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H. G. Muller wrote on Fri, Oct 5, 2018 08:14 AM UTC:
graphicsDir=/membergraphics/MSelven-chess/ whitePrefix=w blackPrefix=b graphicsType=png squareSize=35 symmetry=none promoZone=0 weak::vrWfF:marshall:h1 king::::h2,,d4

End-Game Tables with Fairy Pieces

I created an on-line EGT generator, which can be used to investigate mating potential of simple fairy pieces (non-divergent leaper / slider compounds) on an 8x8 board. It can also be used to practice end-games of (orthodox) King + one piece vs (orthodox) King. On my website I also added an interface where the user can define the moves of the piece he wants to investigate and then practice with. (See here.) In this comment I just set it to handle a fixed piece.

I wonder if it would be a good idea to host something like this on the CVP website. E.g. as a standard component of the Piececlopedia. An obvious problem would be that mating potential can be dependent on board size, while the piece descriptions are supposed to be board-size independent. We could also devote an article to it with a more flexible version (which can do all kinds of pieces, like on my website), but I am afraid it would be buried there just as much as it would be buried on my website or in this comment. If it wouldn't at least get a special mention in the topical index, I think we might as well not bother at all.

Some Challenges, for Fun

I have been toying with this a bit, to address the following questions:

  • What is the weakest piece that still has mating potential on an 8x8 board?
  • What would be the piece that might require most time to force such a mate in the worst case?
The Interactive Diagram above shows my attempt to answer the first question: a leaper with only 5 moves seems to be able to do the job. The moves are a subset of those of an orthodox King; in fact it is a Gold General that cannot step orthogonally to the left. There is a fairly large number of positons that are drawn, because the piece is isolated from its King, and can be chased by the bare King until it runs into the board edge, and is lost. (The same holds for a normal Gold General, but to a lesser extent.) But with the strong side to move, 9 out of 10 of all possible positions is a forced win. It is not proven that this is actually the least mobile (and thus presumably least valuable) piece with mating potential, so someone might come up with something even weaker.

For the second question I came up with the fhNfAbFbD. Although this must be a pretty strong piece (9 moves, very good forwardness, speed faster than Knight forward, and faster than King backward, reasonably good manoeuvrability.) This apparently needs up to 97 moves to force checkmate! Any move I deleted to handicap it would make it lose the mating potential altogether. Also here, people are encouraged to find even slower maters.

[Edit]I already found an even slower mater, which takes up to 130 moves!

Generating end-game table; Please wait.


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