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Mate with Bishop and Generalized Leaper
Posted: Fri Oct 30, 2015 1:31 am
by 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.
Re: Mate with Bishop and Generalized Leaper
Posted: Sat Feb 20, 2016 6:25 pm
by 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