x/y | 0 | 1 | 2 | 3 | 4 | 5 |
0 | = | + | + | = | = | = |
1 | + | + | + | + | + | = |
2 | + | + | = | + | = | = |
3 | = | + | + | = | = | = |
4 | = | + | = | = | = | = |
5 | = | = | = | = | = | = |
x/y | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
0 | = | + | + | = | = | = | = |
1 | + | + | + | + | + | = | = |
2 | + | + | = | + | = | = | = |
3 | = | + | + | = | = | = | = |
4 | = | + | = | = | = | = | = |
5 | = | = | = | = | = | = | = |
6 | = | = | = | = | = | = | = |
K + 2 Grasshoppers + [0,2] - K | |
![]() | Kb2 Dabbaba a2 Grasshopper a1b1 - Kd3, chessboard 7x7 1.Ga1-a3 Kd3-c4 2.DAa2-c2+ Kc4-b4 3.Ga3-c1 Kb4-a5 4.Kb2-c3 Ka5-b6 5.Kc3-d4 Kb6-c6 6.Kd4-e5 Kc6-b5 7.Ke5-d5 Kb5-a4 8.Gb1-d1 Ka4-b4 9.Kd5-d4 Kb4-a3 10.Gc1-c3 Ka3-b4 11.DAc2-c4 Kb4-b5 12.Gc3-c5 Kb5-a5 13.Kd4-d5 Ka5-b4 14.Gd1-d6+ Kb4-a3 15.Gd6-d4 Ka3-b3 16.Gc5-e5 Kb3-a2 17.Ge5-c3 Ka2-b3 18.Gc3-c5 Kb3-a2 19.Kd5-e4 Ka2-b3 20.Ke4-d3 Kb3-b2 21.Gc5-e3 Kb2-c1 22.Ge3-c3 Kc1-d1 23.Kd3-e3 Kd1-e1 24.Gc3-f3 Ke1-d1 25.Gf3-d3 Kd1-c1 26.Gd3-d5 Kc1-d1 27.Ke3-d3 Kd1-c1 28.Gd4-d2 Kc1-b2 29.Kd3-d4 Kb2-a3 30.Kd4-c3 Ka3-a2 31.Gd5-b3 Ka2-a3 32.Gd2-b4 Ka3-a2 33.Gb3-b5 Ka2-a3 34.Gb4-d2 Ka3-a2 35.Kc3-d4 Ka2-b3 36.Gd2-d5+ Kb3-b4 37.Gb5-d3 Kb4-a5 38.Kd4-c5 Ka5-a6 39.Gd5-b3 Ka6-b7 40.Kc5-d6 Kb7-b6 41.Kd6-d5 Kb6-a7 42.Gd3-b5 Ka7-a6 43.Kd5-c5 Ka6-a5 44.Gb3-d5 Ka5-a6 45.Kc5-c6 Ka6-a7 46.Gb5-d7 Ka7-a6 47.Kc6-c5 Ka6-b7 48.DAc4-c6+ Kb7-c7 49.Gd5-b5 Kc7-b7 50.DAc6-e6 Kb7-a6 51.Kc5-b4 Ka6-b7 52.Gd7-f5 Kb7-c7 53.Kb4-c5 Kc7-b7 54.Gb5-d5 Kb7-a6 55.Kc5-b4 Ka6-b7 56.Gd5-f7 Kb7-c7 57.Kb4-c5 Kc7-b7 58.Gf7-f4 Kb7-a6 59.Kc5-b4 Ka6-b7 60.Kb4-a5 Kb7-a7 61.Ka5-b5 Ka7-b7 62.Gf4-f6 Kb7-a7 63.DAe6-c6 Ka7-b7 64.Kb5-c5 Kb7-c7 65.Gf5-b5 Kc7-b7 66.Gf6-b6+ Kb7-a7 67.Gb6-b4 Ka7-b7 68.Gb4-d6 Kb7-a7 69.Kc5-d5 Ka7-b7 70.Gb5-e5 Kb7-a7 71.Kd5-c4 Ka7-b7 72.Kc4-b5 Kb7-a7 73.Ge5-a5 Ka7-b7 74.Gd6-b6 Kb7-a7 75.DAc6-e6 Ka7-b7 76.DAe6-e4 Kb7-a7 77.Kb5-c6 Ka7-a6 78.Ga5-c7 Ka6-a7 79.DAe4-c4 Ka7-a6 80.DAc4-a4+ Ka6-a7 81.Gc7-c5# |
K + 2 Grasshoppers + [0,2] - K | |
![]() | Lze si všimnout, že pro dababu existují 3 typy polí, můžeme je symbolicky označit jako typ A1, typ B1 a typ B2. Typ B1 je symetrický s A2. Výhra je možná jen při pozici dababy na polích typu A1 a B1. Při pozici na poli typu B2 je koncovka remízová. For the dabbaba, there are three types of square, which we can denote by A1, B1, and B2. Type B1 is symmetrically equivalent to A2. A win is possible only in the cases A1 and B1. If the dabbaba is on a square of type B2, the ending is drawn. Kd4 Dabbaba a1 Grasshopper c4d3 - Kg7, chessboard 7x7 1.Kd4-e5 Kg7-f7 2.DAa1-a3 Kf7-g6 3.DAa3-c3 Kg6-g7 4.Ke5-e6 Kg7-g6 5.Gc4-c2 Kg6-g5 6.Ke6-e5 Kg5-g6 7.Gc2-e4 Kg6-f7 8.DAc3-c5 Kf7-e7 9.Ke5-d5 Ke7-d7 10.Gd3-f5 Kd7-e7 11.DAc5-e5+ Ke7-f6 12.Gf5-d3 Kf6-f7 13.Kd5-d4 Kf7-g6 14.Kd4-e3 Kg6-f6 15.Ke3-f4 Kf6-g6 16.Gd3-f5+ Kg6-f6 17.Gf5-f3 Kf6-g6 18.Gf3-d5 Kg6-f6 19.Gd5-f5 Kf6-f7 20.Kf4-g5 Kf7-g7 21.Gf5-d3 Kg7-f7 22.Kg5-f5 Kf7-g7 23.Kf5-e6 Kg7-g6 24.Gd3-f5+ Kg6-g7 25.DAe5-e7# Kd4 Dabbaba b1 Grasshopper c4d3 - Kg7, chessboard 7x7 1.Kd4-e5 Kg7-f7 2.DAb1-b3 Kf7-e7 3.DAb3-b5 Ke7-d7 4.Ke5-d5 Kd7-e7 5.Gc4-e2 Ke7-d7 6.Gd3-d6 Kd7-c7 7.Kd5-c5 Kc7-d7 8.Ge2-a6 Kd7-e7 9.DAb5-d5 Ke7-f7 10.Kc5-d4 Kf7-f6 11.Kd4-e4 Kf6-e7 12.Ke4-e5 Ke7-f7 13.Ga6-e6 Kf7-e7 14.Ge6-e4 Ke7-f7 15.Ge4-c6 Kf7-e7 16.Gd6-f4 Ke7-f7 17.Ke5-d4 Kf7-e6 18.Gf4-c4+ Ke6-d6 19.Gc6-e4 Kd6-c7 20.Kd4-c5 Kc7-b7 21.Gc4-e6 Kb7-a6 22.Kc5-b4 Ka6-b6 23.Kb4-c4 Kb6-a7 24.Ge4-c6 Ka7-b7 25.Kc4-c5 Kb7-c7 26.Ge6-c4 Kc7-b7 27.Kc5-b5 Kb7-a7 28.Gc6-a4 Ka7-b7 29.Kb5-c5 Kb7-a6 30.DAd5-b5+ Ka6-a5 31.Gc4-c6 Ka5-a6 32.DAb5-b3 Ka6-b7 33.Kc5-d6 Kb7-a6 34.Ga4-c2 Ka6-a5 35.Kd6-c5 Ka5-a6 36.Gc6-c4 Ka6-b7 37.Kc5-d6 Kb7-a6 38.Gc4-a2 Ka6-a5 39.Kd6-c5 Ka5-a6 40.Ga2-d2 Ka6-b7 41.Kc5-d6 Kb7-a6 42.Kd6-c7 Ka6-a7 43.Kc7-c6 Ka7-a6 44.Gd2-b2 Ka6-a7 45.DAb3-b5 Ka7-a6 46.Kc6-c5 Ka6-a5 47.Gc2-c6 Ka5-a6 48.Gb2-b6+ Ka6-a7 49.Gb6-d6 Ka7-a6 50.Gd6-b4 Ka6-a7 51.Kc5-c4 Ka7-a6 52.Gc6-c3 Ka6-a7 53.Kc4-d5 Ka7-a6 54.Kd5-c6 Ka6-a7 55.Gc3-c7 Ka7-a6 56.Gb4-b6 Ka6-a7 57.DAb5-d5 Ka7-a6 58.DAd5-f5 Ka6-a7 59.Kc6-b5 Ka7-b7 60.Gc7-a5 Kb7-a7 61.DAf5-f7 Ka7-b7 62.DAf7-d7+ Kb7-a7 63.Ga5-c5# |
K + 2 Grasshoppers + [1,3] - K | |
![]() | Kb1 Camel a2 Grasshopper a1b2 - Kd2, chessboard 7x7 1.CAa2-b5 Kd2-d3 2.Kb1-c1 Kd3-c4 3.CAb5-a2 Kc4-d5 4.CAa2-d1 Kd5-c6 5.Kc1-d2 Kc6-b6 6.Kd2-d3 Kb6-c5 7.Ga1-c3 Kc5-b4 8.Gb2-d4 Kb4-c5 9.Gd4-d2 Kc5-d5 10.Gc3-e3 Kd5-c5 11.Kd3-e4 Kc5-d6 12.Ke4-d4 Kd6-c6 13.CAd1-a2 Kc6-b6 14.CAa2-d3 Kb6-b5 15.Ge3-c3 Kb5-b6 16.Kd4-c4 Kb6-c7 17.Kc4-c5 Kc7-d7 18.Gd2-d4 Kd7-e7 19.Kc5-d5 Ke7-f6 20.CAd3-c6 Kf6-e7 21.Gc3-e5 Ke7-d7 22.CAc6-b3 Kd7-c7 23.Ge5-c5 Kc7-d7 24.Kd5-e5 Kd7-c7 25.Ke5-e6 Kc7-b7 26.Ke6-d6 Kb7-a7 27.Gc5-e7 Ka7-b6 28.CAb3-e4 Kb6-a5 29.Kd6-c5 Ka5-a4 30.Ge7-b4+ Ka4-a3 31.Kc5-c4 Ka3-b2 32.Kc4-d3 Kb2-c1 33.Kd3-c3 Kc1-b1 34.CAe4-b5 Kb1-c1 35.Gb4-d2 Kc1-b1 36.CAb5-c2 Kb1-c1 37.CAc2-d5 Kc1-b1 38.Gd4-d6 Kb1-c1 39.CAd5-a6 Kc1-b1 40.Gd2-b4 Kb1-c1 41.Kc3-d3 Kc1-b1 42.CAa6-b3 Kb1-c1 43.Gd6-d2 Kc1-b1 44.Kd3-c3 Kb1-a1 45.Gb4-b2 Ka1-b1 46.CAb3-e4 Kb1-a1 47.Kc3-b3 Ka1-b1 48.Gb2-b4 Kb1-c1 49.Kb3-c3 Kc1-b1 50.Gb4-f4 Kb1-a2 51.Kc3-b4 Ka2-b2 52.CAe4-b5 Kb2-b1 53.Kb4-a3 Kb1-a1 54.CAb5-c2 Ka1-b1 55.Ka3-b3 Kb1-a1 56.Gf4-c1 Ka1-b1 57.Gc1-e3 Kb1-a1 58.Gd2-b2 Ka1-b1 59.Ge3-a3 Kb1-a1 60.CAc2-d5 Ka1-b1 61.CAd5-e2+ Kb1-a1 62.Ga3-c3# |
K + 2 Grasshoppers + [1,3] - K | |
![]() | Kb1 Camel c1 Grasshopper a1b2 - Kd3, chessboard 7x7 1.Kb1-a2 Kd3-c2 2.CAc1-b4 Kc2-d3 3.Ka2-b3 Kd3-d4 4.Ga1-c3+ Kd4-c5 5.CAb4-a1 Kc5-d5 6.Kb3-b4 Kd5-c6 7.Kb4-c4 Kc6-d6 8.CAa1-b4 Kd6-e6 9.Gb2-b5 Ke6-f5 10.Kc4-d4 Kf5-f4 11.CAb4-e5 Kf4-g5 12.CAe5-d2 Kg5-f6 13.CAd2-c5+ Kf6-g5 14.Gb5-d5 Kg5-f5 15.Gd5-d3 Kf5-e6 16.Gc3-c6 Ke6-d6 17.Gc6-c4 Kd6-e6 18.Kd4-e4 Ke6-d6 19.CAc5-b2 Kd6-c6 20.Ke4-e5 Kc6-c7 21.Ke5-d5 Kc7-b7 22.CAb2-e3 Kb7-c7 23.CAe3-b4+ Kc7-d7 24.Gc4-e6 Kd7-e7 25.CAb4-e3 Ke7-d7 26.CAe3-d6 Kd7-c7 27.Kd5-c5 Kc7-b7 28.Gd3-d7 Kb7-a6 29.Gd7-f5 Ka6-b7 30.CAd6-a5 Kb7-a6 31.CAa5-d4 Ka6-b7 32.Gf5-d7 Kb7-a6 33.Kc5-c6 Ka6-a7 34.Ge6-b6 Ka7-a6 35.Gb6-d6 Ka6-a7 36.Gd6-d3 Ka7-a6 37.Gd3-d5 Ka6-a7 38.Gd5-b7+ Ka7-a6 39.Gb7-e7 Ka6-a7 40.Kc6-b5 Ka7-b7 41.CAd4-c7+ Kb7-a7 42.CAc7-b4+ Ka7-b7 43.Ge7-c7# |
K + 2 Grasshoppers + [1,3] - K | |
![]() | Tento diagram demonstruje rozdíl při umístění velblouda na polích různých barev, v obou případech je však koncovka na šachovnici 7x7 vyhrávající. This diagram demonstrates the difference made by putting the camel on a light or a dark square. However, in both cases the ending is won on a 7x7 board. |
K + 2 Grasshoppers + [1,4] - K | |
![]() | Ka2 Giraffe a1 Grasshopper b1b2 - Kc3, chessboard 7x7 1.GIa1-b5 Kc3-b4 2.GIb5-f4 Kb4-c3 3.GIf4-b3 Kc3-d4 4.Ka2-a3 Kd4-c5 5.Ka3-a4 Kc5-d4 6.Ka4-b4 Kd4-d3 7.GIb3-f2 Kd3-d2 8.Kb4-b3 Kd2-e3 9.GIf2-e6 Ke3-d3 10.GIe6-a5 Kd3-d4 11.Kb3-b4 Kd4-d3 12.Gb1-e4 Kd3-c2 13.Gb2-b5 Kc2-d3 14.Kb4-c5 Kd3-c3 15.Gb5-d5 Kc3-d3 16.Ge4-c6 Kd3-c3 17.Gc6-c4 Kc3-d3 18.Gd5-b5+ Kd3-e3 19.Kc5-d5 Ke3-d2 20.Kd5-d4 Kd2-c2 21.GIa5-e6 Kc2-b3 22.GIe6-f2+ Kb3-b4 23.Gb5-d3 Kb4-a5 24.Kd4-c5 Ka5-a4 25.Gc4-e2 Ka4-a3 26.Gd3-f1 Ka3-b2 27.Kc5-d4 Kb2-c2 28.Gf1-f3 Kc2-d2 29.Ge2-g2 Kd2-c2 30.Gg2-e4 Kc2-b2 31.Kd4-c4 Kb2-a3 32.GIf2-e6 Ka3-b2 33.Gf3-d5 Kb2-a3 34.GIe6-d2 Ka3-b2 35.GId2-c6+ Kb2-a3 36.Ge4-b4 Ka3-a2 37.Kc4-c3 Ka2-a3 38.Gd5-b7 Ka3-a4 39.Gb7-b3 Ka4-a5 40.GIc6-b2 Ka5-b6 41.Kc3-d4 Kb6-c7 42.Kd4-e5 Kc7-d7 43.Gb3-b5 Kd7-e7 44.GIb2-c6 Ke7-f7 45.Gb4-b6 Kf7-g6 46.Gb6-d6 Kg6-f7 47.Gb5-d7 Kf7-g6 48.Gd7-d5 Kg6-f7 49.GIc6-g5 Kf7-g6 50.GIg5-c4 Kg6-f7 51.Gd5-b3 Kf7-e7 52.GIc4-g3 Ke7-d7 53.Ke5-d5 Kd7-c7 54.GIg3-c2 Kc7-d7 55.Gb3-e6 Kd7-c7 56.Gd6-d4 Kc7-b7 57.Ge6-c4 Kb7-c7 58.Gc4-e4 Kc7-b7 59.Kd5-c5 Kb7-a6 60.Ge4-c4 Ka6-a5 61.Gd4-b4 Ka5-a6 62.GIc2-d6 Ka6-b7 63.Gb4-d4 Kb7-a6 64.Gd4-d7 Ka6-a5 65.Gc4-c6 Ka5-a4 66.Kc5-c4 Ka4-a5 67.GId6-c2 Ka5-a4 68.GIc2-b6 Ka4-a5 69.GIb6-f7 Ka5-a4 70.Gd7-b5+ Ka4-a3 71.Kc4-c3 Ka3-a2 72.GIf7-e3+ Ka2-b1 73.GIe3-a4 Kb1-a2 74.GIa4-e5 Ka2-b1 75.Gc6-c2 Kb1-a2 76.Gc2-c4 Ka2-b1 77.Gb5-d3 Kb1-a2 78.Gd3-b3+ Ka2-b1 79.GIe5-d1 Kb1-a1 80.Gc4-c2 Ka1-a2 81.GId1-c5 Ka2-a1 82.GIc5-g6 Ka1-a2 83.GIg6-f2 Ka2-a3 84.GIf2-e6 Ka3-a2 85.GIe6-a5 Ka2-a3 86.GIa5-e4+ Ka3-a2 87.Gb3-d3 Ka2-a1 88.GIe4-a3 Ka1-a2 89.GIa3-b7 Ka2-a1 90.GIb7-f6 Ka1-a2 91.GIf6-b5 Ka2-a3 92.Gd3-b3 Ka3-a2 93.Gc2-a4 Ka2-b1 94.Gb3-d3 Kb1-a2 95.Gd3-a6 Ka2-b1 96.Ga6-c4 Kb1-a2 97.Ga4-c6 Ka2-b1 98.Gc4-c7 Kb1-a2 99.Gc7-c5 Ka2-b1 100.Gc5-a5 Kb1-a2 101.Gc6-a4 Ka2-b1 102.Ga4-a6 Kb1-a2 103.GIb5-f6 Ka2-b1 104.GIf6-g2 Kb1-a2 105.Ga6-a4 Ka2-b1 106.Kc3-b3 Kb1-a1 107.Kb3-c2 Ka1-a2 108.GIg2-f6 Ka2-a1 109.GIf6-e2+ Ka1-a2 110.Ga5-a3# |
