Comments/Ratings for a Single Item

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

Thanks for reporting this. This is now fixed.

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.

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.

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

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.

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.

@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.

Back on 2009-02-20 Nuno asked the question:

"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)."

Jeremy Gabriel Good has played a few games here with a variety of camel-compounds. Quoting from his Grand Combination Courier preset page:

"Promoted form of the Camel-Ferz is the Caliph or Camel Bishop."

"Promoted form of the Camel Wazir is the Canvasser or Camel Rook."