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Recognized Chess Variant: Wildebeest Chess. Now a Recognized Chess Variant![All Comments] [Add Comment or Rating]
David Paulowich wrote on Fri, Apr 13, 2007 03:08 AM UTC:Excellent ★★★★★

The linked game page already has several Excellent ratings. I will also give this variant an Excellent rating, assuming that, in general, King and Wildebeest versus King leads to a stalemate victory. The Wildebeest, while a useful piece, should be no stronger than a Rook on 10x10 and larger boards. It is much weaker than a Gryphon, which is halfway between a Rook and a Queen - see Ralph Betza's analysis of bent riders.

I suspect that the longest possible forced stalemate [K and N versus K] is four moves, as in Joost Brugh's [2006-04-03] comment.

Strangely enough, the Bison (Camel + Zebra) does not share the Wildebeest's checkmating problem (covered in Joost Brugh's earlier comment). See Comments/Ratings for a forced mate in six on the BISON page.


David Paulowich wrote on Mon, Apr 3, 2006 11:15 PM UTC:
Very little is written in English about forcing stalemate. Roger Hare writes on his Chu Shogi page: 'The old texts say that a kinsho and osho against a bare osho wins.' I assume this means that a King and Gold General can force a 'stalemate position' on the 12x12 board and then capture the enemy King (after it moves).

Can we force a stalemate victory in the ending King and Silver General versus King? I once tried running a Zillion - Zillions test game for over 250 moves on an 8x8 board, at one minute per move, with no success. Perhaps the problem here is the fact that the Silver General cannot lose a tempo (triangulate). Neither can the Knight, which alternates colors each move - stalemate wins probably happen in rare situations where the lone King is already trapped in the corner. Even the ending King and Bishop versus King seems to be a draw - I do not see any way to force the lone King to the edge of the board - I have a K+B versus K test game (325 moves) on my hard drive.


Joost Brugh wrote on Mon, Apr 3, 2006 10:35 PM UTC:
If stalemate is a loss, can a King and a single Knight force checkmate? White King on b3, White Knight on d3 and Black King on b1 (Black to move). 1 ...,Kb1-a1 2. Nd3-c1, Ka1-b1, 3. Nc1-a2, Kb1-a1 4. Na2-c3 stalemate. The question is how many positions are won and how many are drawn.

David Paulowich wrote on Mon, Apr 3, 2006 06:31 PM UTC:
Good point, Andrew! I am certain that two Knights can do the job. In fact, King and just about any two pieces should be able to force stalemate. I have examined the Wildebeest.zrf and discovered the line:

(loss-condition (White Black) (checkmated King))

So Zillions was not even trying to stalemate the Black King. When this ZRF has been corrected, we should be able test the endgame King and Wildebeest against King.


J Andrew Lipscomb wrote on Mon, Apr 3, 2006 05:36 PM UTC:
Keeping in mind, however, that stalemate is a win in Wildebeest Chess, can a Wildebeest or two Camels (or for that matter two Knights, or Knight+Camel) defeat a lone king with that rule in place?

David Paulowich wrote on Mon, Apr 3, 2006 04:09 PM UTC:
Thanks for the information. I suspected that a pair of Camels would have the same problems mating as a pair of Knights or a pair of cannons.

Endgames are my favorite part of chess - but not when they end in a draw due to insufficient mating material! I am unhappy with the limitations of the Wildebeest. Ralph Betza's Half-Duck is a fascinating leaper that does have the ability to mate in the endgame. Under the name 'Lion', it can be found in Greg Strong's Opulent Chess, along with Daniel C. Macdonald's Wizard (Camel+Ferz).


Joost Brugh wrote on Mon, Apr 3, 2006 11:43 AM UTC:
By the Way: The possibility with both the Wildebeest and the King on b3
would be stalemate anyway.

For the Camels: the Checkmate positions are:

White King (a3 or b3), White Camel (b4 or d2) White Camel (a4, c4 or e2)
Black King a1
White's (b4 or d2)-Camel moved last, so before that move, the Camel was
on (c1, e3, e5, c7, a7, a3, c5, g3 or g1) (No a1 because of the Black
King).
Black moved Kb1-a1:
Position before that:
White King (a3 or b3), White Camel (c1, e3, e5, c7, a7, a3, c5, g3 or g1)
White Camel (a4, c4 or e2) Black King b1.
Blacks Kb1-a1 must be forced, so c1 must be covered by a Camel (The King
doesn't cover it). So there must be a Camel on b4, d4 or f2, but there
isn't. So no mate with King + two Camels against lone King.

Joost Brugh wrote on Mon, Apr 3, 2006 11:30 AM UTC:
There is no forced mate with Wildebeest + King against lone King:

There are two different checkmates with a Wildebeest and King against a
lone King (not counting mirror images or rotated images):
a. White Wildebeest d2, White King b3 and Black King a1
b. White Wildebeest d2, White King a3 and Black King a1
The Wildebeest moved last. Before that move, the positions were
a. White Wildebeest X, White King b3 and Black King a1
b. White Wildebeest X, White King a3 and Black King a1
X is a position from where a Wildebeest can move to d2
Blacks last move is Kb1-a1. Before that move, the positions were
a. White Wildebeest X, White King b3 and Black King b1
b. White Wildebeest X, White King a3 and Black King b1
Blacks Kb1-a1 must be forced, so all other squares must be covered. Square
c1 can't be covered by the White King, so c1 must be covered by the
Wildebeest, so X is a position that both covers d2 and c1. There is only
one solution: X = b3. So possibility a is impossible, because both the
Wildebeest and the King must be on b3. This leaves possibility b, but
there, the Black King can move to c2

David Paulowich wrote on Sun, Apr 2, 2006 10:30 PM UTC:
WILDEBEEST CHESS CHALLENGE

Can anyone find a forced mate in this position: White King c3, White Wildebeest d4, Black King a1? What if we remove the Wildebeest and add two White Camels to d4 and e4? Running Zillions at 3 minutes per move for 20 moves in these positions did not result in a mate.

Glenn E. Overby II writes, on the Recognized Chess Variants page, 'The Wildebeest is markedly superior to a Rook, although not quite the Queen's equal.' I am inclined to value the Wildebeest (Gnu) halfway between the Rook and the Queen. Perhaps less than that, if there is no forced mate against the lone King.


Charles Gilman wrote on Sun, Jun 15, 2003 10:31 AM UTC:
I like the game (still directly accessible 2 entries up if anyone comes here by mistake!), but do not understand your analysis of it. Do you mean that the Camel interacts with the Knight nearly as effectively as the Bishop does with the Rook, or that the Camel is as weak compared to the Knight as the Bishop is compared to the Rook? Either of these would make sense as the Camel is a colourbound Knight in the sense that the Bishop is a colourbound Rook (b1-a3-c4 triangle and all that). For the same reason you surely cannot mean that the Camel is nearly as powerful as the Rook, as your text could suggest to those familiar with the (approximate) Bishop-Knight equivalence.

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