x/y | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
0 | = | + | = | = | = | = | = | = |
1 | + | + | + | = | = | = | = | = |
2 | = | + | = | + | = | = | = | = |
3 | = | = | + | = | = | = | = | = |
4 | = | = | = | = | = | = | = | = |
5 | = | = | = | = | = | = | = | = |
6 | = | = | = | = | = | = | = | = |
7 | = | = | = | = | = | = | = | = |
K + 2 Grasshoppers + [0,1] - K | |
![]() | Ka1 Grasshopper a2b2 Wazir b1 - Kd4 1.WAb1-c1 Kd4-c3 2.WAc1-c2+ Kc3-b3 3.Ka1-b1 Kb3-c4 4.Gb2-d2 Kc4-b3 5.WAc2-b2+ Kb3-c3 6.Kb1-c1 Kc3-b4 7.Kc1-c2 Kb4-c5 8.Kc2-d3 Kc5-d5 9.WAb2-b3 Kd5-e5 10.WAb3-b4 Ke5-d6 11.Kd3-e4 Kd6-c5 12.WAb4-b3 Kc5-d6 13.WAb3-c3 Kd6-e6 14.Gd2-b4 Ke6-d7 15.Ke4-d5 Kd7-e7 16.Kd5-e5 Ke7-f7 17.WAc3-c4 Kf7-g6 18.Ke5-f4 Kg6-f6 19.Ga2-d5 Kf6-e6 20.WAc4-c5 Ke6-f6 21.Gd5-b5 Kf6-e6 22.Gb5-b3 Ke6-f7 23.Kf4-f5 Kf7-g7 24.Kf5-g5 Kg7-f7 25.WAc5-d5 Kf7-g7 26.WAd5-d6 Kg7-f7 27.Kg5-f5 Kf7-g7 28.WAd6-e6 Kg7-h6 29.Kf5-g4 Kh6-g6 30.Gb4-b2 Kg6-h6 31.WAe6-f6 Kh6-h7 32.Kg4-g5 Kh7-g8 33.WAf6-e6 Kg8-f8 34.Kg5-f6 Kf8-e8 35.WAe6-d6 Ke8-d8 36.Kf6-e6 Kd8-c7 37.Gb2-b4 Kc7-b6 38.Ke6-d5 Kb6-c7 39.Gb3-b5 Kc7-d8 40.Kd5-e6 Kd8-c7 41.Ke6-e5 Kc7-d8 42.Ke5-d5 Kd8-c7 43.WAd6-c6+ Kc7-d8 44.Kd5-e6 Kd8-c8 45.Gb4-b6 Kc8-d8 46.Ke6-f7 Kd8-c8 47.Kf7-e8 Kc8-b8 48.Ke8-d7 Kb8-a7 49.Kd7-d6 Ka7-b8 50.WAc6-c7 Kb8-a7 51.Kd6-c5 Ka7-a6 52.WAc7-b7 Ka6-a5 53.Gb6-b4 Ka5-a4 54.Kc5-c4 Ka4-a3 55.Kc4-c3 Ka3-a4 56.WAb7-b6 Ka4-a5 57.Kc3-c4 Ka5-a4 58.WAb6-a6 Ka4-a3 59.Kc4-c3 Ka3-a2 60.WAa6-a5 Ka2-b1 61.Kc3-d2 Kb1-a2 62.Kd2-c2 Ka2-a3 63.Gb4-b6 Ka3-a2 64.WAa5-a4 Ka2-a1 65.WAa4-b4 Ka1-a2 66.WAb4-b3 Ka2-a1 67.Gb5-b2 Ka1-a2 68.Gb2-d2 Ka2-a1 69.Gb6-b2 Ka1-a2 70.Gb2-b4 Ka2-a1 71.Gd2-a5 Ka1-a2 72.Ga5-c3 Ka2-a1 73.WAb3-b2# |
K + Grasshopper + Grasshopper + [0,1] - K | |
![]() | Černý může remizovat jen tehdy, pokud se mu podaří chytit některý z bílých kamenů (v tomto případě cvrčka), obecně je ale koncovka pro silnější stranu vyhraná. The Black king can draw only if he can play to capture one of the White pieces (in this case one of the grasshoppers). In general, the ending is won for the stronger side. |
K + 2 Grasshoppers + [1,1] - K | |
![]() | Ka1 Fers a2 Grasshopper b1b2 - Kd4 1.FEa2-b3 Kd4-c3 2.Ka1-a2 Kc3-d4 3.Ka2-a3 Kd4-c5 4.Gb2-b4 Kc5-d4 5.Ka3-b2 Kd4-d3 6.Kb2-c1 Kd3-c3 7.Gb4-b2 Kc3-d3 8.Gb1-d1 Kd3-c3 9.FEb3-c2 Kc3-b4 10.Kc1-d2 Kb4-c4 11.FEc2-d3+ Kc4-d5 12.Kd2-c3 Kd5-c5 13.Gd1-d4 Kc5-d5 14.Gd4-d2 Kd5-e5 15.Kc3-c4 Ke5-d6 16.Kc4-d4 Kd6-c7 17.Kd4-d5 Kc7-d8 18.Gd2-d4 Kd8-e7 19.Gb2-e5 Ke7-f7 20.FEd3-e4 Kf7-g6 21.Kd5-e6 Kg6-g5 22.Ke6-f7 Kg5-h4 23.Kf7-g6 Kh4-g3 24.Ge5-e3 Kg3-g4 25.Kg6-f6 Kg4-g3 26.Kf6-g5 Kg3-g2 27.Kg5-f4 Kg2-f1 28.Kf4-f3 Kf1-e1 29.FEe4-d3 Ke1-d1 30.Ge3-c5 Kd1-c1 31.FEd3-c4 Kc1-d2 32.Gd4-b4 Kd2-d1 33.Kf3-e3 Kd1-e1 34.Gc5-c3 Ke1-d1 35.FEc4-b3 Kd1-e1 36.Gb4-d2+ Ke1-f1 37.Ke3-f3 Kf1-g1 38.FEb3-c2 Kg1-h2 39.Kf3-g4 Kh2-g2 40.Gc3-c1 Kg2-f1 41.Kg4-f3 Kf1-e1 42.Gd2-b2 Ke1-f1 43.FEc2-d1 Kf1-g1 44.FEd1-e2 Kg1-h2 45.Kf3-g4 Kh2-g2 46.Kg4-h4 Kg2-h2 47.Gb2-f2 Kh2-g2 48.Gf2-d2 Kg2-h2 49.Gc1-e3 Kh2-g2 50.Ge3-e1 Kg2-h2 51.FEe2-f3 Kh2-g1 52.Kh4-g3 Kg1-f1 53.Ge1-c3 Kf1-g1 54.FEf3-g4 Kg1-f1 55.Kg3-f3 Kf1-g1 56.FEg4-h3 Kg1-h2 57.FEh3-g2+ Kh2-g1 58.Gc3-g3# |
K + 2 Grasshoppers + [1,1] - K | |
![]() | Kb2 Fers f7 Grasshopper a2b1 - Kh8 1.Gb1-b3 Kh8-g7 2.FEf7-e6 Kg7-f6 3.FEe6-d5 Kf6-e5 4.Ga2-c4 Ke5-d4 5.Kb2-c2 Kd4-e3 6.Kc2-c3 Ke3-f4 7.Kc3-d3 Kf4-e5 8.FEd5-e4 Ke5-f6 9.Gc4-f4 Kf6-e5 10.Gf4-d4 Ke5-e6 11.Gb3-e3 Ke6-d6 12.Kd3-c4 Kd6-c6 13.Gd4-f4 Kc6-d6 14.Kc4-d4 Kd6-c6 15.Kd4-e5 Kc6-c5 16.FEe4-d3 Kc5-c6 17.Ke5-e6 Kc6-c7 18.Ge3-c3 Kc7-b6 19.Ke6-d6 Kb6-b5 20.Gc3-e3 Kb5-a6 21.Kd6-c6 Ka6-a7 22.FEd3-c4 Ka7-a6 23.Gf4-b4 Ka6-a5 24.Kc6-c5 Ka5-a4 25.FEc4-d3 Ka4-b3 26.Gb4-d6 Kb3-a4 27.Gd6-d2 Ka4-a5 28.Ge3-c3 Ka5-a6 29.Kc5-c6 Ka6-a5 30.FEd3-c2 Ka5-a6 31.Gd2-b4 Ka6-a7 32.FEc2-b3 Ka7-b8 33.Kc6-d7 Kb8-b7 34.Gc3-a3 Kb7-a6 35.Kd7-c6 Ka6-a5 36.Gb4-b2 Ka5-a6 37.FEb3-a4 Ka6-a7 38.FEa4-b5 Ka7-b8 39.Kc6-d7 Kb8-b7 40.Kd7-d8 Kb7-b8 41.Gb2-b6 Kb8-b7 42.Gb6-b4 Kb7-b8 43.Ga3-c5 Kb8-b7 44.Gc5-a5 Kb7-b8 45.FEb5-c6 Kb8-a7 46.Kd8-c7 Ka7-a8 47.Ga5-c3 Ka8-a7 48.FEc6-d7 Ka7-a8 49.FEd7-c8 Ka8-a7 50.Kc7-c6 Ka7-b8 51.FEc8-b7+ Kb8-a7 52.Gc3-c7# Jak je vidět z diagramu, není zde barva pole ferse nijak významná. As can be seen from the diagram, the colour of square on which the fers runs is immaterial. |
K + 2 Grasshoppers + [1,1] - K | |
![]() | Černý král může udržet remízu, pokud chytí některou z bílých figur, obecně je ale koncovka pro silnější stranu vyhraná. The Black king can draw only if he can play to capture one of the White pieces. In general, the ending is won for the stronger side. |
K + 2 Grasshoppers + [1,2] - K | |
![]() | Tuto koncovku jsem již důkladně probíral v dřívějších článcích a zde ji uvádím jen pro úplnost. Viz např. Alybadix 2005 and (fairy) chess endgames I gave a complete analysis of this ending in my earlier articles and include it here only for completeness. See for example Alybadix 2005 and (fairy) chess endgames. |
K + 2 Grasshoppers + [2,3] - K | |
![]() | Ka2 Grasshopper b1b2 Zebra a1 - Ke3 1.ZEa1-c4 Ke3-d3 2.ZEc4-f6+ Kd3-c3 3.Ka2-a3 Kc3-d2 4.Gb1-b3 Kd2-c3 5.Gb3-d3 Kc3-c2 6.Gb2-g7 Kc2-c3 7.Gd3-b3 Kc3-d4 8.Ka3-b4 Kd4-d5 9.ZEf6-c4+ Kd5-e4 10.Kb4-c5 Ke4-e5 11.Gg7-d4 Ke5-e4 12.Gd4-b4 Ke4-e5 13.Gb3-b5 Ke5-e4 14.Kc5-d6 Ke4-f5 15.Kd6-d5 Kf5-f4 16.ZEc4-e7 Kf4-e3 17.Gb5-e5 Ke3-f4 18.ZEe7-b5 Kf4-f5 19.Ge5-c5 Kf5-f4 20.Kd5-d4 Kf4-f5 21.ZEb5-d2+ Kf5-f4 22.Gb4-d6 Kf4-f3 23.Gc5-e3 Kf3-e2 24.ZEd2-b5 Ke2-f3 25.Kd4-e5 Kf3-e2 26.Ke5-e4 Ke2-d1 27.Ge3-e5 Kd1-c2 28.Ke4-d4 Kc2-b3 29.ZEb5-e3 Kb3-c2 30.Gd6-f4 Kc2-b3 31.Ge5-c3 Kb3-b4 32.Gf4-d2+ Kb4-a4 33.Kd4-c4 Ka4-a5 34.Gd2-b4+ Ka5-b6 35.Kc4-d4 Kb6-b7 36.Kd4-c5 Kb7-c7 37.ZEe3-b5 Kc7-d7 38.Kc5-d5 Kd7-e8 39.Kd5-e6 Ke8-f8 40.Gb4-b6 Kf8-e8 41.Gb6-f6 Ke8-f8 42.Gf6-b2 Kf8-g7 43.ZEb5-e3 Kg7-f8 44.Gb2-d4 Kf8-e8 45.ZEe3-g6 Ke8-f8 46.Gc3-e5 Kf8-g7 47.ZEg6-e3 Kg7-f8 48.Gd4-f6 Kf8-e8 49.Ge5-e7 Ke8-f8 50.Ge7-g5 Kf8-g7 51.Gf6-d6 Kg7-f8 52.ZEe3-g6 Kf8-e8 53.Gd6-f6 Ke8-f8 54.Gf6-h4 Kf8-e8 55.Gg5-g7 Ke8-f8 56.Ke6-f6 Kf8-e8 57.Gh4-e7 Ke8-f8 58.Gg7-e5 Kf8-g8 59.ZEg6-e3 Kg8-h7 60.ZEe3-h5 Kh7-h6 61.Ge7-g5 Kh6-h7 62.Gg5-d5 Kh7-h6 63.ZEh5-f2 Kh6-h7 64.Kf6-f7 Kh7-h8 65.Kf7-g6 Kh8-g8 66.ZEf2-h5 Kg8-h8 67.Gd5-f5 Kh8-g8 68.Ge5-g5 Kg8-h8 69.Gf5-h7 Kh8-g8 70.Gh7-h4 Kg8-h8 71.Gh4-f6 Kh8-g8 72.Gf6-h6 Kg8-h8 73.ZEh5-e7 Kh8-g8 74.Gg5-g7 Kg8-h8 75.ZEe7-g4 Kh8-g8 76.ZEg4-d6+ Kg8-h8 77.Gh6-f6# |
K + 2 Grasshoppers + [2,3] - K | |
![]() | Na rozdíl od cvrčka, ferse nebo vezíra, zebru nelze "chytit" i když je hodně vzdálena od vlastního krále. Koncovka se zebrou je vyhraná z obecné pozice. The zebra, unlike the grasshopper, fers, or wazir, cannot be "caught" even if it is far away from its king. In general, the ending with a zebra is won for the stronger side. |
K + 2 Grasshoppers + [0,2] - K | |
