💡📝H. G. Muller wrote on Thu, May 16, 2019 10:10 PM UTC:
Well, it is a computer program written in a Turing-complete programming language, so anything is possible. But by themselves (i.e. in 3-men end-games like the applet calculates) pure hoppers like Paos, Vaos or Grasshoppers will never have any mates (i.e. they are 'insufficient-mating-material draws'), because they could only attack the bare King by hopping over their own King, effectively giving the latter King an extra sliding move. But even a Queen alone, which has all possible sliding moves, cannot checkmate a King. One doesn't need to generate an EGT to see that. So it is a bit pointless.
Pieces that have hopper moves in addition to normal captures might be able to force mate, but due to their own King being the only available 'mount', it would be very unlikely that their hopping move has any influence near the bare King when their normal moves do. And I don't know any variant that has such pieces anyway.
Hoppers could become of interest in 4-men situations, but making a 4-men version of the applet would be a challenge in itself. It would probably be more useful to first generalize the applet to handle divergent pieces, or bent sliders. Even if the generator supports that, there still would have to be some extra functionality in the user interface for defining pieces that have such moves.
Well, it is a computer program written in a Turing-complete programming language, so anything is possible. But by themselves (i.e. in 3-men end-games like the applet calculates) pure hoppers like Paos, Vaos or Grasshoppers will never have any mates (i.e. they are 'insufficient-mating-material draws'), because they could only attack the bare King by hopping over their own King, effectively giving the latter King an extra sliding move. But even a Queen alone, which has all possible sliding moves, cannot checkmate a King. One doesn't need to generate an EGT to see that. So it is a bit pointless.
Pieces that have hopper moves in addition to normal captures might be able to force mate, but due to their own King being the only available 'mount', it would be very unlikely that their hopping move has any influence near the bare King when their normal moves do. And I don't know any variant that has such pieces anyway.
Hoppers could become of interest in 4-men situations, but making a 4-men version of the applet would be a challenge in itself. It would probably be more useful to first generalize the applet to handle divergent pieces, or bent sliders. Even if the generator supports that, there still would have to be some extra functionality in the user interface for defining pieces that have such moves.