Activity in the Endgame

I teach my students three easy steps to evaluate and play endgames.
1) Activity of pieces.
2) Activity of kings.
3) Pawn structure.
Pieces are priority as they have the power and can compensate for material deficit.
Have a look now how Vladimir Kramnik (not my student;) used the force to save himself in his round three encounter against the Italian GM Daniele Vocaturo in Doha:
A game that I liked (ChessBase 13)

[Event "Qatar Masters Open"]
[Site "?"]
[Date "2015.12.22"]
[Round "3.6"]
[White "Vocaturo, Daniele"]
[Black "Kramnik, Vladimir"]
[Result "1/2-1/2"]
[WhiteElo "2597"]
[BlackElo "2796"]
[Annotator "Bojkov, Dejan"]
[PlyCount "101"]
[EventDate "2015.??.??"]
[WhiteClock "0:04:30"]
[BlackClock "0:05:23"]

1. e4 e5 {It seems as Kramnik had given up the Pirc for good. Against the
talanted and sharp Vocaturo he wants to play it save.} 2. Nf3 Nc6 3. Bc4 {
Diagram [#] What else would you expect from Italian GM?!} Bc5 4. c3 Nf6 5. d3
d6 6. Bb3 a6 7. O-O h6 {Black often retreats the dark-squared bishop early in
the game, but Kramnik is not afraid of the d3-d4 advance.} 8. Nbd2 {Black has
no problems at all after} (8. d4 Ba7 9. dxe5 Nxe5 10. Nxe5 dxe5 11. Qxd8+ Kxd8
12. Nd2 (12. Bxf7 Rf8 $1) 12... Ke7 13. h3 Be6 {Bisby,D (2288)-Jones,G (2644)
England 2013}) 8... O-O 9. Re1 Be6 10. Bxe6 {An ultra-solid aproach by White
too.} ({Roughly two months ago Ivanchuk preferred to swap the bishops off on
b3, but got nothing out of the opening after} 10. Nf1 Bxb3 11. Qxb3 Re8 12. Be3
Bxe3 13. Nxe3 Qd7 14. h3 Ne7 15. Nh2 c6 16. Rad1 d5 {Ivanchuk,V (2726)-Kramnik,
V (2777) Skopje 2015}) 10... fxe6 11. b4 Ba7 12. Nf1 $146 {Diagram [#] A
novelty which does not change the evaluation of the position-it is equal. The
predecessor saw a quick draw after} ({Predecessor:} 12. a4 Qd7 13. Nb3 Rf7 14.
b5 Ne7 15. bxa6 bxa6 16. d4 Nc6 17. h3 Rb8 {1/2-1/2 (17) Bok,B (2587)-Vishnu,P
(2477) Moscow 2015}) 12... Qe8 {Black's plan is easy- Nf6-h5-f4 or
Nc6-e7-g6-f4 and attack along the half-open"f" file. If White is not careful,
he may easily get into big trouble. Fortunately, A. Karpov is here to help.
The former world champion demonstrated the optimal set-up on the kingside
which every "Italian" player knows.} 13. a4 Ne7 {[%cal Ge7g6,Gg6f4,Yf6h5,Yh5f4]
Diagram [#]} ({Also good is} 13... Nh5 14. Be3 Nf4 ({As if} 14... Bxe3 15. fxe3
{takes away the f4 square from the black knight.})) 14. Be3 Bxe3 15. Nxe3 ({
Here} 15. fxe3 {is also possible but Vocaturo is more ambitious.}) 15... Ng6
16. Ra2 {[%csl Yf2][%cal Ga2d2,Gd3d4,Yd2f2] Diagram [#] To shift the rook in
the center. White could have already started Karpov's set up with.} (16. g3)
16... Rd8 17. Rd2 Qf7 {White's reply would be the same no matter what.} (17...
Nh5 18. Kh1) (17... Nf4 18. Kh1) 18. Kh1 {[%cal Gf3g1,Gf2f3,Gg2g3] Diagram [#]
The king steps away to free the g1 square for the knight. Then once that it
goes back White can repel the active black knights with f2-f3 and g2-g3. This
is what Anatoly Yevgyenievich did against Artur Jussupow in 1986.} b5 {Kramnik
plays all over the board.} (18... Nf4 19. Ng1) 19. Qc2 Nf4 20. axb5 {White
opens the file only to abandon it.} (20. c4 $5 {makes more sense to me.}) 20...
axb5 21. Ng1 (21. Ra1 Ra8 $11 (21... Qh5)) 21... d5 {Now the more experienced
player enjoys some initiative. Still, the game did not leave the boarders of
equality.} 22. f3 ({Or} 22. g3 Ng6 23. f3 $11) 22... Qd7 {Keeps the tension
and creates an obvious threat of capturing on e4.} ({Black could have taken
the open file too} 22... Ra8) 23. Nf1 $1 {[%csl Rd5,Ye5][%cal Re4d5,Ge1e5]
Diagram [#] A nice maneuver which forces Kramnik to clarify his intentions in