![]() | Koncovka s dababou ([0,2] skokanem) je na rozdíl od šachovnic 6x6 a 7x7 na šachovnici 8x8 remízová. Soupeřova krále nelze z obecné pozice zatlačit do rohu šachovnice. The ending with a dabbaba ([0,2] leaper), in contrast to what happens on 6x6 and 7x7 boards, is only drawn on an 8x8. It is not possible to force the Black king back to a corner of the board. |
K + 2 Grasshoppers + [0,2] - K | |
![]() | Kd5 Dabbaba b4 Grasshopper c4c5 - Ka8 1.Kd5-c6 Ka8-b8 2.DAb4-b6+ Kb8-c8 3.DAb6-d6 Kc8-b8 4.Gc5-c3 Kb8-c8 5.Gc4-c7 Kc8-b8 6.Kc6-b6 Kb8-a8 7.DAd6-d4 Ka8-b8 8.DAd4-b4 Kb8-a8 9.Kb6-c6 Ka8-b8 10.Kc6-d7 Kb8-a7 11.Gc7-e7 Ka7-b7 12.Ge7-a3 Kb7-a6 13.Kd7-c6 Ka6-a7 14.Ga3-d3 Ka7-b8 15.Kc6-d7 Kb8-a7 16.Kd7-c8 Ka7-a8 17.Kc8-c7 Ka8-a7 18.Gd3-b3 Ka7-a8 19.DAb4-b6 Ka8-a7 20.Kc7-c6 Ka7-a6 21.Gc3-c7 Ka6-a7 22.Gb3-b7+ Ka7-a8 23.Gb7-d7 Ka8-a7 24.Gd7-b5 Ka7-a8 25.Kc6-c5 Ka8-a7 26.Gc7-c4 Ka7-a8 27.Kc5-d6 Ka8-a7 28.Kd6-c7 Ka7-a8 29.Gc4-c8 Ka8-a7 30.Gb5-b7 Ka7-a8 31.DAb6-d6 Ka8-a7 32.DAd6-f6 Ka7-a8 33.Kc7-b6 Ka8-b8 34.Gc8-a6 Kb8-a8 35.DAf6-f8 Ka8-b8 36.DAf8-d8+ Kb8-a8 37.Ga6-c6# Pokud už je černý král zatlačen do rohu šachovnice, lze v některých případech mat vynutit, ale jak je vidět z diagramu, musí být bílý král hodně blízko. If the Black king is already trapped in a corner of the board, it is possible in some cases to force mate, but as can be seen from the diagram the White king must be very close. |
K + 2 Grasshoppers + [0,2] - K | |
![]() | Ke5 Dabbaba b6 Grasshopper e6f5 - Kh8 1.DAb6-d6 Kh8-g8 2.DAd6-f6 Kg8-g7 3.Ge6-e4 Kg7-h8 4.Ke5-f4 Kh8-g7 5.Kf4-g5 Kg7-h7 6.Ge4-g6+ Kh7-g7 7.Gg6-g4 Kg7-h7 8.Gg4-e6 Kh7-g7 9.Ge6-g6 Kg7-g8 10.Kg5-h6 Kg8-h8 11.Gg6-e4 Kh8-g8 12.Kh6-g6 Kg8-h8 13.Kg6-f7 Kh8-h7 14.Ge4-g6+ Kh7-h8 15.DAf6-f8# Pro mat dababou musí být na šachovnici 8x8 navíc splněna podmínka jejího umístění jen na některých typech polí šachovnice (porovnejte se šachovnicí 7x7) To give mate, the dabbaba must run on certain squares (compare the 7x7 board). |
K + 2 Grasshoppers + [1,3] - K | |
![]() | Koncovka s velbloudem ([1,3] skokanem) je na rozdíl od šachovnic 6x6 a 7x7 na šachovnici 8x8 remízová. Soupeřova krále nelze z obecné pozice zatlačit do rohu šachovnice. The ending with a camel ([1,3] leaper), in contrast to what happens on 6x6 and 7x7 boards, is only drawn on an 8x8. It is not possible to force the Black king back to a corner of the board. |
K + 2 Grasshoppers + [1,3] - K | |
![]() | Kd5 Camel b4 Grasshopper c4c5 - Ka8 1.Kd5-c6 Ka8-b8 2.Gc5-c7 Kb8-c8 3.CAb4-a7 Kc8-b8 4.Kc6-b6 Kb8-a8 5.Kb6-a6 Ka8-b8 6.CAa7-b4 Kb8-a8 7.Gc4-c8 Ka8-b8 8.Gc8-c6 Kb8-a8 9.Gc7-c5 Ka8-b8 10.CAb4-c7 Kb8-a8 11.Ka6-b6 Ka8-b8 12.Gc5-a7 Kb8-a8 13.Ga7-d7 Ka8-b8 14.Gd7-b5 Kb8-a8 15.Gb5-b7+ Ka8-b8 16.Gc6-a6 Kb8-a8 17.CAc7-d4 Ka8-b8 18.CAd4-e7+ Kb8-a8 19.Ga6-c6# Mat lze vynutit jen pokud už je černý král zatlačen do rohu šachovnice a bílý král je nablízku. Mate can be forced only if the Black king is already trapped in a corner of the board and the White king is close. |
K + 2 Grasshoppers + [1,3] - K | |
![]() | Kd5 Camel g8 Grasshopper c5d6 - Ka8 1.Kd5-c6 Ka8-b8 2.Gc5-c7+ Kb8-a7 3.Gd6-b6 Ka7-b8 4.CAg8-f5 Kb8-a7 5.CAf5-e8 Ka7-b8 6.CAe8-d5 Kb8-a7 7.Gc7-a5 Ka7-b8 8.Ga5-e5 Kb8-a7 9.Kc6-c7 Ka7-a8 10.Gb6-d8 Ka8-a7 11.Ge5-c5 Ka7-a8 12.Gc5-c8 Ka8-a7 13.Gc8-e8 Ka7-a8 14.Kc7-b6 Ka8-b8 15.CAd5-c8+ Kb8-a8 16.CAc8-b5+ Ka8-b8 17.Ge8-c8# Kd5 Camel h2 Grasshopper c5d6 - Ka8 1.Kd5-c6 Ka8-b8 2.Gc5-c7+ Kb8-c8 3.Gd6-b6 Kc8-b8 4.CAh2-g5 Kb8-c8 5.CAg5-f8 Kc8-b8 6.Gc7-c5 Kb8-a8 7.CAf8-e5 Ka8-b8 8.CAe5-b4 Kb8-c8 9.Gc5-c7 Kc8-b8 10.Gb6-b3 Kb8-a8 11.Kc6-b6 Ka8-b8 12.CAb4-a7 Kb8-a8 13.Gb3-b7 Ka8-b8 14.Gb7-b5 Kb8-a8 15.CAa7-d8 Ka8-b8 16.Kb6-c6 Kb8-c8 17.CAd8-e5 Kc8-b8 18.Gc7-c5 Kb8-a7 19.Gc5-f5 Ka7-a6 20.CAe5-f2 Ka6-a7 21.Gf5-f1 Ka7-a8 22.Kc6-c7 Ka8-a7 23.CAf2-e5 Ka7-a8 24.Kc7-d8 Ka8-b7 25.Kd8-d7 Kb7-b8 26.CAe5-b6 Kb8-a8 27.Kd7-c8 Ka8-a7 28.Kc8-c7 Ka7-a8 29.Gf1-a6 Ka8-a7 30.Ga6-c6 Ka7-a8 31.Gb5-b7+ Ka8-a7 32.Gc6-c8 Ka7-a8 33.CAb6-c3 Ka8-a7 34.CAc3-d6+ Ka7-a8 35.Gc8-c6# Postupy se liší podle barvy pole velblouda, ale v obou případech se v této pozici podaří vynutit mat. Obecně je ale koncovka na šachovnici 8x8 remízová. The play up to the mate depends on the colour of the squares on which the camel runs, but in both cases it is possible to force mate. In general, however, the ending on an 8x8 board is drawn. |
K + 2 Grasshoppers + [1,4] - K | |
![]() | Koncovka s žirafou ([1,4] skokanem) je na rozdíl od šachovnic 6x6 a 7x7 na šachovnici 8x8 remízová. Soupeřova krále nelze z obecné pozice zatlačit do rohu šachovnice. The ending with a giraffe ([1,4] leaper), in contrast to what happens on 6x6 and 7x7 boards, is only drawn on an 8x8. It is not possible to force the Black king back to a corner of the board. Věci znalého čtenáře možná ale napadne jedna věc. V případě této koncovky na šachovnici 7x7 bylo potřeba k vynucení matu více jak 100 tahů. Alybadix přitom umí testovat vícetažky maximálně do 126 tahů. Nemohl by proto být v případě šachovnice 8x8 matový postup přesahující 126 tahů a koncovka přeci jen vyhrávající ? Není tomu tak. Směrodatným ukazatelem je v tomto případě (Alybadixem zobrazovaný) počet všech možných pozic. Pokud se od určitého tahu již nezvyšuje, všechny možnosti dané pozice byly probrány a koncovka je tudíž (pokud se do té doby nenašlo žádné řešení) nutně remízová. Zde taková situace nastává od 114. tahu, viz screenshot zobrazující stav po více jak 4 hodinové práci Alybadixu. Celkový počet pozic 18527259 se nezmění až do 126. tahu. One point may have occurred to knowledgeable readers. In some cases, these endings require more than 100 moves to mate on a 7x7 board. Alybadix cannot test problems in more than 126 moves. On an 8x8 board, might there not be a winning ending whose longest mate exceeds 126 moves? No, there isn't. A conclusive indication is given by the count of all possible positions which is displayed by Alybadix. Once this stops increasing, all possible positions have been examined, and (if no solution has been discovered so far) the ending is necessarily drawn. Here, such a situation arises after move 114, as is shown by the screenshot after more than four hours of calculation by Alybadix. The total number of positions remains unchanged right up to move 126. |
K + 2 Grasshoppers + [1,4] - K | |
![]() | Kh5 Giraffe a8 Grasshopper d5e5 - Kh8 1.Kh5-g6 Kh8-g8 2.Kg6-f6 Kg8-f8 3.GIa8-e7 Kf8-g8 4.Gd5-f5 Kg8-h7 5.GIe7-a8 Kh7-g8 6.GIa8-b4 Kg8-f8 7.Ge5-g7 Kf8-e8 8.Kf6-e6 Ke8-f8 9.GIb4-c8 Kf8-e8 10.Gf5-d7 Ke8-d8 11.GIc8-b4 Kd8-e8 12.Gg7-c7 Ke8-d8 13.Gc7-e7 Kd8-e8 14.GIb4-c8 Ke8-f8 15.GIc8-d4 Kf8-g7 16.Ke6-f5 Kg7-h8 17.Kf5-g6 Kh8-g8 18.Gd7-f7 Kg8-f8 19.Kg6-f6 Kf8-g8 20.Ge7-g7 Kg8-h8 21.Gg7-e5 Kh8-h7 22.Gf7-f5 Kh7-g8 23.Gf5-d5 Kg8-h8 24.Kf6-g6 Kh8-g8 25.Ge5-c3 Kg8-f8 26.Kg6-f6 Kf8-g8 27.Gd5-d3 Kg8-h8 28.Kf6-g6 Kh8-g8 29.Gc3-e3 Kg8-f8 30.Kg6-f6 Kf8-g8 31.Gd3-f3 Kg8-h8 32.Kf6-f7 Kh8-h7 33.Gf3-f8 Kh7-h6 34.Kf7-f6 Kh6-h7 35.Ge3-c5 Kh7-g8 36.Gf8-b4 Kg8-h7 37.Gb4-d6 Kh7-g8 38.Gd6-g6 Kg8-f8 39.Gg6-e6 Kf8-g8 40.Kf6-g6 Kg8-f8 41.Gc5-e3 Kf8-g8 42.Ge6-h6 Kg8-f8 43.Kg6-f6 Kf8-g8 44.Gh6-d2 Kg8-h8 45.Kf6-g6 Kh8-g8 46.Gd2-f4 Kg8-f8 47.Kg6-f6 Kf8-g8 48.Ge3-g5 Kg8-f8 49.Gf4-h6 Kf8-g8 50.Kf6-g6 Kg8-f8 51.Gh6-f6 Kf8-g8 52.Gf6-c3 Kg8-f8 53.Kg6-f6 Kf8-g8 54.GId4-e8 Kg8-h8 55.Kf6-f7 Kh8-h7 56.GIe8-d4 Kh7-h6 57.Kf7-f6 Kh6-h7 58.Gc3-e5 Kh7-g8 59.Ge5-g7+ Kg8-f8 60.Gg5-e7 Kf8-g8 61.GId4-h5 Kg8-f8 62.GIh5-d6 Kf8-e8 63.GId6-h7 Ke8-f8 64.Gg7-e5 Kf8-g8 65.GIh7-d8 Kg8-f8 66.GId8-e4+ Kf8-g8 67.Ge5-g7 Kg8-h8 68.Kf6-g6 Kh8-g8 69.Ge7-e3 Kg8-h8 70.Gg7-g5 Kh8-g8 71.Ge3-h6 Kg8-h8 72.Gg5-g7 Kh8-g8 73.Gh6-f8 Kg8-h8 74.Kg6-f7 Kh8-h7 75.GIe4-d8+ Kh7-h8 76.Gf8-f6# Také v případě žirafy lze někdy matu dosáhnout, pokud už je soupeřův král v rohu šachovnice, ale tento případ je spíše vyjímečný a obecně je koncovka remízová. Again, in the case of the giraffe it is sometimes possible to force mate if the enemy king is already confined to a corner of the board, but this case is somewhat exceptional and the ending is in general drawn. |
