H. G. Muller wrote on Fri, Aug 10, 2018 07:55 PM UTC:
Interesting questions. I hacked my 4-men EGT generator to also handle hoppers. It indeed says that in KVNK, KCCK and KNNK mate can in general not be forced. For the latter this always hold: there are no forced mate-in-2 position on boards of any size. KCCK in addition has some forced mate-in-2 positions (when the bare King already starts in a corner, pushed against the edge by the other King). For KVNK there are some longer forced mates, of up to 16 moves, but the positions that are lost for the side to move make up only 0.2% of all positions on 8x8, and less than 0.05% on 12x12.
KCNK and KCBK are generally won, though. (Max DTM 50 and 39 moves on 12x12, respectively.) For comparison, KBNK takes at most 64 moves on 12x12.
I had no easy way to check if the results are correct, as the program only produces statistics (number of mate-in-N and mated-in-N for each N), and does not contain code to probe the DTM or best move for a specific position. The hack seemed simple enough, though. (Just skip to the first occupied square in the applicable direction before starting to generate captures in the normal way.)
Interesting questions. I hacked my 4-men EGT generator to also handle hoppers. It indeed says that in KVNK, KCCK and KNNK mate can in general not be forced. For the latter this always hold: there are no forced mate-in-2 position on boards of any size. KCCK in addition has some forced mate-in-2 positions (when the bare King already starts in a corner, pushed against the edge by the other King). For KVNK there are some longer forced mates, of up to 16 moves, but the positions that are lost for the side to move make up only 0.2% of all positions on 8x8, and less than 0.05% on 12x12.
KCNK and KCBK are generally won, though. (Max DTM 50 and 39 moves on 12x12, respectively.) For comparison, KBNK takes at most 64 moves on 12x12.
I had no easy way to check if the results are correct, as the program only produces statistics (number of mate-in-N and mated-in-N for each N), and does not contain code to probe the DTM or best move for a specific position. The hack seemed simple enough, though. (Just skip to the first occupied square in the applicable direction before starting to generate captures in the normal way.)