Knight endgame

from Wikipedia, the free encyclopedia

A Springer final is a final in a game of chess or study, involving not only the two kings only one or more jumpers and farmers on the board are.

Knight endings without pawns are largely trivial: a single knight cannot checkmate himself in theory . Two knights only win if their opponent has made a gross mistake, otherwise they can only achieve a stalemate . On the other hand, three knights (at least one of which must have been created by moving a pawn) win without any problems; however, according to a complete retrograde computer analysis, a forced checkmate of the opposing king is only possible on marginal fields.

Different material distributions

In practice, a distinction is made between several typical initial constellations:

A knight against one or more pawns

Although a knight is nominally worth more than a pawn, the knight's party usually fights for a draw , as a pawn conversion usually leads to a profit for the opposing party. The knight party must therefore reliably control the pawn's field of conversion, and if its king is too far away, the knight may have to sacrifice himself against the pawn . Since the knight has a relatively short range and, especially at the edge of the board, has fewer opportunities to move than in the center, he has the most difficulty fighting opposing pawns on the a- or h-file. Because of its short range, the knight also has difficulty coming up against several pawns. The more lines the pawns are apart, the more difficult it is for the knight party to achieve a draw. The further the pawns are from the field of conversion, the better the defense chances of the knight party. In most cases she has no chance against three pawns, although there are a few exceptions.

The only way the knight party can make a profit is when the king of the peasant party is imprisoned in front of his own marginal farmer. Can be made by the Peasant Party Zugzwang be compelled to pull their king in the board area and to take with their own farmers the last flight field, the Springer, a smothered mate give.

Knight and pawn against knight

This endgame often ends in a draw because the losing party can sacrifice its knight against the remaining pawn . In some situations in which the pawn is already well advanced and is supported by his king, the stronger side has the option of sacrificing its own knight in order to distract the defending knight from the control of the pawn's conversion square .

Example: Study by Ladislav Prokeš , Groš, 1938

Josif Kricheli
Schachmatna Misl, 1984
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White to move wins

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But the motive of distraction is also suitable for defense, as this study demonstrates. In this position the pawn is only supported by the knight. Caution is therefore advised when catching figures .

Solution:
1. Nb5 Kc8
2. Kc2 would be missed? Sa3 +! distracts the white knight from his main task 3. Nxa3 Kc7! The white king adjusted c2 for his knight. 4. Nc4 Kb8 and the pawn is lost or 4. a7 Kb7! 5. Nb5 Ka8! with taking a fortress and a theoretical draw. Therefore better
2. Kc1! Sa3
3.Nxa3 Kc7
4.Nc2! Kb6
5. Nb4 wins

Knight and pawn against knight and pawn

Similar to pawn endings and in contrast to heavy piece endings with queen or rook, in knight endings a material preponderance of one side is often sufficient to win. Otherwise, as in other endgames, it depends on positional factors such as active position of the pieces, passed pawns, etc.

Two knights against pawn

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White to move wins

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Although two knights against the sole king that Matt can not force, there are ways to win, if the weaker side still has a farmers and this has not yet advanced far. The winning procedure, which Alexei Troizki explains in detail, stipulates that a knight prevents the pawn from advancing by blocking . The other knight, together with the king, drives the opposing king into a corner. Then the blockade jumper is introduced to mate. You can deprive the king of all possible moves because Black can move again with the pawn.

However, if the pawn has already advanced far enough, he can prevent the impending mate by threatening to convert . In a higher sense, the pawn is inviolable because capturing this pawn causes the game to be elementarily drawn . This endgame, which is rare in practice, is very difficult and winning is made more difficult by the 50- move rule .

The Troitski line is an orientation aid for every pawn blocked with a knight when assessing the position. If the pawn has not advanced further than this line, the endgame is won in any position of the king belonging to the pawn.

In order to win the diagram position, 115 moves are required for both sides of the best game. A completely flawless analysis of such positions was only possible through the use of computer-generated endgame databases , which confirmed Troizki's fundamental findings.

The following game illustrates essential phases in this type of endgame.

Sergei Karjakin - Samuel Sevian
Isle of Man Masters, 10/24/2018
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58 ... g6 – g5! The pawn leaves the Troitski line, Black can hold a draw.
59. Nd4 + Kc5
60. Nf5 g4 The further the pawn moves forward, the fewer the opportunities for White.
61. Ng3 Kd4 A simple strategy for a draw would be to keep the black king near a8.
62. Kf2 Kc3 Black tries to make it difficult for his king to be driven away .
63. Nd1 + Kd3
64. Ke1 Kc4
65. Kd2 Kd4
66.
Nc3 Kc4 67. Sce2 Kd5
68. Kc3 Kc5
69. Nf4 Kc6
70. Kc4 Kd6
71. Nd3 Kc6
72. Ne5 + Kd6

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Position after White's 81st move

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73. Kd4 Ke6 The black king is pushed further to the edge.
74. Nc4 Kf6
75. Ne3 Ke6
76. Nef5 Kd7
77. Kd5 Kc7
78. Nd4 Kd7
79. Ne6 Ke7
80. Nc5 Kf7
81. Kd6 Kf6? misses the last opportunity to go to corner a8. It only saves 81 ... Ke8! 82. Ke6 Kd8! 83. Kd6 Kc8
82. Nce4 +! Kf7 Karjakin demonstrates winning through precise play.
83. Kd7! Kf8 The noose around the black king continues to tighten.
84. Nd6 Kg7
85. Ke6 Kg6

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Position after the 85th move

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86. Nde4 Kg7
87. Ke7 Kg8 87.… Kg6 88. Kf8 Kh7 89. Kf7 Kh6 90. Kf6 Kh7 91. Nf5 Kg8 92. Ke7 g3 93. Nf6 +! Kh8 94. Kf8! g2 95. Nh6 g1D 96. Nf7 #
88. Kf6 Kh7 or 88.… Kf8 89. Nd6! Kg8 90. Nb5 Kf8 91. Nc7 Kg8 92. Ne6 Kh7 93. Nf5 g3 94. Kf7 g2 95.Ng5 + Kh8 96.Nh4 g1D 97.Ng6 #
89.Nf5 Kg8
90. Ke7 g3
91.Nf6 +! Kh8
92. Kf8! Black resigned because g2 93. SD (h) 6 G1d 94. Sf7 matt

literature

  • Juri Awerbach : runner and knight finals . Sportverlag, Berlin 1988, ISBN 3-328-00234-0 .
  • Yuri Awerbach: Textbook of the finals. Part II . Sportverlag, Berlin 1960, pp. 161-271.

Web links

Wiktionary: Knight endgame  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. ↑ 37th Federal Computer Science Competition 2018/2019: The tasks of the 2nd round, task 3B. BWINF, January 24, 2019, accessed July 30, 2019 .
  2. ↑ 37th Federal Computer Science Competition 2018/2019, 2nd round: Solution tips and evaluation criteria, task 3rd BWINF, July 29, 2019, accessed on July 30, 2019 .