6x6 | 7x7 | 8x8 | |
K + Rook - K + Knight | = | = | = |
K + Rook - K + Bishop | + | = | = |
K + Rook + Grasshopper - K + Knight | + | + | + |
K + Rook + Grasshopper - K + Bishop | + | + | + |
K + Rook - K + Bishop | |
![]() | Kf1 Te1 - Kd2 Ld5, chessboard 6x6 1.Kf1-f2 Ld5-c4 2.Te1-e3 Lc4-d5 3.Te3-e5 Ld5-c4 4.Te5-a5 Kd2-d3 5.Ta5-a3+ Kd3-e4 6.Kf2-e1 Ke4-d4 7.Ke1-d2 Lc4-b5 8.Ta3-a5 Kd4-c4 9.Ta5-a1 Kc4-d4 10.Ta1-a3 Kd4-c4 11.Ta3-f3 Kc4-b4 12.Kd2-c2 Lb5-c4 13.Tf3-f6 Lc4-b3+ 14.Kc2-d3 Lb3-a2 15.Tf6-b6+ Kb4-c5 16.Tb6-b2 La2-e6 17.Kd3-e4 Kc5-c4 18.Tb2-c2+ Kc4-b3 19.Tc2-c6 Le6-c4 20.Ke4-d4 Lc4-e2 21.Tc6-c3+ Kb3-b2 22.Tc3-e3 Le2-b5 23.Te3-e5 Lb5-c6 24.Te5-e2+ Kb2-b3 25.Kd4-c5 Lc6-a4 26.Te2-e4 Kb3-a3 27.Kc5-c4 Ka3-b2 28.Te4-e2+ Kb2-a3 29.Te2-f2 La4-c6 30.Tf2-f6 Lc6-e4 31.Kc4-d4 Le4-b1 32.Kd4-c3 Ka3-a4 33.Tf6-f2 Ka4-a5 34.Kc3-c4 Lb1-e4 35.Kc4-c5 Ka5-a4 36.Tf2-f4 Ka4-b3 37.Tf4:e4 Kb3-c2 38.Kc5-d4 Kc2-d2 39.Kd4-c4 Kd2-c2 40.Te4-e2+ Kc2-d1 41.Kc4-d3 Kd1-c1 42.Kd3-c3 Kc1-b1 43.Te2-e1+ Kb1-a2 44.Te1-f1 Ka2-a3 45.Tf1-a1# Na šachovnici 6x6 lze převahu kvality v případě střelce přetvořit do matu. On the 6x6 board, it is possible to convert the advantage of rook against bishop into a win. |
K + Rook - K + Knight | |
![]() | Proti jezdci věž ale nevyhraje ani na šachovnici 6x6. However, against a knight the ending is not a win even on a 6x6 board. |
K + Rook - K + Bishop | |
![]() | Na šachovnici 7x7 nevyhraje věž už ani proti střelci. On a 7x7 board, the rook does not win even against a bishop. |
K + Rook - K + Bishop | |
![]() | Kc4 Ta2 - Kg7 Lf6 1.Kc4-d5 Kg7-f7 2.Ta2-a7+ Kf7-g6 3.Kd5-e6 Kg6-g5 4.Ta7-a5+ Kg5-g6 5.Ta5-c5 Lf6-g7 6.Tc5-c2 Kg6-g5 7.Tc2-g2+ Kg5-f4 8.Tg2:g7 Kf4-e3 9.Ke6-d5 Ke3-f4 10.Kd5-d4 Kf4-f5 11.Tg7-e7 Kf5-f6 12.Te7-e5 Kf6-f7 13.Kd4-c5 Kf7-g6 14.Kc5-d6 Kg6-f7 15.Te5-f5+ Kf7-g7 16.Kd6-e7 Kg7-g6 17.Ke7-e6 Kg6-g7 18.Tf5-g5# Pouze v případě, je-li soupeřův král již v rohu šachovnice, lze někdy matu na šachovnici 7x7 proti střelci dosáhnout. Obecně je to remíza. Only in the case where the enemy king is already in a corner of the board may it be possible to force mate on a 7x7 board. In general, the ending is drawn. |
K + Rook - K + Bishop | |
![]() | Ještě výraznější je remis v případě bělopolného střelce (což je na šachovnici 7x7 vlastně trochu jiný kámen...) The draw is even more emphatic in the case of a bishop on light squares (which on a 7x7 board is by nature a slightly different piece). |
K + Rook + Grasshopper - K + Knight | |
![]() | Ka1 Tb1 Grasshopper a2 - Kc2 Sd5 1.Tb1-b5 Sd5-c3 2.Tb5-b2+ Kc2-c1 3.Tb2-g2 Sc3-d5 4.Ga2-h2 Sd5-b4 5.Tg2-g4 Sb4-c2+ 6.Ka1-a2 Sc2-e3 7.Tg4-g3 Kc1-d2 8.Ka2-b3 Kd2-d3 9.Tg3-g8 Kd3-d4 10.Tg8-h8 Kd4-e4 11.Kb3-b4 Ke4-d5 12.Kb4-c3 Se3-d1+ 13.Kc3-d2 Sd1-b2 14.Th8-h5+ Kd5-e4 15.Th5-h4+ Ke4-d5 16.Gh2-h5 Sb2-c4+ 17.Kd2-c3 Sc4-d6 18.Kc3-d3 Kd5-e5 19.Gh5-h3 Ke5-f6 20.Th4-g4 Kf6-e5 21.Tg4-a4 Sd6-c8 22.Kd3-e3 Ke5-d5 23.Ta4-d4+ Kd5-e5 24.Td4-c4 Sc8-b6 25.Tc4-c5+ Sb6-d5+ 26.Ke3-d3 Ke5-e6 27.Kd3-e4 Sd5-f6+ 28.Ke4-d4 Ke6-d6 29.Tc5-f5 Kd6-e7 30.Kd4-e3 Sf6-e8 31.Tf5-e5+ Ke7-d7 32.Ke3-e4 Se8-c7 33.Ke4-d4 Kd7-c6 34.Te5-c5+ Kc6-d6 35.Tc5-f5 Sc7-e8 36.Tf5-f4 Kd6-e6 37.Tf4-e4+ Ke6-d7 38.Kd4-e5 Se8-c7 39.Te4-g4 Kd7-c6 40.Gh3-f5 Kc6-c5 41.Tg4-g2 Kc5-c6 42.Tg2-c2+ Kc6-d7 43.Gf5-b1 Sc7-b5 44.Tc2-d2+ Kd7-c6 45.Td2-a2 Sb5-c7 46.Ta2-c2+ Kc6-d7 47.Tc2-c4 Sc7-e8 48.Tc4-g4 Kd7-c6 49.Ke5-d4 Kc6-b5 50.Tg4-g5+ Kb5-c6 51.Tg5-g6+ Kc6-b5 52.Kd4-d5 Se8-c7+ 53.Kd5-d6 Sc7-a6 54.Tg6-g4 Kb5-a5 55.Tg4-g2 Ka5-b4 56.Tg2-c2 Kb4-a5 57.Tc2-b2 Sa6-b4 58.Tb2-d2 Ka5-b6 59.Td2-e2 Kb6-a5 60.Te2-e5+ Ka5-a4 61.Te5-b5 Sb4-a6 62.Kd6-c6 Sa6-b4+ 63.Kc6-c5 Sb4-d5 64.Tb5-b7 Sd5-e3 65.Tb7-b2 Ka4-a3 66.Tb2-d2 Se3-f5 67.Td2-f2 Sf5-e7 68.Tf2-f7 Se7-g8 69.Kc5-d6 Sg8-h6 70.Tf7-f3+ Ka3-b2 71.Kd6-e6 Kb2-c2 72.Tf3-g3 Kc2-b2 73.Gb1-b3 Kb2-c2 74.Tg3-g6 Kc2-d3 75.Tg6:h6 Kd3-e4 76.Th6-h4+ Ke4-d3 77.Ke6-d5 Kd3-e3 78.Th4-e4+ Ke3-d3 79.Gb3-e6 Kd3-c3 80.Te4-d4 Kc3-b3 81.Td4-c4 Kb3-a2 82.Kd5-d4 Ka2-b2 83.Kd4-d3 Kb2-b1 84.Tc4-b4+ Kb1-a2 85.Kd3-c2 Ka2-a3 86.Tb4-c4 Ka3-a2 87.Tc4-a4# Síla cvrčka je poměrně malá, ale jak je vidět stačí na vynucení matu při převaze kvality i na šachovnici 8x8. The grasshopper is relatively feeble, but as can be seen it is sufficient to convert the advantage of the exchange into a mate even on an 8x8 board. |
K + Rook + Grasshopper - K + Bishop | |
![]() | Kb2 Tb1 Grasshopper a2 - Kc4 Ld6 1.Tb1-c1+ Kc4-d5 2.Tc1-d1+ Kd5-e5 3.Kb2-c3 Ld6-f8 4.Td1-e1+ Ke5-d5 5.Kc3-d3 Lf8-d6 6.Te1-e4 Ld6-f8 7.Te4-f4 Lf8-e7 8.Tf4-f5+ Kd5-d6 9.Kd3-e4 Le7-h4 10.Tf5-d5+ Kd6-c6 11.Ga2-e6 Lh4-f6 12.Td5-f5 Lf6-g7 13.Ge6-g4 Lg7-c3 14.Tf5-f8 Lc3-g7 15.Tf8-d8 Kc6-c5 16.Td8-a8 Lg7-b2 17.Gg4-d4 Kc5-d6 18.Ta8-a6+ Kd6-c5 19.Ta6-a2 Lb2-c3 20.Ta2-c2 Kc5-b4 21.Ke4-d3 Lc3-e1 22.Gd4-d2 Le1-f2 23.Gd2-g2 Lf2-b6 24.Kd3-e4 Lb6-g1 25.Gg2-d5 Kb4-b3 26.Tc2-c1 Lg1-f2 27.Gd5-f3 Lf2-a7 28.Ke4-d3 Kb3-b4 29.Tc1-c8 La7-b6 30.Gf3-c3 Kb4-b5 31.Gc3-e3 Kb5-b4 32.Kd3-e4 Lb6-c5 33.Ge3-e5 Kb4-c4 34.Tc8-c7 Kc4-b4 35.Ke4-d5 Lc5-f2 36.Tc7-c1 Lf2-e3 37.Tc1-c4+ Kb4-b3 38.Ge5-c5 Le3-g1 39.Tc4-g4 Lg1-f2 40.Tg4-f4 Lf2-e1 41.Kd5-d4 Kb3-b4 42.Gc5-e3 Kb4-b5 43.Kd4-d5 Kb5-b6 44.Tf4-e4 Kb6-b5 45.Ge3-e5 Le1-d2 46.Te4-h4 Kb5-b6 47.Th4-c4 Ld2-g5 48.Tc4-g4 Lg5-d2 49.Tg4-g6+ Kb6-b7 50.Tg6-g2 Ld2-h6 51.Tg2-f2 Lh6-e3 52.Tf2-f3 Le3-g5 53.Kd5-d6 Kb7-b6 54.Tf3-b3+ Kb6-a5 55.Kd6-c5 Lg5-e7+ 56.Kc5-c4 Le7-f8 57.Tb3-b2 Ka5-a6 58.Ge5-a1 Lf8-e7 59.Tb2-b3 Le7-f8 60.Kc4-d4 Lf8-g7+ 61.Kd4-c5 Lg7-f8+ 62.Kc5-c6 Ka6-a5 63.Ga1-a6 Ka5-a4 64.Tb3-b1 Lf8-e7 65.Ga6-d6 Le7-g5 66.Kc6-d5 Ka4-a5 67.Gd6-d4 Lg5-d8 68.Kd5-c5 Ld8-e7+ 69.Kc5-c4 Ka5-a6 70.Tb1-b5 Le7-d6 71.Tb5-d5 Ld6-f8 72.Td5-d8 Lf8-e7 73.Td8-d7 Le7-f8 74.Td7-f7 Lf8-a3 75.Gd4-b4 La3-b2 76.Kc4-c5 Lb2-c3 77.Tf7-f5 Ka6-b7 78.Kc5-b5 Lc3-e1 79.Tf5-f7+ Kb7-c8 80.Kb5-c6 Kc8-d8 81.Tf7-d7+ Kd8-e8 82.Kc6-d6 Le1-g3+ 83.Kd6-e6 Lg3-f4 84.Td7-f7 Lf4-b8 85.Tf7-b7 Lb8-f4 86.Tb7-d7 Lf4-b8 87.Td7-d3 Lb8-f4 88.Gb4-g4 Lf4-g5 89.Gg4-g6 Ke8-f8 90.Td3-d7 Kf8-g8 91.Td7-f7 Lg5-d2 92.Gg6-e8 Ld2-c3 93.Tf7-d7 Lc3-b4 94.Ge8-e5 Lb4-e1 95.Td7-f7 Le1-h4 96.Tf7-f4 Lh4-e1 97.Tf4-f6 Le1-h4 98.Tf6-g6+ Kg8-f8 99.Tg6-g1 Lh4-d8 100.Tg1-g4 Ld8-c7 101.Tg4-d4 Kf8-g8 102.Td4-d7 Lc7-b6 103.Td7-f7 Lb6-d8 104.Ge5-e7 Ld8-c7 105.Ke6-f6 Lc7-e5+ 106.Kf6-g6 Le5-c7 107.Ge7-g7 Lc7-g3 108.Tf7-f3 Lg3-h2 109.Tf3-h3 Lh2-b8 110.Th3-d3 Kg8-f8 111.Td3-d8+ Kf8-e7 112.Td8:b8 Ke7-d6 113.Tb8-b5 Kd6-c6 114.Tb5-e5 Kc6-d7 115.Gg7-c7 Kd7-c6 116.Gc7-f4 Kc6-b7 117.Kg6-f7 Kb7-c6 118.Kf7-e8 Kc6-b7 119.Ke8-d7 Kb7-b6 120.Te5-f5 Kb6-b7 121.Tf5-f6 Kb7-a8 122.Kd7-c8 Ka8-a7 123.Gf4-f7 Ka7-a8 124.Tf6-a6# |
Leo | Pao | Vao | Lion | Grasshopper | |
K + 2 Bishops | = | + | + | + | + |
K + Bishop + Knight | = | +/= | + | + | + |
K + 2 Knights | = | = | + | = | + |
K + 2 Knights - K + Lion | |
![]() | Tato koncovka je (na rozdíl od koncovky proti cvrčkovi) remízová. This ending, unlike endings against a grasshopper, is drawn. |
K + 2 Knights - K + Lion | |
![]() | Kf2 Sb4 Sb5 - Ka8 Lion h2 1.Kf2-e3 Ka8-b7 2.Ke3-d4 Kb7-b6 3.Kd4-c4 Kb6-b7 4.Kc4-c5 Kb7-b8 5.Sb4-c6+ Kb8-c8 6.Kc5-d4 Kc8-d7 7.Kd4-d5 Kd7-c8 8.Sc6-e7+ Kc8-d7 9.Se7-g6 Kd7-d8 10.Kd5-e6 Kd8-c8 11.Sg6-e7+ Kc8-b7 12.Ke6-d5 Kb7-b6 13.Kd5-c4 Kb6-a5 14.Sb5-d4 Ka5-b6 15.Sd4-e6 Kb6-a5 16.Se7-c8 Ka5-a6 17.Kc4-c5 Ka6-b7 18.Sc8-b6 Kb7-a6 19.Se6-d8 Ka6-a7 20.Kc5-c6 Ka7-b8 21.Sd8-b7 Kb8-a7 22.Sb6-d7 Ka7-a8 23.Kc6-c7 Ka8-a7 24.Sb7-c5 Ka7-a8 25.Sd7-b6+ Ka8-a7 26.Sb6-c8+ Ka7-a8 27.Sc5-d7 LIh2-b8 28.Sd7-b6# Výhra je možná jen pokud už je soupeřův král v rohu šachovnice a vlastní král není příliš daleko, jak ukazuje tento diagram. A win is possible only when the enemy king is already on the corner of the board and the attacking king is not too far away, as the diagram shows. |