the center. Vocaturo threatens to capture on d5.} d4 {This was Kramnik's
general idea. The pawn will separate the b4 trooper form the remaining forces.}
(23... dxe4 24. dxe4 $11) 24. g3 {Better than both} (24. cxd4 Qxd4) (24. Rc1 $6
dxc3 25. Qxc3 Nxd3 {when the black knight is too active on f4.}) 24... Ng6 25.
Rc1 $1 {Vocaturo plays with great precision.} Ra8 $6 {[%csl Yb5,Yc7] Diagram
[#] This leads to difficulties for Black. It was time for Kramnik to think
about equality with} (25... Ne7 26. cxd4 Qxd4 {when} 27. Qxc7 $2 {drops
material to} Rc8) 26. cxd4 Qxd4 ({Or else Black's pawn structure will be
horrific-} 26... exd4 $2 27. f4) 27. Qc5 $1 {One more precise move and White
proves that he has the better pawn structure.} (27. Qxc7 Qxb4 {should be OK
for Black.}) 27... Qxc5 (27... Rfb8 28. Qxd4 exd4 29. Rxc7 $16) 28. Rxc5 Rfb8
29. Rxc7 Ra4 30. Rb2 Ra3 31. Nd2 Rxd3 32. Nb3 {[%csl Yb5,Ye5,Ye6,Rf6,Rg6][%cal
Gc7h7,Gc7a7,Rb3c5,Rc5e6] Diagram [#] The forced play is over and White enjoys
serious advantage thanks to his more active pieces.} Nf8 33. Nc5 Rd1 34. Re7
Re8 {An inaccuracy which could have costed Kramnik dearly. The immediate
activation of the rook was mandatory} (34... Ra8 35. Kg2 Ne8 $1 ({Better than}
35... N6d7 36. Nxe6 Nxe6 37. Rxe6 Rd3 $16) 36. Nxe6 Nxe6 37. Rxe6 Nd6 {[%cal
Gd6c4] Diagram [#] with serious chances to survive.}) 35. Rb7 Ra8 $1 {Better
late than never. The former world champion is too good to stay passive and
wait.} 36. Kg2 g5 {Activity is the slogan for Black's survival.} ({It is too
late for} 36... Ne8 37. Rxb5 Nd6 38. Ra5 $16) 37. Rxb5 Rad8 ({Or} 37... g4 38.
fxg4 Nxg4 39. Nf3 {and White is close to winning.}) 38. Nb3 ({My bet is that
Kramnik would have chosen the solid} 38. Nh3 $5 R8d2+ (38... g4 39. Nf2) 39.
Rxd2 Rxd2+ 40. Nf2 {if he had had the white pieces here.}) 38... g4 $1 {
The best practical chance, or else White will consolidate (both positionally
and on the clock!)} 39. Rxe5 Ng6 40. Rxe6 Kf7 {[%csl Gb4,Ge4,Gf3] Diagram [#]
Black is three pawns down but is ready to show his knights.} 41. Nc5 ({Perhaps
White needed to swap offf a pair of rooks to relieve the pressure} 41. Rc6 Ne5
42. Rc1 (42. Rc7+ Kg6 43. Rc1) 42... Rxc1 43. Nxc1 Nc4 44. Rb3 gxf3+ 45. Nxf3
Nxe4 46. b5 ({Or} 46. Ne2 {in both cases White should be winning.})) 41... h5
42. e5 $2 {Only this move can be definitely claimed a mistake. Why give these
knights squares?} (42. f4 R1d2+ 43. Rxd2 Rxd2+ 44. Kf1 {looked way easier.})
42... Nd5 {[%csl Re6,Rg2][%cal Rg6f4,Rd5f4] Diagram [#] All of a sudden
Kramnik has a threat.} 43. Kf2 ({Say} 43. b5 $2 {and there it comes} Ndf4+ 44.
gxf4 Nxf4+ 45. Kf2 Nxe6 $17) ({White will be very happy to activate his rook,
however} 43. Ra2 {is met by} Rb8 $1 ({But not} 43... Nxb4 $2 44. Ra7+) (43...
Ndf4+ $2 44. gxf4 Nxf4+ 45. Kf2 Nxe6 46. Ra7+ $18)) ({Finally,} 43. fxg4 {
leads to another draw after} Ndf4+ 44. gxf4 Nxf4+ 45. Kf2 Nxe6 46. gxh5 $11)
43... Ra8 $1 {[%csl Rf2,Rg1][%cal Ga8a1,Rd1f1,Rf1g1,Ra1g1] Diagram [#] All the
black pieces are active, he is save now.} 44. Ra6 ({A bit better was} 44. fxg4
hxg4 45. Ra6 Rxa6 46. Nxa6 Nxe5 {but should be also a draw.}) (44. b5 Raa1 45.
b6 Rxg1 46. b7 Raf1+ 47. Ke2 Rg2+ 48. Kxf1 Rxb2 {and Black is better.}) 44...
Rxa6 45. Nxa6 Nxe5 46. Nc5 {The alternatives leave no winning chances to White
neither} (46. Rb3 Rd2+) (46. Rc2 Rb1 $11) 46... Nc4 47. Re2 Nce3 {Diagram [#]
The mating threat forces either perpetual} 48. Re1 ({Or all the material will
disappear after} 48. Rxe3 Nxe3 49. Kxe3 Rxg1 50. fxg4 hxg4 51. Kf4 Rg2 $11)
48... Rd2+ 49. Re2 Rd1 50. Re1 Rd2+ 51. Re2 1/2-1/2

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