|David2009: This NN vs P ending is not as difficult as its reputation. The ending starts at
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With perfect play there is mate in 43 (Nalimov). With imperfect play against the program KCHESS (1997 edition, for Windows 95, runs under Windows XP) the game might end
[BLACK to Play]
WP C3; BN F3; BN G3; WK A5; BK C6
1 Ng3-e4 2 Ka5-b4 Ne4-c5 3 Kb4-c4 Kc6-d6
4 Kc4-b4 Kd6-d5 5 c3-c4+ Kd5-d4 6 Kb4-b5 Nf3-e5
7 Kb5-b4 Ne5-d7 8 Kb4-b5 Kd4-c3 9 Kb5-c6 Kc3-b4
10 Kc6-c7 Kb4-a5 11 Kc7-c6 Ka5-a6 12 Kc6-c7 Nd7-e5
13 Kc7-d6 Ne5-d3 14 Kd6-c6 Ka6-a7 15 Kc6-d5 Ka7-b7
16 Kd5-d4 Kb7-c6 17 Kd4-c3 Kc6-d6 18 Kc3-d4 Kd6-e6
19 Kd4-e3 Ke6-e5 20 Ke3-f3 Nd3-b4 21 Kf3-e2 Ke5-e4
22 Ke2-d2 Ke4-f3 23 Kd2-c3 Nb4-c6 24 Kc3-d2 Kf3-f2
25 Kd2-c2 Kf2-e2 26 Kc2-c1 Nc6-d4 27 Kc1-b2 Ke2-d2
28 Kb2-b1 Nd4-e2 29 Kb1-b2 Ne2-c1 30 Kb2-b1 Nc1-d3
31 Kb1-a2 Kd2-c3 32 Ka2-a3 Nd3-b2 33 Ka3-a2 Nb2-d3
34 Ka2-a3 Kc3-c2 35 Ka3-a2 Nd3-b4+ 36 Ka2-a3 Nb4-c6
37 Ka3-a2 Nc5-a4 38 Ka2-a3 Na4-c3 39 c4-c5 Nc3-b5+
40 Ka3-a4 Nb5-c7 41 Ka4-a3 Kc2-c3 42 Ka3-a4 Kc3-c4
43 Ka4-a3 Nc7-b5+ 44 Ka3-b2 Kc4-d3 45 Kb2-c1 Nb5-d4
46 Kc1-d1 Nd4-c2 47 Kd1-c1 Nc2-e3 48 Kc1-b2 Kd3-c4
49 Kb2-c1 Kc4-c3 50 Kc1-b1 Ne3-d1 51 Kb1-a1 Nd1-b2
52 Ka1-a2 Nb2-c4 53 Ka2-b1 Kc3-d2 54 Kb1-a2 Kd2-c2
55 Ka2-a1 Nc6-d4 56 Ka1-a2 Nd4-b3 57 c5-c6 Nb3-c1+
58 Ka2-a1 Nc4-a5 59 c6-c7 Na5-b3 checkmate
White's time 7 min 20 s Black's time 10 min 9 s (computer playing White matches user's time).
I was playing Black and had a long think at around move 33 since the thematic Nc4 is impossible (c4 is occupied by the WP). I also became worried about the looming 50 move draw, hence had to allow the P advance. I am sure that there are better plans for both sides: the point is, the ending is winnable.
KCHESS is an old program, but plays reasonably well. When I bought KCHESS circa 1998, I used to win comfortably playing the Windows 3.1 version. When I upgraded to Windows 98 so using KCHESS for Windows 95, the tables were turned.
White's play and Black's play are far from optimal: the point is, the ending can be won without expending enormous thought by the player with the NN (one simply looks for patterns/ positions which drive the defending K back). It is noteworthy that in Topalov vs Karpov, 2000 Topalov won at fast-chess time limits: his moves were almost automatic (as were mine in the ending above up to move 32). Karpov lost partly through ignorance (he should have moved his K towards the blockading N and P) partly through bad luck (without time to calculate his 'instinctive' moves turned out to be bad).
I am sure Anand would have won without difficulty in normal chess: the double handicap of blindfold plus fast play shows that even world champions are human. This ending, of NN versus blockaded Bishop's pawn was won very efficiently by Seitz in 1931, see Znosko-Borovsky vs J A Seitz, 1931
For useful general comments on this ending (blockaded RP as example) see Game Collection: Two Knights versus Pawn by <Resignation Trap>.
Apologies for the length of this post!