Mate with Bishop and Generalized Leaper

[byakuugan]

I feel like Bishop + any non-colorbound leaper or 2-way colorbound leaper (opposite bishop's color) should be able to force mate on a board that has mating corners, but I am observing through tablebase analysis that Bishop + 6,1 leaper is generally a draw on 8x8. I was thinking that Bishop + 6,1 leaper might actually be able to force checkmate on a 16x16 instead, though I don't have the means to generate the tablebase.
My reasoning is that King + Bishop alone can prevent King from crossing a certain diagonal, and will gain tempo whenever defender's K is forced to switch directions to try to penetrate the diagonal. It seems like the leaper should always have enough tempo to control 1 of the squares on the diagonal adjacent to bishop's diagonal and closer to mating corner; then bishop can take over next smaller diagonal of its color while king and other piece control diagonal of opposite color to keep defender's K within the shrinking triangular region.

[h.g.muller]

Interesting. It seems your intuition that larger boards are better is right, at least considering the Flamingo (F'). On 8x8 and 10x10 boards KBF'.K is a general draw, but on 12x12 it is a general win:

Code: Select all

$ ./4men
allocate 432988480 bytes at 6fa040
        mated    mate
King captures 66718336
mates    1800         ( 2.84 sec)
in-1     1800    8520 ( 4.15 sec)
in-2     1664    5040 ( 5.46 sec)
in-3     1720   14336 ( 6.76 sec)
in-4    12032   19280 ( 8.07 sec)
in-5    10488   68488 ( 9.39 sec)
in-6    43120   82032 (10.71 sec)
in-7    27296  195716 (12.07 sec)
in-8    45808  121128 (13.40 sec)
in-9    22632  160632 (14.76 sec)
in-10   24828   76608 (16.08 sec)
in-11   10664   72520 (17.40 sec)
in-12   11864   32844 (18.71 sec)
in-13   24796   63112 (20.03 sec)
in-14   56972  117576 (21.36 sec)
in-15   83832  215692 (22.73 sec)
in-16  108080  281184 (24.12 sec)
in-17  118304  320696 (25.53 sec)
in-18  139140  352688 (26.94 sec)
in-19  145460  393956 (28.38 sec)
in-20  156656  409416 (29.82 sec)
in-21  115788  378880 (31.25 sec)
in-22   54844  250252 (32.65 sec)
in-23   24808  109484 (33.99 sec)
in-24   35060   66664 (35.31 sec)
in-25   20056   72488 (36.64 sec)
in-26   38808   67024 (37.96 sec)
in-27   69892  119716 (39.30 sec)
in-28  103728  204696 (40.67 sec)
in-29  154244  299920 (42.07 sec)
in-30  214772  450144 (43.52 sec)
in-31  275768  560332 (45.01 sec)
in-32  332472  654316 (46.54 sec)
in-33  412524  759660 (48.11 sec)
in-34  422640  871088 (49.74 sec)
in-35  419268  854768 (51.36 sec)
in-36  370764  835380 (52.98 sec)
in-37  295224  697276 (54.55 sec)
in-38  285116  580332 (56.08 sec)
in-39  255320  533076 (57.59 sec)
in-40  182572  457764 (59.06 sec)
in-41  122512  310632 (60.49 sec)
in-42   53236  197552 (61.88 sec)
in-43   39136  108644 (63.22 sec)
in-44   38880  100968 (64.55 sec)
in-45   44880  112896 (65.89 sec)
in-46   56696  125656 (67.24 sec)
in-47   60000  144936 (68.59 sec)
in-48   86200  163296 (69.95 sec)
in-49   97280  198080 (71.33 sec)
in-50  116016  231796 (72.73 sec)
in-51  114764  260392 (74.13 sec)
in-52  136636  284156 (75.54 sec)
in-53  176112  324860 (76.96 sec)
in-54  261488  420132 (78.42 sec)
in-55  408396  591648 (79.95 sec)
in-56  566184  822320 (81.55 sec)
in-57  824648 1100112 (83.27 sec)
in-58  985228 1499436 (85.12 sec)
in-59 1049008 1796704 (87.07 sec)
in-60 1089844 1860396 (89.05 sec)
in-61 1000940 1816552 (91.04 sec)
in-62  877356 1663728 (92.96 sec)
in-63  745972 1465668 (94.81 sec)
in-64  633584 1228636 (96.58 sec)
in-65  511720  973192 (98.26 sec)
in-66  340872  749756 (99.86 sec)
in-67  197068  491860 (101.35 sec)
in-68  116116  312280 (102.78 sec)
in-69  111624  228052 (104.17 sec)
in-70  112928  264424 (105.57 sec)
in-71  169832  327144 (106.99 sec)
in-72  281656  523728 (108.47 sec)
in-73  429824  759584 (110.06 sec)
in-74  592120 1067544 (111.76 sec)
in-75  864604 1352208 (113.58 sec)
in-76 1147408 1857532 (115.59 sec)
in-77 1531928 2293384 (117.78 sec)
in-78 1967300 2897672 (120.19 sec)
in-79 2521824 3509748 (122.85 sec)
in-80 3022492 4301368 (125.80 sec)
in-81 3595588 4932504 (128.98 sec)
in-82 4405216 5728152 (132.46 sec)
in-83 5185560 6697052 (136.37 sec)
in-84 6352032 7729480 (140.56 sec)
in-85 7881536 9180628 (145.41 sec)
in-86 10052024 11304988 (151.03 sec)
in-87 13000460 13966072 (157.58 sec)
in-88 16853144 17637144 (165.52 sec)
in-89 21964132 22291916 (174.98 sec)
in-90 28125240 28073228 (186.44 sec)
in-91 35946376 33696612 (200.45 sec)
in-92 42453124 36990616 (216.44 sec)
in-93 43862780 35346232 (233.35 sec)
in-94 38033328 28489768 (249.89 sec)
in-95 26888032 18404060 (263.04 sec)
in-96 14982080 9402984 (271.91 sec)
in-97 6305368 3659908 (277.05 sec)
in-98 1889044 1013520 (279.90 sec)
in-99  338736  173316 (281.64 sec)
in-100   25040   13464 (283.02 sec)
in-101     288     136 (284.32 sec)
in-102       0       0 (285.61 sec)
won:  412023512 ( 99.9%)
lost: 356776064 ( 86.5%)
avg:       -1.5 moves