K + 2 Knights - K + Leo | |
![]() | Dva jezdci proti leo nevyhrávají. Two knights do not win against a leo. |
K + 2 Knights - K + Pao | |
![]() | Dva jezdci nevyhrávají ani proti pao. Two knights do not win against a pao either. |
K + 2 Knights - K + Pao | |
![]() | Ka6 Sb4 Sb5 - Ka8 Pao h2 1.Sb5-a7 PAh2-h3 2.Ka6-b6 PAh3-h6 3.Sb4-d3 PAh6-h7 4.Sd3-e5 PAh7-g7 5.Sa7-c8 Ka8-b8 6.Sc8-e7 Kb8-a8 7.Se5-c6 PAg7-g6+ 8.Kb6-c7 PAg6-g4 9.Se7-d5 PAg4-c4+ 10.Kc7-b6 PAc4-c2 11.Kb6-a6 PAc2-c3 12.Sd5-b6# Dva jezdci proti pao mohou dát někdy mat, když je černý král v rohu šachovnice, ale podobných pozic je jen minimálně. Two knights can sometimes give mate against a pao, if the Black king is in a corner of the board, but the number of such positions is minimal. |
K + 2 Knights - K + Vao | |
![]() | Ka1 Sb1 Sb2 - Ke5 Vao b3 1.Ka1-a2 Ke5-d4 2.Ka2-a3 Kd4-c5 3.Sb1-c3 VAb3-c2 4.Sc3-e2 VAc2-b3 5.Ka3-a4 VAb3-d5 6.Ka4-b3 VAd5-c4 7.Kb3-c3 Kc5-d5 8.Se2-d4 Kd5-e4 9.Sd4-c2 Ke4-d5 10.Sc2-e3+ Kd5-e4 11.Se3-d1 Ke4-d5 12.Kc3-d3 Kd5-e5 13.Sd1-c3 VAc4-f7 14.Kd3-e3 Ke5-d6 15.Ke3-d4 Kd6-e6 16.Sc3-e4 Ke6-f5 17.Se4-c5 Kf5-f4 18.Sb2-c4 VAf7-e6 19.Sc4-d6 Kf4-f3 20.Sc5-d3 VAe6-f7 21.Sd6-c4 Kf3-g4 22.Sc4-e3+ Kg4-g5 23.Kd4-e5 VAf7-d5 24.Sd3-c5 Kg5-g6 25.Sc5-e4 Kg6-f7 26.Ke5-d6 VAd5-e6 27.Se3-d5 Kf7-f8 28.Se4-g5 Kf8-g7 29.Kd6-e5 Kg7-g6 30.Sg5-e4 Kg6-f7 31.Se4-d6+ Kf7-g6 32.Sd5-e7+ Kg6-g5 33.Sd6-f7+ Kg5-g4 34.Ke5-e4 Kg4-g3 35.Se7-c6 Kg3-f2 36.Sc6-d4 Kf2-g3 37.Sf7-e5 VAe6-f5 38.Ke4-e3 Kg3-h4 39.Ke3-f4 Kh4-h5 40.Sd4-e6 Kh5-h4 41.Se6-c5 Kh4-h5 42.Sc5-d7 Kh5-h4 43.Sd7-f6 Kh4-h3 44.Se5-g6 Kh3-g2 45.Sf6-e4 Kg2-f1 46.Kf4-e3 Kf1-e1 47.Sg6-h4 VAf5-h7 48.Sh4-f3+ Ke1-f1 49.Se4-g3+ Kf1-g2 50.Sg3-f5 Kg2-f1 51.Sf3-d2+ Kf1-e1 52.Sf5-d4 VAh7-d3 53.Sd2-e4 VAd3-b1 54.Se4-f2 VAb1-c2 55.Sf2-d3+ Ke1-d1 56.Sd4-c6 VAc2-b3 57.Sd3-b2+ Kd1-c2 58.Sb2-a4 Kc2-d1 59.Sc6-b4 VAb3-c4 60.Sa4-c3+ Kd1-c1 61.Ke3-d3 Kc1-b2 62.Sc3-b5 Kb2-b3 63.Sb4-c6 VAc4-d5 64.Sb5-d4+ Kb3-b2 65.Sd4-e6 VAd5-f3 66.Sc6-d4 Kb2-a3 67.Kd3-c4 Ka3-b2 68.Se6-f4 Kb2-c1 69.Kc4-c3 Kc1-d1 70.Sf4-g2 VAf3-g4 71.Kc3-d3 VAg4-d7 72.Sd4-e6 VAd7-e8 73.Se6-c5 VAe8-a4 74.Sc5-d7 Kd1-c1 75.Sg2-e3 Kc1-b2 76.Sd7-c5 VAa4-b5 77.Kd3-d2 VAb5-c4 78.Se3-d1+ Kb2-a3 79.Kd2-c3 Ka3-a2 80.Sd1-e3 Ka2-a3 81.Se3-c2+ Ka3-a2 82.Sc5-d3 VAc4-d5 83.Sc2-d4 VAd5-b7 84.Kc3-b4 VAb7-a6 85.Sd4-e6 VAa6-c4 86.Se6-c7 VAc4-b3 87.Sc7-b5 Ka2-b1 88.Kb4-c3 Kb1-a1 89.Kc3-d2 Ka1-a2 90.Kd2-c2 Ka2-a1 91.Sb5-c3 VAb3-c4 92.Sd3-c5 VAc4-d5 93.Sc5-b3# Dva jezdci proti vao vyhrávají z obecné pozice. Potřebují k tomu ale 90 tahů, zajímavé je, že téměř nezáleží na pozici vao. Two knights against vao is a general win, though it may take over 90 moves. It is interesting that there is almost no dependence on the position of the vao. |
K + Bishop + Knight - K + Lion | |
![]() | Kb1 La2 Sa1 - Ke5 Lion d5 1.Kb1-b2 Ke5-d4 2.Sa1-c2+ Kd4-e4 3.Kb2-c3 Ke4-e5 4.Kc3-d2 Ke5-d6 5.Kd2-e3 Kd6-e5 6.Sc2-d4 Ke5-d6 7.Ke3-e4 LId5-d7 8.Sd4-f3 Kd6-c6 9.Sf3-e5+ Kc6-d6 10.La2-g8 Kd6-e7 11.Se5-c4 LId7-g7 12.Ke4-e5 Ke7-d7 13.Lg8-e6+ Kd7-c6 14.Ke5-d4 LIg7-a1 15.Kd4-e4 Kc6-c5 16.Sc4-e3 Kc5-d6 17.Le6-b3 Kd6-c5 18.Se3-c2 Kc5-d6 19.Sc2:a1 Kd6-c5 20.Lb3-d5 Kc5-d6 21.Sa1-b3 Kd6-c7 22.Ke4-e5 Kc7-d7 23.Sb3-c5+ Kd7-c7 24.Ke5-e6 Kc7-b6 25.Sc5-d3 Kb6-b5 26.Ld5-b3 Kb5-a5 27.Ke6-d7 Ka5-b6 28.Lb3-a4 Kb6-a5 29.La4-c6 Ka5-b6 30.Kd7-d6 Kb6-a5 31.Kd6-c5 Ka5-a6 32.Sd3-e5 Ka6-a7 33.Kc5-d6 Ka7-b6 34.Se5-c4+ Kb6-a7 35.Kd6-c7 Ka7-a6 36.Lc6-d7 Ka6-a7 37.Ld7-c8 Ka7-a8 38.Sc4-d6 Ka8-a7 39.Sd6-b5+ Ka7-a8 40.Lc8-b7# Střelec s jezdcem proti lionovi vyhrávají z obecné pozice. Bishop and knight against lion is a general win. |
K + Bishop + Knight - K + Leo | |
![]() | Kc5 Lb1 Sa2 - Kb7 Leo e6 1.Sa2-c3 LEe6-h6 2.Kc5-d6 Kb7-b6 3.Lb1-f5 LEh6-f8 4.Lf5-d7 LEf8-d8+ 5.Ld7-e8 Kb6-b7 6.Sc3-a4 LEd8-c8 7.Sa4-b2 LEc8-a8 8.Sb2-c4 LEa8-a1 9.Le8-c6+ Kb7-a6 10.Sc4-b2 LEa1-c1 11.Lc6-d7 Ka6-b7 12.Sb2-a4 Kb7-a6 13.Kd6-c6 Ka6-a5 14.Kc6-c5 Ka5-a6 15.Ld7-g4 Ka6-b7 16.Kc5-d6 Kb7-a6 17.Kd6-c6 Ka6-a5 18.Sa4-b2 LEc1-c2 19.Kc6-c5 Ka5-a6 20.Lg4-f3 LEc2-c3 21.Sb2-d1 LEc3-c1 22.Sd1-e3 Ka6-a5 23.Lf3-e2 LEc1-c3 24.Se3-f5 Ka5-a4 25.Le2-d1+ Ka4-a3 26.Sf5-e3 Ka3-b2 27.Kc5-b4 LEc3-d4 28.Ld1-b3 LEd4-d3 29.Lb3-a4 LEd3-b1+ 30.Kb4-c4 LEb1-e4 31.Se3-d1+ Kb2-a3 32.La4-e8 LEe4-f5 33.Kc4-c3 LEf5-h3 34.Sd1-b2 Ka3-a2 35.Sb2-c4 Ka2-b1 36.Sc4-d2+ Kb1-c1 37.Le8-a4 LEh3-g3 38.Sd2-e4 LEg3-e3 39.Se4-g5 Kc1-b1 40.La4-c2+ Kb1-a2 41.Sg5-f3 LEe3-c5 42.Lc2-b3+ Ka2-b1 43.Sf3-d4 LEc5-a3+ 44.Lb3-c2+ Kb1-a2 45.Lc2-g6 LEa3-c5 46.Sd4-b5 LEc5-e7 47.Kc3-c2 Ka2-a1 48.Kc2-b3 LEe7-b7+ 49.Kb3-a3 LEb7-c8 50.Sb5-d4 LEc8-h3 51.Lg6-h7 LEh3-g3 52.Lh7-f5 LEg3-f3 53.Lf5-e6 Ka1-b1 54.Sd4:f3 Kb1-c2 55.Le6-c4 Kc2-c3 56.Lc4-b5 Kc3-c2 57.Ka3-b4 Kc2-b1 58.Kb4-c3 Kb1-a2 59.Lb5-d3 Ka2-a1 60.Sf3-d4 Ka1-a2 61.Sd4-b3 Ka2-a3 62.Ld3-b1 Ka3-a4 63.Sb3-d4 Ka4-a5 64.Kc3-c4 Ka5-b6 65.Sd4-b5 Kb6-b7 66.Lb1-f5 Kb7-c6 67.Lf5-e6 Kc6-b6 68.Le6-d7 Kb6-a5 69.Sb5-c7 Ka5-b6 70.Sc7-d5+ Kb6-a5 71.Kc4-b3 Ka5-a6 72.Kb3-a4 Ka6-b7 73.Ka4-b5 Kb7-a7 74.Ld7-c8 Ka7-b8 75.Lc8-a6 Kb8-a7 76.Sd5-e7 Ka7-b8 77.Kb5-b6 Kb8-a8 78.La6-b7+ Ka8-b8 79.Se7-c6# Koncovka střelec + jezdec proti leo je obecně remízová. Naprosto unikátní je pozice s bílým králem na c5, kterou lze vyhrát. The ending of bishop and knight against leo is generally drawn. Quite unique is the position with the White king on c5, where it is possible to win. |
K + Bishop + Knight - K + Leo | |
![]() | Ke8 Lb1 Sa2 - Kb8 Leo e6 1.Ke8-d7 LEe6-g8 2.Kd7-c6 Kb8-c8 3.Lb1-g6 Kc8-d8 4.Kc6-d6 Kd8-c8 5.Lg6-e4 Kc8-d8 6.Le4-c6 LEg8-g6 7.Lc6-d7 LEg6-d3 8.Ld7-b5 LEd3-g6 9.Sa2-c3 Kd8-c8 10.Lb5-d3 LEg6-g8 11.Ld3-a6+ Kc8-d8 12.La6-b5 Kd8-c8 13.Lb5-c6 LEg8-g5 14.Lc6-f3 Kc8-d8 15.Sc3-d5 LEg5-d2+ 16.Sd5-f4 Kd8-e8 17.Lf3-h5+ Ke8-d8 18.Sf4-e6+ Kd8-c8 19.Lh5-f3 LEd2-c1 20.Lf3-e4 LEc1-e3 21.Se6-g5 Kc8-d8 22.Le4-c6 Kd8-c8 23.Sg5-f7 Kc8-b8 24.Lc6-f3 Kb8-a7 25.Kd6-c6 Ka7-a6 26.Sf7-d6 LEe3-a7 27.Lf3-g4 Ka6-a5 28.Kc6-c5 Ka5-a4 29.Lg4-d1+ Ka4-a5 30.Sd6-b7+ Ka5-a6 31.Ld1-f3 LEa7-a8 32.Sb7-d8 Ka6-a7 33.Kc5-d6 Ka7-b8 34.Sd8-f7 LEa8-a1 35.Kd6-c6 Kb8-a7 36.Lf3-e2 LEa1-g7 37.Le2-d3 LEg7-f6 38.Kc6-c7 LEf6-f4 39.Ld3-e2 Ka7-a8 40.Kc7-b6 Ka8-b8 41.Le2-g4 LEf4-f6 42.Sf7-e5 LEf6-h6 43.Lg4-f5 LEh6-f6 44.Se5-d7+ Kb8-c8 45.Sd7:f6+ Kc8-d8 46.Kb6-c5 Kd8-e7 47.Sf6-h7 Ke7-f7 48.Kc5-d6 Kf7-g8 49.Kd6-e7 Kg8-h8 50.Ke7-f6 Kh8-g8 51.Lf5-g6 Kg8-h8 52.Sh7-g5 Kh8-g8 53.Sg5-f7 Kg8-f8 54.Lg6-h7 Kf8-e8 55.Sf7-e5 Ke8-d8 56.Kf6-e6 Kd8-c7 57.Se5-d7 Kc7-b7 58.Lh7-d3 Kb7-c6 59.Ld3-c4 Kc6-c7 60.Lc4-b5 Kc7-d8 61.Sd7-c5 Kd8-c7 62.Sc5-a4 Kc7-d8 63.Ke6-d6 Kd8-c8 64.Lb5-c6 Kc8-b8 65.Sa4-b6 Kb8-a7 66.Kd6-c7 Ka7-a6 67.Sb6-c4 Ka6-a7 68.Lc6-b5 Ka7-a8 69.Sc4-b6+ Ka8-a7 70.Sb6-c8+ Ka7-a8 71.Lb5-c6# Kb6 Lb1 Sa2 - Kb8 Leo e6 1.Lb1-f5 LEe6-f7 2.Lf5-g4 Kb8-a8 3.Sa2-b4 LEf7-f6 4.Sb4-d3 Ka8-b8 5.Sd3-e5 LEf6-h6 6.Lg4-f5 LEh6-f6 7.Se5-d7+ Kb8-c8 8.Sd7:f6+ Kc8-d8 9.Kb6-c5 Kd8-e7 10.Sf6-h7 Ke7-f7 11.Kc5-d6 Kf7-g8 12.Kd6-e7 Kg8-h8 13.Ke7-f6 Kh8-g8 14.Lf5-g6 Kg8-h8 15.Sh7-g5 Kh8-g8 16.Sg5-f7 Kg8-f8 17.Lg6-h7 Kf8-e8 18.Sf7-e5 Ke8-d8 19.Kf6-e6 Kd8-c7 20.Se5-d7 Kc7-b7 21.Lh7-d3 Kb7-c6 22.Ld3-c4 Kc6-c7 23.Lc4-b5 Kc7-d8 24.Sd7-c5 Kd8-c7 25.Sc5-a4 Kc7-d8 26.Ke6-d6 Kd8-c8 27.Lb5-c6 Kc8-b8 28.Sa4-b6 Kb8-a7 29.Kd6-c7 Ka7-a6 30.Sb6-c4 Ka6-a7 31.Lc6-b5 Ka7-a8 32.Sc4-b6+ Ka8-a7 33.Sb6-c8+ Ka7-a8 34.Lb5-c6# Pokud je černý král již na okraji šachovnice a bílý král není daleko, lze ji někdy vyhrát, jak ukazují matové postupy. Obecně je to ale remis. As long as the Black king is already on the edge of the board and the White king is not far away, it is sometimes possible to win, as the mating lines show. However, in general this is a draw. |
