No. 70 (Vol. V) January 1983 SOME SPECIAL FEATURES OF superior side free to combat the THE ENDGAME STRUGGLE opposing king.) ROOK and KNIGHT against All of the foregoing motives can be 2 KNIGHTs (GBR Class 0107) present as independent ideas in indi- by A.G. Kopnin vidual studies or can be combined in ons study. Kl is out first illustration. The textbooks on the theory of the Here we have the first motive, the endgame pay no attention to this separation of the Bl force, so the first endgame. Therefore, if one is to draw move is obvious. inferences, and make generalisations A.G. Kopnin 1st Prize, Magyar Sakkelet, concerning the special features of the Analytical Section, 1980 struggle with this force, this can be See EG 69, No. 4612 done only from studies composed with this force. From the material imbalance this endgame should be drawn, as the advantage of the exchange is not decisive, but there may be special features of the position that give the stronger side the chance to play for a win. One may list the following features of this kind, very frequently to be found in studies: 1) The separation of the forces of the 1. Sg6. Permanently isolating bSg2. weaker side, permitting the stron- 1. ..., Sd6! this is best. If 1. ..., ger side either to win one of the Sel + 2. Kd2 Sg2 3. Ke2. Or 1. ..., knights, or to exchange a pair of Sa3 2. Re8 + ! Kf5 3. Re2 Sf4 knights to win the resulting rook (Kxg6;) 4. Sxf4 (Rxg2 + ) 4. ..., vs knight position. Kxf4 (K—;) 5. Rb2. Or 1. ..., Sc7 2) The detection of the weaker side's (a7, Kd5) 2. Rf2 Sel + 3. Kd2. king on the edge of the board, 2. Rf2. Not 2. Rfl? Sf5! with a draw. giving grounds for a mating attack. 2 Cpi I 3) The possibility to execute a fork 3. Ke3!*Not 3. Kd2(c3)? Se4+. 3. (double attack). Ke2? Sc2. 3. Kd4? Sb5 + 4. Ke3 4) The possibility of setting up a Sc3! drawing, while if here 4. Kc5 paralysis of both knights of the Sd3 + , or 4. Ke4 Sc3 + 5. Kd4 weaker side. It is the special pecu- (Ke3, Sdl + ; or Kf4, Sd3 + ;) 5. ..., liarity of this endgame that the Sb5+ 6. Kc4 Sd6 + 7. Kd4 Sb5 + king of the stronger side can tie drawn. down, indeed immobilise, both the Now Bl has 2 continuations: 3. ..., opposing knights, while the latter Kd5 (I), and 3. ..., Sc4 + (II), defend one another. (This would since 3. ..., Sf5+ (dS—) 4. Kd2 leave the rook and knight of the wins. 89 K2 A.G. Kopnin I After Black's 7. ..., Ke4 3. ..., Kd5 3. ..., Kd7 4. Rd2! comes to the same thing. 4. Rd2+ Not 4. Re2?Sc4+! 4. ..., Kc5! 4. ..., Ke6 5. Sf4+ Ke7 (Ke5; Rd5 or Kd7; Kf2) 6. Re2 Sc4(f5 + )7. Kf2. 4. ..., Kc6 5. Se5+ Kc5 6. Re2 Kd5(Sf5 + ;Kf2)7. Kf4. 5. Se5 Sc4 + If 5. ..., Sf5+ 6. Kf2. 