On 10x10 this is

Code: Select all

$ ./4men
allocate 101010064 bytes at 683040
        mated    mate
King captures 18521528
mates    1320         ( 0.82 sec)
in-1     1168    5048 ( 1.13 sec)
in-2     1104    3096 ( 1.43 sec)
in-3     1184    8760 ( 1.73 sec)
in-4     6696   11632 ( 2.04 sec)
in-5     5872   34000 ( 2.35 sec)
in-6    19648   39488 ( 2.66 sec)
in-7    14904   82428 ( 2.98 sec)
in-8    22240   59624 ( 3.30 sec)
in-9    12024   76484 ( 3.63 sec)
in-10   14268   41632 ( 3.94 sec)
in-11    6672   43972 ( 4.26 sec)
in-12    8280   21492 ( 4.57 sec)
in-13   15836   40624 ( 4.88 sec)
in-14   36508   68664 ( 5.21 sec)
in-15   51500  125456 ( 5.55 sec)
in-16   57436  153564 ( 5.90 sec)
in-17   55500  151216 ( 6.25 sec)
in-18   63020  154688 ( 6.60 sec)
in-19   54568  159784 ( 6.95 sec)
in-20   60692  147916 ( 7.30 sec)
in-21   42344  142148 ( 7.65 sec)
in-22   26592   95432 ( 7.98 sec)
in-23   10360   51544 ( 8.31 sec)
in-24    5000   19144 ( 8.62 sec)
in-25    1152    9472 ( 8.92 sec)
in-26     120    2928 ( 9.22 sec)
in-27       0     152 ( 9.53 sec)
won:   20271916 ( 21.5%)
lost:    596008 (  0.6%)
avg:       15.9 moves