K + Bishop + Knight - K + Pao | |
![]() | Koncovka střelec + jezdec proti pao je nejzajímavější z této série a nelze ji obecně označit za jako vyhranou ani jako remízovou. Záleží hodně na pozici. Na šachovnicích větších rozměrů by zřejmě byla již remízová, ale zde je počet vyhratelných případů tak velký, že ji jednoznačně za remízovou označit nelze. V pozici na tomto diagramu však černý udrží remízu ať je bílý král kdekoliv. The ending of bishop and knight against pao is the most interesting in this series, and it cannot be classified as either a general win or a general draw. It depends very much on the position. On boards of larger dimension it would obviously become drawn, but here the number of winning positions is so large that it cannot be unequivocally be given as drawn. In the position in this diagram, however, Black can hold the draw wherever the White king may be. |
K + Bishop + Knight - K + Pao | |
![]() | Kf5 Lc4 Se3 - Kb7 Pao d6 1.Kf5-e4 Kb7-c6 2.Ke4-d4 PAd6-d8 3.Se3-f5 Kc6-d7+ 4.Kd4-c5 PAd8-f8 5.Lc4-g8 PAf8-d8 6.Kc5-c4 Kd7-c6 7.Kc4-d4 Kc6-d7+ 8.Kd4-e5 PAd8-b8 9.Sf5-g7 Kd7-c6 10.Lg8-d5+ Kc6-d7 11.Ld5-f3 PAb8-h8 12.Lf3-h5 Kd7-e7 13.Sg7-e8 Ke7-d7 14.Se8-f6+ Kd7-e7 15.Lh5-g6 PAh8-f8 16.Lg6-e8 PAf8-h8 17.Le8-b5 Ke7-f7 18.Sf6-e4 Kf7-e7 19.Se4-d6 PAh8-b8 20.Sd6-f5+ Ke7-f7 21.Lb5-c4+ Kf7-g6 22.Sf5-d6 Kg6-g5 23.Sd6-f7+ Kg5-g6 24.Ke5-e6 PAb8-f8 25.Lc4-d3+ Kg6-h5 26.Ke6-e5 PAf8-b8 27.Ke5-f5 Kh5-h4 28.Ld3-e2 Kh4-g3 29.Kf5-e4 Kg3-f2 30.Ke4-d3 PAb8-c8 31.Sf7-g5 PAc8-c7 32.Sg5-e4+ Kf2-e1 33.Se4-f6 Ke1-f2 34.Kd3-d2 PAc7-c8 35.Sf6-e4+ Kf2-g2 36.Le2-h5 Kg2-h3 37.Kd2-e3 PAc8-a8 38.Ke3-f4 Kh3-g2 39.Se4-c3 PAa8-a3 40.Sc3-d1 Kg2-f1 41.Kf4-f3 Kf1-e1 42.Kf3-e3 Ke1-f1 43.Lh5-e2+ Kf1-g2 44.Ke3-f4 PAa3-a4 45.Le2-f3+ Kg2-f1 46.Kf4-e3 PAa4-a7 47.Sd1-b2 PAa7-h7 48.Lf3-e4 PAh7-h3 49.Sb2-d1 PAh3-h8 50.Sd1-f2 PAh8-e8+ 51.Le4-d5 PAe8-h8 52.Sf2-h3 Kf1-e1 53.Ld5-b3 Ke1-f1 54.Sh3-f4 PAh8-e8 55.Lb3-d5 Kf1-e1 56.Ld5-f3 Ke1-f1 57.Sf4-g2 Kf1-g1 58.Lf3-d5 Kg1-f1 59.Ke3-f3 Kf1-g1 60.Kf3-g3 PAe8-e3 61.Ld5-c4 PAe3-c3 62.Sg2-f4 PAc3-a3 63.Sf4-e6 PAa3-a4 64.Se6-c5 PAa4-a5 65.Sc5-b3 PAa5-a3+ 66.Sb3-d4 PAa3-c3 67.Sd4-c2 PAc3-b3 68.Lc4:b3 Kg1-f1 69.Lb3-c4+ Kf1-g1 70.Sc2-d4 Kg1-h1 71.Kg3-f2 Kh1-h2 72.Lc4-f1 Kh2-h1 73.Lf1-g2+ Kh1-h2 74.Sd4-f3# Zde je převážná většina pozic vyhratelná. Přesto černý udrží remízu při pozicích jeho krále na polích označených "=". Here, the great majority of positions are winning, but the Black king can hold the draw if he is on one of the squares marked "=". |
K + Bishop + Knight - K + Pao | |
![]() | Kf3 La1 Sh1 - Ka8 Pao b8 1.Kf3-e4 Ka8-b7 2.Ke4-d5 PAb8-d8 3.La1-e5 Kb7-b6 4.Sh1-g3 PAd8-a8 5.Sg3-e2 PAa8-a5 6.Kd5-c4 Kb6-c6 7.Se2-d4+ Kc6-d7 8.Sd4-b3 Kd7-e6 9.Kc4-d4 PAa5-a8 10.Le5-b8 Ke6-f5 11.Kd4-d5 PAa8-a4 12.Sb3-d4+ Kf5-g4 13.Sd4-c2 Kg4-f3 14.Kd5-d4 PAa4-a6 15.Lb8-d6 PAa6-a8 16.Ld6-f8 Kf3-f4 17.Lf8-h6+ Kf4-f5 18.Kd4-d5 Kf5-f6 19.Lh6-f8 PAa8-b8 20.Sc2-e3 PAb8-e8 21.Lf8-d6 Kf6-g5 22.Ld6-c7 PAe8-e7 23.Lc7-d8 Kg5-f4 24.Se3-g2+ Kf4-g3 25.Sg2-e1 PAe7-e8 26.Se1-d3 Kg3-f3 27.Sd3-e5+ Kf3-f2 28.Ld8-g5 Kf2-e2 29.Lg5-h6 Ke2-f2 30.Se5-c6 PAe8-e1 31.Sc6-d4 PAe1-d1+ 32.Kd5-e4 PAd1-e1 33.Lh6-f8 PAe1-h1 34.Lf8-d6 PAh1-a1 35.Ld6-e7 PAa1-a4+ 36.Sd4-f5 Kf2-e2 37.Le7-g5 PAa4-b4 38.Lg5-e3 PAb4-a4 39.Sf5-g3+ Ke2-e1 40.Le3-b6 PAa4-a3 41.Lb6-c5 PAa3-a8 42.Ke4-d3 PAa8-d8 43.Kd3-e3 Ke1-d1 44.Lc5-b4 Kd1-c2 45.Ke3-d4 Kc2-b3 46.Kd4-c5 PAd8-e8 47.Sg3-f5 PAe8-g8 48.Sf5-d4+ Kb3-a4 49.Sd4-f3 Ka4-b3 50.Kc5-b5 PAg8-h8 51.Sf3-d4+ Kb3-b2 52.Lb4-a5 PAh8-h1 53.Kb5-c4 PAh1-c1 54.La5-b4 PAc1-h1 55.Sd4-f3 PAh1-h3 56.Sf3-e5 Kb2-c2 57.Se5-d3 PAh3-h4 58.Sd3-e1+ Kc2-c1 59.Kc4-c3 PAh4-h3 60.Se1-g2 Kc1-d1 61.Lb4-d6 Kd1-e2 62.Sg2-f4+ Ke2-f3+ 63.Sf4:h3 Kf3-e4 64.Kc3-c4 Ke4-f3 65.Sh3-g5+ Kf3-e3 66.Ld6-g3 Ke3-d2 67.Kc4-d4 Kd2-e2 68.Kd4-e4 Ke2-f1 69.Ke4-f3 Kf1-g1 70.Sg5-h3+ Kg1-f1 71.Sh3-f2 Kf1-g1 72.Lg3-f4 Kg1-f1 73.Lf4-h2 Kf1-e1 74.Sf2-e4 Ke1-d1 75.Kf3-e3 Kd1-c2 76.Se4-d2 Kc2-b2 77.Lh2-d6 Kb2-c3 78.Ld6-e7 Kc3-c2 79.Le7-b4 Kc2-d1 80.Sd2-e4 Kd1-c2 81.Se4-c5 Kc2-d1 82.Ke3-d3 Kd1-c1 83.Sc5-a4 Kc1-d1 84.Sa4-b2+ Kd1-c1 85.Kd3-c3 Kc1-b1 86.Sb2-d3 Kb1-a2 87.Kc3-c2 Ka2-a1 88.Lb4-c5 Ka1-a2 89.Sd3-c1+ Ka2-a1 90.Lc5-d4# Také zde bílý v převážné většině pozic vyhraje, i když na to potřebuje až 90 tahů. Při pozicích bílého jezdce na polích označených "=" však nestačí ani to, že je černý král v rohu šachovnice - černý udrží remízu. Here also the great majority of positions are winning, even though it may take up to 90 moves. However, if the White knight is on one of the squares marked "=", it is not even sufficient that the Black king is in a corner of the board - Black can hold the draw. |
K + Bishop + Knight - K + Pao | |
![]() | Kf2 La2 Sb1 - Ka8 Pao a7 1.Kf2-e3 Ka8-b7 2.Ke3-d4 Kb7-c6 3.Sb1-c3 PAa7-a5 4.Sc3-e4 Kc6-d7 5.Kd4-e5 Kd7-c6 6.La2-b3 Kc6-b5+ 7.Ke5-d4 PAa5-a3 8.Lb3-c4+ Kb5-c6 9.Lc4-d5+ Kc6-c7 10.Ld5-a8 Kc7-d7 11.Kd4-e5 Kd7-c7 12.Ke5-d5 Kc7-d7 13.Se4-f6+ Kd7-e7 14.Kd5-e5 Ke7-f7 15.La8-d5+ Kf7-g6 16.Sf6-e4 PAa3-e3+ 17.Se4-d6 Kg6-g5 18.Sd6-f7+ Kg5-g4 19.Ke5-e4 PAe3-h3 20.Ld5-e6+ Kg4-g3 21.Sf7-e5 PAh3-h1 22.Le6-b3 Kg3-h4 23.Se5-f7 Kh4-h5 24.Ke4-f5 Kh5-h4 25.Sf7-d6 Kh4-g3 26.Lb3-d1 Kg3-f2 27.Kf5-e4 PAh1-g1 28.Ke4-d3 PAg1-g7 29.Ld1-h5 PAg7-e7 30.Kd3-d4 PAe7-e1 31.Sd6-e4+ Kf2-g2 32.Kd4-c3 Kg2-h3 33.Kc3-d2 PAe1-a1 34.Kd2-e3 PAa1-a8 35.Ke3-f4 Kh3-g2 36.Se4-c3 PAa8-a3 37.Sc3-d1 Kg2-f1 38.Kf4-f3 Kf1-e1 39.Kf3-e3 Ke1-f1 40.Lh5-e2+ Kf1-g2 41.Ke3-f4 PAa3-a4 42.Le2-f3+ Kg2-f1 43.Kf4-e3 PAa4-a7 44.Sd1-b2 PAa7-h7 45.Lf3-e4 PAh7-h3 46.Sb2-d1 PAh3-h8 47.Sd1-f2 PAh8-e8+ 48.Le4-d5 PAe8-h8 49.Sf2-h3 Kf1-e1 50.Ld5-b3 Ke1-f1 51.Sh3-f4 PAh8-e8 52.Lb3-d5 Kf1-e1 53.Ld5-f3 Ke1-f1 54.Sf4-g2 Kf1-g1 55.Lf3-d5 Kg1-f1 56.Ke3-f3 Kf1-g1 57.Kf3-g3 PAe8-e3 58.Ld5-c4 PAe3-c3 59.Sg2-f4 PAc3-a3 60.Sf4-e6 PAa3-a4 61.Se6-c5 PAa4-a5 62.Sc5-b3 PAa5-a3+ 63.Sb3-d4 PAa3-c3 64.Sd4-c2 PAc3-b3 65.Lc4:b3 Kg1-f1 66.Lb3-c4+ Kf1-g1 67.Sc2-d4 Kg1-h1 68.Kg3-f2 Kh1-h2 69.Lc4-f1 Kh2-h1 70.Lf1-g2+ Kh1-h2 71.Sd4-f3# Tuto koncovku by bylo podle předchozích kritérií možné označit za remízovou. Když je bílý král příliš daleko od svého černého jmenovce, nevyhraje. Celkový počet vyhrávajících případů je však asi větší než těch remízových, takže si takto jednoznačně tuto koncovku označit netroufám. According to the criteria used hitherto, this ending could be classified as drawn. When the White king is too far from his Black adversary, there is no win. However, the total number of winning positions is perhaps greater than that of drawing positions, and I hesitate to classify it so. |
K + Bishop + Knight - K + Pao | |
![]() | Opět zajímavý případ, kdy většina pozic je pro silnější stranu vyhraná, ale černý udrží remízu, pokud je jeho pao v zóně na 8. řadě! Another interesting case, where the majority of cases are winning for the stronger side but Black can hold the draw if his pao is in a certain zone on the eighth rank! |
K + Bishop + Knight - K + Vao | |
![]() | Ka2 Lb1 Sa1 - Ke5 Vao e6 1.Ka2-b3 Ke5-d4 2.Sa1-c2+ Kd4-e4 3.Sc2-e1+ Ke4-d4 4.Se1-f3+ Kd4-d5+ 5.Kb3-c3 VAe6-f7 6.Kc3-d2 Kd5-e6 7.Kd2-e3 Ke6-d5 8.Lb1-g6 VAf7-e6 9.Lg6-f7 Kd5-d6 10.Sf3-g5 VAe6-c8 11.Ke3-d4 VAc8-b7 12.Sg5-e4+ Kd6-e7 13.Lf7-c4 VAb7-a8 14.Kd4-e5 Ke7-d7 15.Lc4-b5+ Kd7-e7 16.Se4-f6 Ke7-f7 17.Lb5-c6 VAa8-b7 18.Lc6:b7 Kf7-g6 19.Lb7-e4+ Kg6-g7 20.Sf6-e8+ Kg7-f7 21.Se8-d6+ Kf7-g7 22.Ke5-e6 Kg7-g8 23.Ke6-e7 Kg8-g7 24.Sd6-f7 Kg7-g8 25.Ke7-f6 Kg8-f8 26.Le4-h7 Kf8-e8 27.Sf7-e5 Ke8-d8 28.Kf6-e6 Kd8-c7 29.Se5-d7 Kc7-b7 30.Lh7-d3 Kb7-c6 31.Ld3-c4 Kc6-c7 32.Lc4-b5 Kc7-d8 33.Sd7-c5 Kd8-c7 34.Sc5-a4 Kc7-d8 35.Ke6-d6 Kd8-c8 36.Lb5-c6 Kc8-b8 37.Sa4-b6 Kb8-a7 38.Kd6-c7 Ka7-a6 39.Sb6-c4 Ka6-a7 40.Lc6-b5 Ka7-a8 41.Sc4-b6+ Ka8-a7 42.Sb6-c8+ Ka7-a8 43.Lb5-c6# Střelec a jezdec vyhrává proti vao v obecné pozici. Bishop and knight against vao win in general. |
