BrainKing - 讨论板 (Chess variants (10x8))

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Chess variants (10x8)

Sam has closed his piano and gone to bed ... now we can talk about the real stuff of life ... love, liberty and games such as
Janus, Capablanca Random, Embassy Chess & the odd mention of other 10x8 variants is welcome too

For posting:
- invitations to games (you can also use the New Game menu or for particular games: Janus; Capablanca Random; or Embassy)
- information about upcoming tournaments
- disussion of games (please limit this to completed games or discussion on how a game has arrived at a certain position
... speculation on who has an advantage or the benefits of potential moves is not permitted while that particular game is in progress)
- links to interesting related sites (non-promotional)

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24. 三月 2003, 11:01:40

Grim Reaper

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题目: Re: Piece Values

One way to think about the piece values subjectively is to imagine what you are discussing in an ending against a lone enemy king. While it is true the Archbishop is stronger than a Rook, would you like to try and win Rook vs. King or Archbishop vs. King?

:)

I posted a mate in 8 for Archbishop vs. King at:

http://www.geocities.com/bow_of_odysseus/deadly_arch.html

It is a real brain teaser of a problem to mate with the Archbishop on an empty board!

One way we can compare something like a Bishop Pair to an Archbishop is to try and find "Longest Wins" in the endgame. I know in chess, the Longest win from a Bishop Pair is about 67 moves. That was on an 8x8 board.

But in Gothic Chess, examine the ending of King vs. Knight + Bishop. It is almost a draw! Whereas in chess the N+B will mate in either of two squares, those of the same color as the Bishop, in Gothic, you can only force mate on one of the squares! The square of the same color as the Bishop that is closest to the enemy king vertically (not horizontally across the files) is the only one the mate can be forced in.

So, we need to look deeper at the discussion of piece values in the endgame, because in Gothic, even things like the Lucena Rook and Pawn vs. Rook ending need complete rewriting.

24. 三月 2003, 13:01:41

juangrande

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题目: Re: Piece Values

According to Reuben Fine in "Basic Chess Endings," the "longest mates" (on an 8x8 board) are as follows:

Pieces.................Longest Mate
----------.................--------------------
K+Q vs K.................10 moves
K+R vs K.................17 moves
K+B+B vs K.............18 moves
K+B+N vs K.............34 moves

All but the K+B+N vs K should be essentially the same on a 10x8 board, where any extra number of required moves would be small and due only to the extra space on a 10x8 board. The K+B+N vs K on a 10x8 board is more interesting, as Ed has pointed out. Once the lone King has been forced to a corner opposite in color from the Bishop, the lone King must be forced to the closer corner of the same color as the Bishop, otherwise the corralling procedure will fail. I haven't studied this enough to know for sure if it can be forced at all (although I suspect Ed has worked it out). The K+C vs K is easy since a Chancellor can be used as a "supercharged Rook." The K+A vs K is not really hard, but the procedure certainly has no counterpart in regular 8x8 chess, so seems strange when an 8x8 chessplayer first tries it.

I'm not sure I understand why Ed thinks the Lucena position needs a complete rewriting on a 10x8 board. The winning procedure is independent of the "width" of the board and would be the same on a 20x8 board. I suspect that many, if not most, endings do not really depend a great deal on the "width" of the board (the K+B+N vs K ending being a notable exception); the "height" of the board is the determining factor. I freely admit that I don't have a proof of this assertion, but it would surprise me if 8x8 endgame theory changed significantly on a 10x8 board. For those who are interested, a more dramatic geometric effect is produced by using an Omega Chess board (10x10 with 4 corner squares). On this board, several strange things happen:
1. K+R can no longer force mate on a lone K.
2. K+B+N can no longer force mate on a lone K.
3. An _unassisted_ Queen can force mate on a lone King.
4. K+N+N _can_ force mate on a lone K.
Omega Chess turns out to be a much slower game than Gothic Chess, and I'll leave it at that, since this is a Gothic Chess discussion board (and Gothic Chess is more exciting anyway).