6. Sxc4 Kxc4 7. Re2 Sd3 Win 8. Rc2 + . Variation I shows the win of the isolated bS. In Variation II 7. ...,Ke4 (Diagram K2) the struggle is more varied, being 8. Rxel + Kxf4 characterised by the typical posi- 9. Re6 Sb5+ 9. ..., Sbl + 10. Kd3 tion K2, K3 and K4. Sa3 ll.Rb6. 10. Kc4 Sa3+ 10. ..., Sc7 11. Re7 II Sa6 12. Rb7. Or 10. ..., Sa7 11. 3. ..., Sc4 + Kc5. Or 10. ..., Kf5 11. Rc6 Sa3 + 4. Kd4 Sa3 4. ..., Sd6 5. Re2+ Kf6 12. Kb4Sbl 13.Rc2. 6. Rxel Sf5 + 7. Ke4 Kxg6 (Sd6 +; 11. Kd3 Sb5 Otherwise 12. Rb6. Kd5 or Sg3 + ; Kf3) 8. Rgl + Kf6 12. Rc6 Kf3 The well known R6ti 9. Rfl. composition has arisen (Tidskrift 4. ..., Sa5 5. Re2 + Kf6 6. Rxel f5r Schack, 1929). Kxg6 7. Rf6 + K—8. Rb6. 13. Kc4 Sa3+ 14. Kc3! Sb5+ 15. 4. ..., Sd2?!? 5. Sh4! Sb3+ (Sbl; Kd3 Kf4. If 15. ..., Kf2 16. Rb6 Re2 + ) 6. Kc4! Scl (Sa5 + ; Kc3) Sc7 17. Ke4 Se8 18. Ke5 Sg7 19. 7. Sg2! eSd3 8. Sf4 + Sxf4 9. Rxf4. Rh6. 16. Kc4 Sa3+ 17. Kd4 5. Sf4 + Kd6 Sb5+ 18. Kd5 Sa3 19. Rcl(c3) 6. Kc3! This leaves Bl with 3 possible Sb5 20. Rc5 Sa3 21. Kd4 Sbl 22. continuations: Kd3 and 23. Ra5. In "a-1" then, a) 6. ..., Ke5; the struggle has switched to the b) 6. ..., eSc2; ending of R against S. c) 6. ..., aSc2; Since 6. ..., Sb5+ 7. Kd2, or 6. ..., Sbl + 7. Kb2, while after 6. A.G. Kopnin ..., Kc5 7. Rfl variations "a-2" After Black's 7. ..., eSc2 and "a-3" arise. a) 6. ..., Ke5 7. Rfl 7. Sg6 + ? Kd5. But now Bl has yet again 3 continuations: a-l)7. ...,Ke4; a-2) 7. ...,eSc2; a-3)7. ...,aSc2; Since 7. ..., Sb5 8. Kd2, or 7. ..., Sbl + 8. Kb2 Sd2 9. Sg6 + K— 10. Rxel. 'a-2" "a-1" 7. ..., eSc2 (Diagram K3) 90 8. Sg6+ Ke4 8. ..., Ke6 9. Rf4 Sal. "a-3" (If now 9. ..., Se3(el) 10. Re4 + 7. ..., aSc2 (Diagram K4) Kf6 11. RxS Kxg6 12. Re6 + K— 8. Sg6+ Ke4 13. Rb6.) 10. Kb2 Sc2 (K—) 11. 9. Rhl! 9. Kd2? Sg2! Rh4 as in the main line method. 9. ..., Ke3 8. ..., Kd6 9. Rf6+ K— 10. Kb3. 10. Se5 Ke2 8. ..., Kd5 9. Rf5 + Ke6 10. Rf4. 11. Sc4 Kf2 11. ..., Kdl 12. Rh2 Kcl 9. Rf4 + Ke3 (Sal; Se3 + , Kcl; Rhl) 13. Rd2 10. Kb2 wK has tied down bSS and Kbl (Kal; Se3) 14. Rdl + Ka2 now the win is attained, either by 15.Rcl. a propitious exchange of Ss, or Or 11. ..., Sal 12. Sa3 and 13. by driving bK to the edge and Kb2. stalemating him -- or by com- 12. Rh2 + Kfl 12. ..., Kg3(gl) 13. bining both methods. Rh8 Kf2 14. Re8. 10. ..., Kd2 12. ..., Kf3 13. Kd2 Ke4 14. Rh5 11. Se5 Kdl 11. ..., Sb5 12. Rf2 + Kf4 (Kd4; Sd6!) 15. Rh8 (main K— 13. Rxc2. 11. ..., Ke3 12. Rf8 line method). (main line method). 13. Rd2 Kgl 12. Rf8 Kd2 12. ..., Sb5 13. Rd8 + 14. Rd8 Kf2 Sd4 14. Sf3. 12. ..., Ke2 13. Rd8 15. Re8 Kf3 (main line method). 