K + 2 Bishops - K + Lion | |
![]() | Ka2 La1 Lb1 - Kd5 Lion d6 1.Ka2-b3 LId6-d2 2.La1-g7 LId2-d7 3.Kb3-c3 Kd5-e6 4.Kc3-d4 Ke6-d6+ 5.Kd4-e4 Kd6-c5 6.Lg7-f8+ Kc5-c6 7.Ke4-e5 LId7-a4 8.Lb1-g6 LIa4-d7 9.Lg6-e4+ Kc6-c7 10.Ke5-e6 LId7-a7 11.Lf8-c5 LIa7-h7 12.Lc5-d6+ Kc7-b6 13.Le4:h7 Kb6-a6 14.Lh7-d3+ Ka6-a5 15.Ke6-d7 Ka5-a4 16.Ld3-c4 Ka4-a5 17.Kd7-c6 Ka5-a4 18.Ld6-e7 Ka4-a5 19.Lc4-b3 Ka5-a6 20.Le7-b4 Ka6-a7 21.Kc6-c7 Ka7-a8 22.Lb4-a5 Ka8-a7 23.La5-b6+ Ka7-a8 24.Lb3-d5# Dva různopolní střelci vyhrávají proti lionovi v obecné pozici. Two bishops on squares of different colours win against a lion from a general position. |
K + 2 Bishops - K + Leo | |
![]() | Dva střelci proti leo nevyhrávají. Bílý král může být kdekoliv. Two bishops do not win against a leo. The White king can be anywhere. |
K + 2 Bishops - K + Leo | |
![]() | Zde je názorně vidět, že černý král musí být už na okraji šachovnice, aby bylo možno v některých pozicích vynutit mat. Here it is graphically shown how the Black king must already be on the edge of the board for mate to be forced. |
K + 2 Bishops - K + Leo | |
![]() | Kf3 La1 Lb1 - Ka8 Leo b8 1.Lb1-e4+ Ka8-a7 2.La1-d4+ Ka7-a6 3.Le4-c6 LEb8-c7 4.Kf3-e4 Ka6-a5 5.Ld4-e5 LEc7-h7 6.Le5-c3+ Ka5-b6 7.Ke4-d5 LEh7-c2 8.Lc3-f6 Kb6-c7 9.Lf6-g5 LEc2-g6 10.Kd5-c5 LEg6-e6 11.Lg5-h4 LEe6-g6 12.Lh4-g3+ Kc7-d8 13.Lc6-e4 LEg6-g4 14.Kc5-d6 Kd8-e8 15.Le4-g6+ Ke8-f8 16.Lg3-e5 LEg4-e2 17.Le5-d4 LEe2-d2+ 18.Kd6-e6 LEd2-h6+ 19.Lg6-h5 LEh6-h7 20.Ke6-f6 LEh7-f7 21.Ld4-b6 Kf8-e8 22.Kf6-e6 Ke8-f8 23.Lh5:f7 Kf8-g7 24.Lb6-c5 Kg7-h8 25.Lc5-f8 Kh8-h7 26.Ke6-e7 Kh7-h8 27.Lf7-e6 Kh8-h7 28.Ke7-f7 Kh7-h8 29.Lf8-g7+ Kh8-h7 30.Le6-f5# Pokud je černý král v rohu šachovnice, lze jej někdy zmatit, pokud bílý král není příliš daleko. Obecně je ale koncovka remízová. If the Black king is already in the corner, it is sometimes possible to force mate, provided that the White king is not too far away. In general, however, the ending is drawn. |
K + 2 Bishops - K + Pao | |
![]() | Ka1 Lb1 Lc1 - Ke5 Pao c6 1.Lb1-h7 Ke5-d4 2.Lh7-g8 Kd4-e5 3.Lc1-b2+ Ke5-e4 4.Lb2-g7 Ke4-f5 5.Ka1-b2 Kf5-g6 6.Lg7-f8 Kg6-f5 7.Kb2-c3 Kf5-e4 8.Lf8-d6 PAc6-c8 9.Kc3-c4 PAc8-d8 10.Lg8-h7+ Ke4-f3 11.Lh7-c2 Kf3-e3 12.Ld6-e7 PAd8-h8 13.Le7-g5+ Ke3-f3 14.Kc4-d5 Kf3-g4 15.Lg5-h6 PAh8-e8 16.Lc2-g6 PAe8-h8 17.Kd5-e4 Kg4-g3 18.Lh6-d2 PAh8-h4 19.Lg6-h5 Kg3-f2 20.Ke4-f4 PAh4-h1 21.Ld2-e3+ Kf2-e1 22.Kf4-g3 PAh1-f1 23.Lh5-f3 PAf1-f2 24.Le3-b6 Ke1-d2 25.Kg3:f2 Kd2-d3 26.Lf3-c6 Kd3-c4 27.Kf2-e3 Kc4-c3 28.Lc6-b5 Kc3-b4 29.Lb5-d3 Kb4-c3 30.Lb6-a5+ Kc3-b2 31.Ke3-d2 Kb2-b3 32.La5-c3 Kb3-a4 33.Kd2-c2 Ka4-a3 34.Ld3-b5 Ka3-a2 35.Lc3-d4 Ka2-a3 36.Ld4-c5+ Ka3-a2 37.Lb5-c4+ Ka2-a1 38.Lc5-d4# Dva různopolní střelci vyhrávají proti pao v obecné pozici (případná pozice pao na tomto diagramu na první řadě s vazbou střelců nenarušuje obecnost) Two bishops on squares of different colours win against a pao from a general position (the case in the diagram where the pao is pinning the bishops on the first rank does not invalidate the general result). |
K + 2 Bishops - K + Vao | |
![]() | Ka2 La1 Lb1 - Kd5 Vao d6 1.Ka2-b3 VAd6-e7 2.Kb3-c2 Kd5-e4 3.Kc2-d2+ Ke4-d5 4.Kd2-e3 Kd5-c6 5.Ke3-e4 Kc6-d6 6.La1-g7 Kd6-c5 7.Lg7-f8 Kc5-d6 8.Lb1-a2 Kd6-d7 9.Ke4-d5 Kd7-e8 10.Lf8-g7 Ke8-d7 11.La2-b3 Kd7-c7 12.Lg7-e5+ Kc7-b6 13.Kd5-d6 Kb6-b5 14.Kd6:e7 Kb5-c5 15.Ke7-d7 Kc5-b4 16.Lb3-e6 Kb4-c5 17.Le5-b2 Kc5-b6 18.Lb2-a3 Kb6-b5 19.Kd7-c7 Kb5-a4 20.La3-d6 Ka4-b5 21.Le6-b3 Kb5-a6 22.Lb3-a4 Ka6-a5 23.La4-d7 Ka5-a6 24.Ld6-b4 Ka6-a7 25.Ld7-c8 Ka7-a8 26.Lc8-b7+ Ka8-a7 27.Lb4-c5# Dva různopolní střelci vyhrávají proti vao v obecné pozici. Two bishops on squares of different colours win against a vao from a general position. |
Leo | Pao | Vao | Lion | Grasshopper | |
K + Rook | = | = | + | + | + |
K + Queen | + | + | + | + | + |
K + Queen - K + Lion | |
![]() | Ka1 Db1 - Ke5 Lion e6 1.Ka1-b2 Ke5-f4 2.Kb2-c3 Kf4-e5 3.Db1-b5+ Ke5-e4 4.Kc3-c4 Ke4-e3 5.Db5-b6+ Ke3-f4 6.Db6:e6 Kf4-g5 7.De6-e5+ Kg5-h6 8.Kc4-d5 Kh6-h7 9.Kd5-e6 Kh7-g8 10.De5-g5+ Kg8-h7 11.Ke6-f7 Kh7-h8 12.Dg5-h6# |
K + Queen - K + Leo | |
![]() | Ka1 Db1 - Ke5 Leo e6 1.Ka1-b2 LEe6-f6+ 2.Kb2-c2 Ke5-d4 3.Db1-b6+ Kd4-e5 4.Kc2-d3 Ke5-f5 5.Db6-a5+ Kf5-e6 6.Kd3-d4 LEf6-g7 7.Da5-d5+ Ke6-f6+ 8.Kd4-e4 LEg7-h8 9.Dd5-d6+ Kf6-f7 10.Ke4-e5 LEh8-f8 11.Dd6-e6+ Kf7-g7 12.De6-f6+ Kg7-h7 13.Df6:f8 Kh7-g6 14.Df8-g8+ Kg6-h5 15.Ke5-f5 Kh5-h6 16.Dg8-h8# |
K + Rook - K + Lion | |
![]() | Ka1 Tb1 - Kd5 Lion e6 1.Ka1-b2 Kd5-d4 2.Tb1-d1+ Kd4-e5 3.Kb2-c3 Ke5-e4 4.Td1-b1 Ke4-d5 5.Kc3-d3 Kd5-e5 6.Tb1-b5+ Ke5-f6 7.Kd3-d4 LIe6-g6 8.Tb5-e5 LIg6-d6 9.Kd4-e4 LId6-h6 10.Ke4-d5 Kf6-g6 11.Te5-e8 Kg6-f5 12.Te8-f8+ Kf5-g6 13.Kd5-e5 Kg6-h5 14.Ke5-f6 LIh6-h3 15.Kf6-f5 Kh5-h4 16.Tf8-g8 Kh4-h5 17.Tg8-g5+ Kh5-h6 18.Kf5-g4 LIh3-h8 19.Tg5-g8 LIh8-h5 20.Tg8-f8 Kh6-g6 21.Tf8-f4 LIh5-f7 22.Tf4-f5 Kg6-g7 23.Kg4-g5 LIf7-h7 24.Tf5-f6 LIh7-f7 25.Tf6-g6+ Kg7-f8 26.Kg5-f6 Kf8-e8 27.Kf6-e6 LIf7-d5 28.Tg6-g5 Ke8-d8 29.Tg5:d5+ Kd8-c7 30.Td5-c5+ Kc7-b8 31.Ke6-d7 Kb8-b7 32.Tc5-b5+ Kb7-a6 33.Kd7-c6 Ka6-a7 34.Tb5-a5+ Ka7-b8 35.Ta5-a6 Kb8-c8 36.Ta6-a8# Věž proti lionovi vyhrává z obecné pozice. Rook against lion is a general win. |
K + Rook - K + Leo | |
![]() | Ka1 Tb1 - Ka4 Leo e6 1.Tb1-b6 LEe6-f7 2.Ka1-b2 LEf7-e8 3.Tb6-b7 LEe8-f8 4.Kb2-c3 LEf8-f1 5.Tb7-b4+ Ka4-a5 6.Kc3-c4 LEf1-f2 7.Tb4-b5+ Ka5-a6 8.Kc4-c5 LEf2-f3 9.Tb5-b6+ Ka6-a7 10.Kc5-c6 LEf3-e4 11.Kc6-c7 LEe4-h7 12.Tb6-h6 LEh7-g8 13.Th6-h5 LEg8-a8 14.Th5-h4 Ka7-a6 15.Kc7-c6 Ka6-a7 16.Th4-h8 LEa8-b8 17.Kc6-c7 LEb8-b7 18.Th8-b8 LEb7-d5 19.Tb8-b5 LEd5-a8 20.Tb5-b7+ Ka7-a6 21.Kc7-b8 LEa8-a7 22.Tb7:a7+ Ka6-b5 23.Ta7-c7 Kb5-b6 24.Tc7-c2 Kb6-b5 25.Kb8-a7 Kb5-b4 26.Ka7-b6 Kb4-b3 27.Tc2-c6 Kb3-a4 28.Kb6-c5 Ka4-b3 29.Kc5-b5 Kb3-a2 30.Kb5-a4 Ka2-b2 31.Ka4-b4 Kb2-a1 32.Tc6-c2 Ka1-b1 33.Kb4-b3 Kb1-a1 34.Tc2-c1# Koncovka věže proti leo je v obecné pozici remízová. Někdy je ale možné využít nevýhodné pozice soupeřova krále k matu. The endgame of rook against leo is in general drawn, but it is sometimes possible to exploit the unfavourable position of the enemy king. |
K + Rook - K + Leo | |
![]() | Kd3 Tb1 - Kh8 Leo g8 1.Tb1-b7 LEg8-a2 2.Kd3-e4 Kh8-g8 3.Ke4-d5 Kg8-f8 4.Kd5-e6 LEa2-c4 5.Tb7-e7 LEc4-d4 6.Te7-f7+ Kf8-g8 7.Ke6-f6 LEd4-c3 8.Kf6-g6 LEc3-g3 9.Tf7-f1 LEg3-h4 10.Tf1-e1 LEh4-h8 11.Te1-e2 Kg8-f8 12.Kg6-f6 LEh8-h7 13.Te2-e7 LEh7-h8 14.Te7-h7 Kf8-g8 15.Kf6-g6 LEh8-e5 16.Th7-e7 LEe5-h8 17.Te7-g7+ Kg8-f8 18.Kg6-h7 LEh8-g8 19.Tg7:g8+ Kf8-e7 20.Tg8-g6 Ke7-f7 21.Tg6-b6 Kf7-e7 22.Kh7-g8 Ke7-d7 23.Kg8-f7 Kd7-c7 24.Tb6-f6 Kc7-b8 25.Kf7-e8 Kb8-c7 26.Tf6-g6 Kc7-b8 27.Ke8-d7 Kb8-b7 28.Tg6-h6 Kb7-a8 29.Th6-b6 Ka8-a7 30.Kd7-c7 Ka7-a8 31.Tb6-a6# Věž také vyhraje proti leo, pokud je už černý král v rohu šachovnice, jak ukazuje tento diagram. Pokud je však bílý král příliš vzdálen, je koncovka remízová, krále se nepodaří do rohu zatlačit. Rook also wins against leo if the enemy king is already in the corner of the board, as this diagram shows. However, if the White king is too far away, the king cannot be kept in the corner, and the ending is drawn. |
K + Rook - K + Pao | |
