75 or 100 move rule, or possibly only if the game falls into one of these reduced-material mating patterns.

To Kevin Pacey: Your comment that if you used a lone Champion+King it was possible to force mate against a lone King on a "normal" type of Chess board (that is, if the four corner "bolthole" squares were eliminated) sounded wrong to me, so I added that piece to one of the Chess engines I've written and had it compute the endgame database for that piece combination, and sure enough there are only a handful of positions for which a single Champion can force mate, whether on any size of rectangular Chess board or on an Omega Chess board. On the other hand, two Champions can easily force mate either on a rectangular Chess board of any size or on an Omega Chess board. I think you misunderstood Muller's comment - the one I saw says that a WD (or WAD) piece can mate, but doesn't say that this is forced in the typical case.

A word on my qualifications: I am a USCF Expert in standard FIDE Chess as well as the author or co-author of several computer Chess programs including the "Duchess" program that was the runner-up in the World Computer Chess Championships.

Thanks for reporting this. This is now fixed.

In the preset for this game, castling does not work!

For the purpose of trying to invent a 10x8 variant, I thought about reducing this variant to 8 ranks rather than 10 (plus omitting the corner squares with the wizards, optionally). My main worry was that then a charge of the b- or i-pawn by the enemy might prove awkward for developing/castling in relative peace.

I think the biggest problem is the board is too big.  Reduce from 10 ranks to 8.  And you can also solve the problem of KR vs K not being won on this board by adoption the Launch Square rule used in Brouhaha and Apothecary - the hanging corner squares disappear as soon as they are vacated.

A possible mutator variant of Omega Chess would be to simply use the same basic 10x10 setup of Omega Chess, except eliminate the additional 4 edge corner squares and the wizard pieces from the picture (such a mutator variant might be called 'Decimal WAD Chess'). This would, for instance (as in standard chess), allow K+R to always mate lone K, and incidentally allow K+Champion[also known as WAD piece type] to force mate vs. lone K on such a 10x10 board too (the latter Dr. Muller has related elsewhere). One price of this would be that unlike for Omega Chess, 2 knights+K could not force mate vs. lone K (as also is the case in standard chess).

Interesting extra pieces and pawn movement rules here.

The possibility to black out squares already existed in the interactive diagram, although it was not widely advertized: when you define a piece named 'hole' it will black out the square wherever you place it. No piece can move to or slide over such a blacked-out square, nor can such squares be grabbed and moved. The Design Wizard currently does not provide a means to create holes; you would have to add the required line by typing it in the HTML code, like hole::::e4,e5,d4,d5 to blackout the board center of an 8x8 board.

The main problem here was to get the unorthodox e.p. capture right. The XBetza notation uses 'e' as modality to indicate e.p. capture, and this can be used as alternative or in addition to 'c' or 'm'. Its meaning is to capture the last-moved piece on an empty square it passed over. The diagram uses the convention that this can happen on each square where an initial-only non-jumping move (i.e. containing 'in') could have been blocked, but originally the 'n' modifier was implemented only on D or A atoms, testing only one square. This was fine for FIDE Pawns, but in Omega Chess we must deal with an ifmnH as well. The diagram code for handling 'n' has now been beefed up to test two squares for blocking, and test up to two e.p. squares for strictly forward pushes.

Castling

As for the castling with a non-corner piece: the diagram uses an algorithm that always allows castling with a piece that moves like an orthodox Rook, even if it is not a corner piece. Official XBetza notation for this would be isjO2, the 'j' on an O (= castling) atom having the specialmeaning that you 'jump' a square when looking for the castling partner, starting from the edge (or at least the nearest blacked-out square). The diagram description doesn't even need that, but of course would fail if there is a non-corner Rook on the King rank that you don't want to participate in castling.

Omega Chess has 2 interesting new pieces that fit together well tactically
with the original pieces as well as each other. That is its strong point.

The Champion turns out to be the much stronger piece compared to the Wizard
which loses value as the game goes on. The Champion turns out to be one of
the strongest pieces at the end of the game, but its a bit dull to use at
the start like the knight which needs an extra move to attack.

While the 10x10 board makes the Wizard an interesting piece to use, Omega
Chess also suffers from not having enough tension between pawns and
fighting for control of squares as compared to variants that maintain the
same distance between the pawns.

Having more space between the pawns (2 rows) leads to more complex
situations, but having that much space also makes the game a little boring
when pieces are just setting up with apparently no reason for doing so.

If pawns are the soul of chess as Philidor said, then Omega Chess pawns are
not at the soul of the game. The pawns simply don't push away key pieces
often enough creating a space advantage for one player who is moving its
pieces in the right order. So while extra space may seem like a good idea,
it hurts the tactical considerations of pawn move that normal Chess has.

I believe Omega Chess is a step in the right direction in terms of the
evolution of Chess, but its unlikely that a game without enough tension
between pawns and a fight for control of the center will gain that much
popularity among the general population.

The fact that certain options rules in Omega Chess Advanced like temporal
knight have been suggested which gives the knight more range suggests that
the original setup of the pieces is not quite ideal.

The knight and the champion just aren't exciting enough soon enough. With
rooks, bishops, and the queen becoming even more powerful, the short range
jumping pieces need to be in better positions to create more interesting
interaction between sliding and jumping pieces. The wizard is also a little
far away from the action. Even after moving to its general development
square, it still doesn't seem to be that much closer to doing something
interesting except along the right or left flank.

I thought the definition of 'major' was 'able to FORCE checkmate with only the aid of a King'?

If your standard is 'able to deliver a checkmate if the enemy King cooperates', I believe the Rook also qualifies (can checkmate enemy King near the center of an edge if friendly King has opposition).

But I can't for the life of me think of any reason that would matter.  The force mate definition tells you the minimum amount of material you need to preserve to win a simplified endgame.  How does knowing that a Bishop could hypothetically deliver a checkmate *if your opponent decides to help you* have any effect on gameplay, let alone piece values?

This game adds in an ingenious way the movements of several pieces of
Tamerlane chess, which is the 'grandfather' variant of all these XX and
XXI century 'chess variants boom': We have the camels, dabbaba, ferz,
alfil and wazir.

What if they were mixed on the other form? Substitute wazir by ferz (so
the champion is now colorbound) and the ferz by wazir (so now the wizard
is not colorbound). Anyone can try this at home without breaking
copyright. I think... But my idea is not that. Just to say that is is
interesting to try to see if the game becomes more complex or not, more
interesting or not.

http://www.omegachess.com/home.html?action=advanced#undefined

Omega Chess Advanced has added a new piece:Fool.

The Fool assumes the identity of the last piece your opponent has moved.

Here is a board that could be a very good solution for making the Citadel
chess and Omega chess corner squares more playable:

http://www.alessiominiatures.com/Quickstart/ImageLib/citadel.jpg

Interesting ah? : )