The wonderful end-games of Team-Mate Chess

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The wonderful end-games of Team-Mate Chess

Postby h.g.muller » Tue Oct 14, 2014 10:06 am

I created a novel Chess variant, which distinguishes itself by the peculiarity that no single piece occurring in it has mating potential. So Checkmates will also have to be performed by pairs of pieces. Hence the name 'Team-Mate Chess'.

For people that like KBNK this would be the ultimate Chess variant! :lol: To have maximum variety in the possible 3+1 end-games, all eight back-rank pieces are different. This gives 7*6/2 = 21 possible 3+1 end-games. Because there is another piece that can only be obtained through promotion (and it is the strongest piece you can promote to!), there will be another 7 heterogeneous pairs that can occur after promotion. Of those, 28 piece combinations, only one is not a general win. So there are 27 new checkmates. Two of the pieces are color bound, so that when they participate mate might only be forcible in two of the four corners.

The pieces are:

Queen replacement(s):
* Ancaa, a 'double-barrel' Bishop which first makes an orthogonal step before bending in the (outward) diagonal direction. The Ancaa is a color-alternator. Worth about 8. It is not eligible as promotion choice.
* Adjutant, a Queen that skips all odd squares of her Rook moves (irrespective of whether these squares are occupied or not). Color bound, and worth about 7. It can only be obtained through promotion.

Rook replacements:
* Cobra, jumping as Knight, but also able to continue from there (if the square was empty) one outward orthogonal step (for a (1,3) move). Worth about 5.5.
* Unicorn, jumping as Knight or making a single orthogonal step. It is also a color alternator. Worth about 5.

Minor replacements (worth about 3):
* Elephant, moving one step diagonally, or jumping two. Color bound.
* Mammoth, jumping two or three steps diagonally. Color bound. (Perhaps worth only 2.5)
* the orthodox Knight, a color alternator.
* Phoenix, stepping one orthogonally, or jumping two diagonally.

King and Pawn are as in orthodox Chess, except that the King can castle with any of the Rook replacements.

The only pair without mating potential is Knight + Mammothl. I did not include an orthodox Bishop, because the Elephant is very similar as far as forcing the mate goes, and slightly more challenging because it lacks the long-range moves. The two color-bound pieces start on opposite color, and in this case they can force mate. There is a large variety of strategies for the final checkmates; not only the standard corner (a1) and edge (b1) positions with the King on b3, but also on c1, or with the strong King on c3.

The new version of Fairy-Max (which will be included with WinBoard 4.8.0) will play this variant. Surprisingly enough it does not seem any more drawish than orthodox Chess, despite the fact that KPK is always draw. At least in Fairy-Max self-play, about 26% of the games ends in draws.
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Re: The wonderful end-games of Team-Mate Chess

Postby byakuugan » Mon Oct 20, 2014 1:12 am

It sounds fun. If it was a real time chess variant, I think Knight + Mammoth would be a win, but would be the hardest mate in the game. I never see the extremely colorbound pieces (knight or similar leaper with half its choices gone, or x,0 / x,x leaper/rider with x > 2) in any turn-based chess variants; perhaps real time chess variants would be the only variants where you can actually use the extremely colorbound pieces as useful attacking units. I am currently working on proofs that certain pairs of pieces can force checkmate on any sized chessboard in real time chess. I have never gotten anywhere when attempting to develop similar proofs for real-time chess, so perhaps real time chess is the key to developing mathematical formulas for turn-based chess. I tend to think of real-time chess to turn-based chess similarly as integrals to summations.
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Re: The wonderful end-games of Team-Mate Chess

Postby h.g.muller » Mon Oct 20, 2014 5:42 pm

The funny thing is that 'any size board' is not the same as 'infinite board (with 1 corner)'. I am not sure what exactly the extra condition is that you would have to impose on the piece constellation on an infinite board to make it equivalent to 'any size'. I would expect something like "when you can always force checkmate on an infinite board when the bare King is closer to the corner than all pieces of the strong side, you can checkmate on any size board".
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Re: The wonderful end-games of Team-Mate Chess

Postby byakuugan » Fri Oct 24, 2014 12:09 am

Perhaps endgames on a torus could be more easily solved with mathematics, since recurring formations would always be symmetrically equivalent to each other regardless of their coordinates. I've found problems with analyzing symmetrical positions in normal chess, since there is the controversy of how to handle identical positions. I use the Pascal's Triangle method of finding the number of unique squares on a chessboard in a certain number of dimensions with equal measures on each dimension (each diagonal of Pascal's Triangle represents data for # of unique squares). It is confusing when I try to take shortcuts this way, so it might just be easier to start with a torus-shaped board.
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