![]() | Ka1 Tb1 - Ka8 Pao e6 1.Tb1-b6 PAe6-e7 2.Ka1-b2 Ka8-a7 3.Tb6-b4 PAe7-b7+ 4.Kb2-c3 Ka7-b8 5.Tb4-c4 Kb8-a7 6.Tc4-c6 PAb7-b8 7.Kc3-b4 Ka7-b7+ 8.Kb4-c5 PAb8-c8+ 9.Kc5-d6 PAc8-b8 10.Tc6-c7+ Kb7-b6 11.Tc7-c4 Kb6-b7 12.Tc4-e4 Kb7-b6 13.Te4-e8 Kb6-b7 14.Kd6-c5 PAb8-c8 15.Te8-e7+ Kb7-a6 16.Kc5-c6 PAc8-f8 17.Te7-e8 PAf8-f7 18.Te8-a8+ PAf7-a7 19.Kc6-c7 Ka6-b5 20.Ta8:a7 Kb5-c4 21.Kc7-d6 Kc4-d3 22.Ta7-e7 Kd3-c4 23.Te7-e4+ Kc4-d3 24.Kd6-d5 Kd3-c3 25.Te4-d4 Kc3-b3 26.Td4-c4 Kb3-a3 27.Kd5-c5 Ka3-b3 28.Kc5-b5 Kb3-a2 29.Kb5-a4 Ka2-b2 30.Ka4-b4 Kb2-a1 31.Tc4-c2 Ka1-b1 32.Kb4-b3 Kb1-a1 33.Tc2-c1# Pao je sice slabší než leo, ale stále udrží ve většině případů proti věži remízu. A pao is weaker than a leo, but in the majority of cases it can still hold the draw against a rook. |
K + Rook - K + Pao | |
![]() | Kc2 Tb1 - Kh8 Pao g8 1.Tb1-b7 PAg8-g7 2.Kc2-d3 Kh8-h7 3.Tb7-b6 Kh7-g8 4.Kd3-e4 Kg8-f7 5.Ke4-f5 PAg7-h7 6.Tb6-d6 Kf7-g7 7.Td6-d4 Kg7-f7 8.Td4-h4 Kf7-g7 9.Kf5-e6 PAh7-h8 10.Th4-g4+ Kg7-f8 11.Ke6-f6 PAh8-h3 12.Tg4-h4 PAh3-g3 13.Th4-h8+ PAg3-g8 14.Kf6-g6 Kf8-e7 15.Th8:g8 Ke7-d6 16.Kg6-f5 Kd6-c5 17.Tg8-g4 Kc5-d6 18.Tg4-d4+ Kd6-c5 19.Kf5-e5 Kc5-c6 20.Td4-d5 Kc6-c7 21.Td5-d6 Kc7-c8 22.Ke5-e6 Kc8-c7 23.Ke6-e7 Kc7-b8 24.Ke7-d8 Kb8-b7 25.Kd8-d7 Kb7-a8 26.Td6-b6 Ka8-a7 27.Kd7-c7 Ka7-a8 28.Tb6-a6# I zde je zajímavé porovnat tento diagram s podobným diagramem pro leo. Pokud je už soupeřův král v rohu šachovnice, lze koncovku vyhrát, pokud není vlastní král příliš daleko, obecně je to ale remis. Vyhrávající zóna bílého krále je v případě koncovky věž-pao trochu větší než v případě věž-leo. Pěkný příklad porovnání síly obou kamenů. Here also, it is interesting to compare the diagram with the corresponding diagram for a leo. If the king is already in the corner, and the White king is not too far away, the ending can be won. The zone in which the White king wins is a little larger than that against a leo. A nice example of the relative strength of the two pieces. |
K + Rook - K + Vao | |
![]() | Ka1 Tb1 - Kc2 Vao e6 1.Tb1-b8 VAe6-f7 2.Ka1-a2 VAf7-d5 3.Tb8-c8+ Kc2-d3 4.Ka2-b3 Kd3-d4 5.Tc8-d8 Kd4-c5 6.Kb3-c3 VAd5-c6 7.Td8-d4 VAc6-e8 8.Td4-e4 VAe8-d7 9.Te4-e5+ Kc5-d6 10.Kc3-d4 VAd7-c8 11.Te5-d5+ Kd6-e6 12.Kd4-c5 Ke6-e7 13.Td5-d6 VAc8-f5 14.Kc5-d5 VAf5-c2 15.Td6-e6+ Ke7-f7 16.Kd5-e5 VAc2-a4 17.Ke5-f5 VAa4-d7+ 18.Te6-h6 Kf7-e7 19.Kf5-e5 VAd7-b5 20.Th6-h7+ Ke7-d8 21.Ke5-e6 VAb5-a6 22.Th7-d7+ Kd8-c8 23.Ke6-d6 VAa6-b5 24.Td7-c7+ Kc8-b8 25.Kd6-c6 VAb5-c4 26.Kc6-b6 VAc4-b3 27.Tc7-c4 VAb3-a2 28.Kb6-c6 Kb8-c8 29.Tc4-a4 Kc8-d8 30.Kc6-d6 Kd8-e8 31.Ta4:a2 Ke8-f7 32.Ta2-a5 Kf7-f6 33.Kd6-d7 Kf6-g7 34.Kd7-e6 Kg7-g6 35.Ke6-e7 Kg6-g7 36.Ta5-a6 Kg7-h8 37.Ta6-g6 Kh8-h7 38.Ke7-f7 Kh7-h8 39.Tg6-h6# Věž proti vao obecně vyhrává (a jak uvidíme dále, může mít černý dokonce 2 kameny vao a stále prohraje) Rook against vao is a general win (and as we shall see later, Black can have two vaos and still lose). |
Leo + Leo | Pao + Pao | Vao + Vao | Lion + Lion | 2 Grasshoppers | |
K + Rook | = | = | + | = | = |
K + Queen | + | + | + | + | + |
K + Rook - K + Vao + Vao | |
![]() | Ka1 Tb1 - Kd4 Vao d5 Vao e4 1.Tb1-d1+ VAe4-d3 2.Ka1-b2 VAd5-e6 3.Kb2-c1 VAe6-g8 4.Kc1-d2 VAd3-f5 5.Kd2-c2+ Kd4-c4 6.Td1-d2 VAg8-d5 7.Kc2-d1 Kc4-c5 8.Kd1-e2 Kc5-d6 9.Td2-d4 Kd6-e5 10.Ke2-e3 VAd5-c6 11.Td4-e4+ Ke5-d5 12.Te4-e8 VAf5-g6 13.Ke3-f4 VAg6-c2 14.Te8-d8+ Kd5-c4 15.Kf4-e5 Kc4-c5 16.Td8-d5+ Kc5-c4 17.Ke5-d6 VAc6-a4 18.Td5-c5+ Kc4-d3 19.Tc5-c7 VAa4-b3 20.Kd6-c5 VAb3-e6 21.Tc7-d7+ Kd3-c3 22.Td7-d4 VAe6-a2 23.Td4-e4 VAc2-d3 24.Te4-a4 VAa2-b3 25.Ta4-c4+ Kc3-d2 26.Kc5-d4 VAd3-f1 27.Tc4-c5 VAb3-c2 28.Tc5-d5 VAf1-e2 29.Td5-f5 VAe2-d1 30.Tf5-f2+ VAd1-e2 31.Tf2-f3 VAc2-b1 32.Tf3-b3 Kd2-c2 33.Tb3-b5 VAb1-a2 34.Tb5-a5 Kc2-b2 35.Kd4-d3 VAe2-d1 36.Ta5-b5+ VAd1-b3 37.Tb5-b6 VAa2-b1 38.Tb6-b4 VAb1-a2 39.Kd3-d2 VAa2-b1 40.Tb4-c4 VAb1-g6 41.Tc4-c2+ Kb2-a3 42.Kd2-c3 VAg6-h5 43.Tc2-d2 VAb3-a4 44.Td2-b2 VAh5-e8 45.Tb2-b3+ Ka3-a2 46.Kc3-b4 VAa4-d7 47.Tb3-d3 VAd7-g4 48.Td3-d8 VAe8-f7 49.Kb4-c3 Ka2-b1 50.Td8-d1+ Kb1-a2 51.Td1-d4 VAg4-h3 52.Td4-a4+ Ka2-b1 53.Ta4-e4 VAh3-c8 54.Te4-b4+ Kb1-c1 55.Tb4-c4 VAc8-e6 56.Tc4-e4 VAe6-b3 57.Kc3:b3 Kc1-d2 58.Kb3-c4 VAf7-g6 59.Kc4-d4 Kd2-c2 60.Te4-f4 VAg6-e8 61.Tf4-f7 VAe8-a4 62.Tf7-c7+ Kc2-d2 63.Tc7-a7 VAa4-b5 64.Ta7-a2+ Kd2-e1 65.Ta2-a5 VAb5-c6 66.Kd4-e3 Ke1-f1 67.Ta5-a2 VAc6-d7 68.Ta2-f2+ Kf1-g1 69.Ke3-f3 VAd7-e8 70.Tf2-g2+ Kg1-f1 71.Tg2-g7 VAe8-h5 72.Tg7-h7 Kf1-e1 73.Th7:h5 Ke1-d2 74.Th5-h4 Kd2-d3 75.Th4-e4 Kd3-c2 76.Te4-e3 Kc2-b1 77.Te3-e2 Kb1-a1 78.Te2-f2 Ka1-b1 79.Kf3-e4 Kb1-a1 80.Ke4-d3 Ka1-b1 81.Kd3-c3 Kb1-a1 82.Kc3-b3 Ka1-b1 83.Tf2-f1# Ka1 Tb1 - Kd4 Vao d5 Vao c5 1.Ka1-b2 VAd5-e4 2.Tb1-a1 VAc5-d6 3.Ta1-d1+ Kd4-c5 4.Kb2-c3 VAe4-c6 5.Td1-d4 VAd6-e5+ 6.Kc3-d3 VAe5-g3 7.Td4-d7 VAg3-h4 8.Kd3-e4 VAh4-g3 9.Td7-d2 VAc6-b5 10.Td2-g2 VAg3-h4 11.Ke4-e5 VAh4-d8 12.Tg2-c2+ VAb5-c4 13.Ke5-e4 Kc5-b4 14.Ke4-d5 VAc4-a6 15.Tc2-c4+ Kb4-b3 16.Kd5-d4 VAd8-e7 17.Tc4-c6 VAa6-b5 18.Tc6-b6 Kb3-b4 19.Kd4-d5 VAe7-f8 20.Kd5-c6 Kb4-c4 21.Tb6:b5 VAf8-b4 22.Tb5-d5 VAb4-c3 23.Kc6-d6 VAc3-f6 24.Td5-h5 VAf6-g7 25.Th5-h4+ Kc4-d3 26.Kd6-d5 Kd3-e3 27.Th4-e4+ Ke3-d3 28.Te4-f4 VAg7-b2 29.Tf4-f3+ Kd3-e2 30.Tf3-c3 Ke2-d2 31.Kd5-c4 VAb2-c1 32.Kc4-b3 Kd2-d1 33.Tc3-c2 VAc1-e3 34.Kb3-c3 VAe3-f4 35.Tc2-f2 VAf4-g5 36.Kc3-d3 Kd1-e1 37.Tf2-f6 VAg5-c1 38.Kd3-e3 Ke1-d1 39.Tf6-d6+ Kd1-c2 40.Td6-c6+ Kc2-d1 41.Tc6-c3 VAc1-b2 42.Ke3-d3 VAb2-a1 43.Tc3-a3 VAa1-b2 44.Ta3-a1+ VAb2-c1 45.Ta1-b1 Kd1-e1 46.Tb1:c1+ Ke1-f2 47.Tc1-c4 Kf2-f3 48.Kd3-d2 Kf3-g2 49.Kd2-e3 Kg2-g3 50.Ke3-e2 Kg3-g2 51.Tc4-c3 Kg2-h1 52.Tc3-g3 Kh1-h2 53.Ke2-f2 Kh2-h1 54.Tg3-h3# Zjištění, že tato koncovka je vyhrávající (a to dokonce bez ohledu na barvy polí obou Vao) bylo pro mě mírným překvapením. The discovery that this ending was a win (and without regard to the colours of the squares on which the vaos ran) was for me mildly surprising. |
K + Queen - K + Lion + Lion | |
![]() | Ka1 Db1 - Ke5 Lion e6 Lion f5 1.Ka1-b2 Ke5-f4 2.Db1-c1+ Kf4-e5 3.Kb2-c3 Ke5-e4 4.Dc1-g5 Ke4-e5 5.Dg5-g7+ Ke5-d6 6.Dg7-g3+ Kd6-e7 7.Dg3-g5+ Ke7-d6 8.Dg5:f5 LIe6-g4 9.Df5-f6+ Kd6-c5 10.Df6-e5+ Kc5-b6 11.De5-d6+ Kb6-a7 12.Dd6-c7+ Ka7-a8 13.Kc3-b4 LIg4-a4 14.Kb4-a5 LIa4-a6 15.Ka5-b6 LIa6-c6 16.Dc7-d8# Výsledek, že dáma vyhrává proti dvěma lionům je silnější, než že vyhrává proti dvěma cvrčkům. Z malého počtu tahů nutných k matu lze usuzovat, že výhra je snadná. The result that a queen wins against two lions is stronger than that it wins against two grasshoppers. From the small number of moves needed to mate, we can judge that the win is easy. |
K + Queen - K + Leo + Leo | |
![]() | Ka1 Db1 - Ke5 Leo d6 Leo e6 1.Ka1-b2 LEe6-f6+ 2.Kb2-b3 Ke5-d4 3.Db1-g1+ Kd4-e4 4.Dg1-g2+ Ke4-d4 5.Dg2-f2+ Kd4-e5 6.Kb3-c4 LEd6-e6 7.Df2-c5+ Ke5-e4 8.Dc5-d4+ Ke4-f5 9.Dd4-d7 Kf5-e5 10.Dd7-b5+ Ke5-e4 11.Kc4-c5 Ke4-e5 12.Db5-b8+ Ke5-f5 13.Kc5-d5 LEf6-g5+ 14.Kd5-d4 LEe6-e7 15.Db8-c8+ LEe7-e6 16.Dc8-c2+ Kf5-f6 17.Dc2-f2+ LEe6-f5 18.Df2-h4 Kf6-g6 19.Dh4-h8 LEg5-h5 20.Dh8-g8+ Kg6-f6 21.Dg8-d8+ Kf6-g6 22.Kd4-e4 LEf5-f7 23.Ke4-f4 LEh5-h6 24.Kf4-e5 LEf7-g7 25.Dd8-d3+ Kg6-f7 26.Ke5-f5 LEh6-e6 27.Kf5-g5 LEe6-g6+ 28.Kg5-h5 LEg6-f6 29.Dd3-g6+ Kf7-e6 30.Dg6:g7 Ke6-f5 31.Dg7-g5+ Kf5-e6 32.Kh5-g4 LEf6-e7 33.Kg4-f4 LEe7-f8 34.Dg5-h6+ Ke6-e7 35.Dh6-g7+ Ke7-d6 36.Dg7:f8+ Kd6-d5 37.Df8-f5+ Kd5-c6 38.Df5-a5 Kc6-b7 39.Da5-b5+ Kb7-a8 40.Kf4-e5 Ka8-a7 41.Ke5-d6 Ka7-a8 42.Kd6-c7 Ka8-a7 43.Db5-b7# Matový postup proti dvěma Leo je trochu náročnější. Z toho, že je tato koncovka vyhraná vyplývá, že dáma vyhrává i proti jakékoliv slabší kombinaci čínských kamenů, tedy i Pao + Pao, Vao + Vao nebo Pao + Vao nebo Leo + Pao atd. The mating procedure against two leos is a little more difficult. From the fact that this ending is a win, it follows that a queen wins against any weaker combination, pao + pao, vao + vao, pao + vao, leo + pao, and so on. |