16. Kd2 bSS are tied down by wK 13. Rd8+ Ke3 Or 13. ..., Ke2 14. and now it is possible to drive bK Sd3 Ke3 15. Sc5 Ke2 16. Sa4(e4) back to the edge. The method of Ke3(el) 17. Sc3 Kf3(f2) 18. Re8 doing this was discovered by the (main line method). author 28 years ago and written 14. Sc6 Ke2 14. ..., Ke4 15. Sa5 Ke5 up in a short article "Towards 16. Sb3 Ke6(e4) 17. Rc8 Kd7(d3) they Theory of an Endgame" in 18. Rc3( + )K— 19. Sal wins. Shakmaty v SSSR, vi.53. 15. Sa5 Ke3 16. ..., Kf4 16. ...,Kf2 17. Rf8 + . 16. Sb3 Ke2 17. Sd6 Kf3 Or 17. ..., Kg5 18. Rf8. And the "main line method" play 18. Rf8 + Kg3 and the remaining might continue: 17. Sc5 Ke3 18. Kb3 "main line method" moves might Ke2 19. Se4(a4) Ke3(el) 20. Sc3 be 19. Se4+ Kg2 20. Kdl Kgl 21. Kf3(f2) 21. Re8 Kf4 22. Sd5 + Kf3 Sc3(g3) Kg2 22. Se2 Kh3 23. Rg8 23. Kb2 Kf2 24. Sf4 Kg3 25. Sd3 Kf3 Kh2 24. Sf4 Khl 25. Sh3 Kh2 26. 26. Kb3 Kg3(g4) 27. Rb8! This is Sf2. bK is stalemated, and one bS simpler and quicker than restricting is lost! bK to the h-file. 27. ..., Kf3 28. Sb4 Sxb4 29. Rxb4 Sbl 30. Kc2. b) 6. ..., eSc2 7. Kb3 Ke5 8. Sg6+ Kd4 K4 A.G. Kopnin After Black's 7. ..., aSc2 9. Rf8 Kd3 10. Rd8+ Ke2 11. Kb2 (see variation "a-2"). c) 6. ..., aSc2 7. Kd2 Ke5 8. Sg6 + Ke4 9. Rf8, as in variation "a-3". The specification of tying down bSS by wK does not always reap an advantage leading to a win. In particular, when this takes place in 91 the centre of the board then the result K6 is an example of this. The may be drawn. K5 is an example author's solution runs: 1. Rc5 aSc4 2. where we have been unable to find a Sf5 Kg6 3. Ke6 Kh7 4. Rc7+ Kg8 5. win, because here the drive of bK to Se7+ Kf8 6. Sd5 Kg8 7. Sf6+ Kf8 8. the edge is unsuccessful, nor does it Ra7. We may note that not only 8. lead to the advantageous exchange of Ra7 wins, but equally 8. Rh7 and 8. a pair of Ss. (Readers are invited Kd5. If, in this line, 2. ..., Kg8 3. Ke6 either to be convinced of this or to Kh8 4. Rc7 Kg8 5. Se7+ wins. Or if refute the author's assertion.) 2. ..., Sg6+ 3. Kf6 cSe5 4. Rc7 + Kg8 5. Sh6+ Kh8 6. Kf5. K5 A.G. Kopnin (Original?7 The composer's solution has duals (a partially incorrect solution), arising out of the possibility of an advan- tageous exchange of a pair of Ss. After 1. Rc5 aSc4 one should lay the immediate 2. Ke6! Kg6 (K else; Sc6, Sxc6; Rxc4!) 3. Sf5 Kh7 (Kg5(h5); Sd6!) 4. Se7 Kg7(h6,h8) 5. Sc6 Sxc6 6. Rxc4! This idea of a partial second solu- tion leads us to a complete cook: 1. Draw Ke6 Sd3. If 1. ..., a(e)Sc4 2. Rc5 Kg6 3. Sf5 Kh7 4. Se7 Kg7 5. Sc6. Or 1. It is worth pointing out that studies ..., Sg4 2. Rc5 Sb7 3. Rc7. Or 1. ..., with this force set themselves apart Sg6 2.