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.P%1Å‚kný pYíklad porovnání síly obou kameno.Here also, it is interesting to compare the diagram with thecorresponding diagram for a leo.If the king is already in thecorner, and the White king is not too far away, the ending can bewon.The zone in which the White king wins is a little larger thanthat against a leo.A nice example of the relative strength of thetwo pieces. K + Rook - K + VaoKa1 Tb1 - Kc2 Vao e61.Tb1-b8 VAe6-f7 2.Ka1-a2 VAf7-d5 3.Tb8-c8+ Kc2-d3 4.Ka2-b3 Kd3-d45.Tc8-d8 Kd4-c5 6.Kb3-c3 VAd5-c6 7.Td8-d4 VAc6-e8 8.Td4-e4 VAe8-d79.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-e5VAc2-a4 17.Ke5-f5 VAa4-d7+ 18.Te6-h6 Kf7-e7 19.Kf5-e5 VAd7-b520.Th6-h7+ Ke7-d8 21.Ke5-e6 VAb5-a6 22.Th7-d7+ Kd8-c8 23.Ke6-d6VAa6-b5 24.Td7-c7+ Kc8-b8 25.Kd6-c6 VAb5-c4 26.Kc6-b6 VAc4-b327.Tc7-c4 VAb3-a2 28.Kb6-c6 Kb8-c8 29.Tc4-a4 Kc8-d8 30.Kc6-d6 Kd8-e831.Ta4:a2 Ke8-f7 32.Ta2-a5 Kf7-f6 33.Kd6-d7 Kf6-g7 34.Kd7-e6 Kg7-g635.Ke6-e7 Kg6-g7 36.Ta5-a6 Kg7-h8 37.Ta6-g6 Kh8-h7 38.Ke7-f7 Kh7-h839.Tg6-h6#V%1Å‚~ proti vao obecn%1Å‚ vyhrává (a jak uvidíme dále, mo~e mít%0Å„erný 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). 5.Koncovka král + v%1Å‚~/dámaprotikrál + lion/leo/pao/vao + lion/leo/pao/vao5.Endgame king + rook/queenagainstking + lion/leo/pao/vao + lion/leo/pao/vaoLeo + Leo Pao + Pao Vao + Vao Lion + Lion 2 GrasshoppersK + Rook = = + = =K + Queen + + + + +Výsledky pro Vao + Vao platí pro kombinaci roznopolných i stejnopolných kameno.The results for vao + vao are valid whether they run on squares of the same or different colour.Koncovky se cvr%0Å„kem byly ji~ probrány v tomto %0Å„lánku: Grasshopper endgames after 25 years (2002)Endgames with grasshoppers were examined in the article Grasshopper endgames after 25 years (2002). K + Rook - K + Vao + VaoKa1 Tb1 - Kd4 Vao d5 Vao e41.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-d69.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-d324.Te4-a4 VAa2-b3 25.Ta4-c4+ Kc3-d2 26.Kc5-d4 VAd3-f1 27.Tc4-c5VAb3-c2 28.Tc5-d5 VAf1-e2 29.Td5-f5 VAe2-d1 30.Tf5-f2+ VAd1-e231.Tf2-f3 VAc2-b1 32.Tf3-b3 Kd2-c2 33.Tb3-b5 VAb1-a2 34.Tb5-a5 Kc2-b235.Kd4-d3 VAe2-d1 36.Ta5-b5+ VAd1-b3 37.Tb5-b6 VAa2-b1 38.Tb6-b4VAb1-a2 39.Kd3-d2 VAa2-b1 40.Tb4-c4 VAb1-g6 41.Tc4-c2+ Kb2-a342.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-f749.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-e4VAe6-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-b564.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-g7VAe8-h5 72.Tg7-h7 Kf1-e1 73.Th7:h5 Ke1-d2 74.Th5-h4 Kd2-d3 75.Th4-e4Kd3-c2 76.Te4-e3 Kc2-b1 77.Te3-e2 Kb1-a1 78.Te2-f2 Ka1-b1 79.Kf3-e4Kb1-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 c51.Ka1-b2 VAd5-e4 2.Tb1-a1 VAc5-d6 3.Ta1-d1+ Kd4-c5 4.Kb2-c3 VAe4-c65.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-b316.Kd5-d4 VAd8-e7 17.Tc4-c6 VAa6-b5 18.Tc6-b6 Kb3-b4 19.Kd4-d5VAe7-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-e327.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-c3VAe3-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-b242.Ke3-d3 VAb2-a1 43.Tc3-a3 VAa1-b2 44.Ta3-a1+ VAb2-c1 45.Ta1-b1Kd1-e1 46.Tb1:c1+ Ke1-f2 47.Tc1-c4 Kf2-f3 48.Kd3-d2 Kf3-g2 49.Kd2-e3Kg2-g3 50.Ke3-e2 Kg3-g2 51.Tc4-c3 Kg2-h1 52.Tc3-g3 Kh1-h2 53.Ke2-f2Kh2-h1 54.Tg3-h3#Zjiat%1Å‚ní, ~e tato koncovka je vyhrávající (a to dokonce bezohledu na barvy polí obou Vao) bylo pro m%1Å‚ mírnýmpYekvapením.The discovery that this ending was a win (and without regard tothe colours of the squares on which the vaos ran) was for memildly surprising
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