Salvaging a Draw from a Hopeless Position

…or Knowing When NOT to Trust an Engine.  In a recent correspondence game I reached the following position as Black:

It should be fairly obvious that Black is lost.  Houdini suggests that the position favors White by about one Pawn but it is probably won for White with correct play so should be a lot more than one P. However, here I began asking what would happen if you removed the minor pieces?  With just R’s on the board the game is easily won for White because my K is so far away as to be useless. Any elementary endgame book will show that if you remove the minor pieces, Black’s K must be at least on the c-file in order to draw. 

Then I asked what about if the R’s were off the board?  In the diagrammed position, if you remove the R’s the game is a draw. Finally a plan began to emerge: bring the King closer to the P’s and trade R’s at the right time.  Unfortunately the R trade cannot be forced so if White keeps them on the board he will probably win…eventually.  My hope was that in his haste to force the win he would believe the engine evaluations that after the trade of R’s White still has a large advantage…1-1/2 P’s.
 

In the above position it is obvious that the attacked N must move, but where? 41...Rg1+ 42.Kc2 Ne3+ 43.Kd3 Nd1 does not look too inviting.

My pieces are too scattered and far from the action. So I selected 41…Nb4 and play continued 42.Kc1 Kf7 Moving the K closer to the P’s.

If instead of 42…Kf7 I had played 42...Nd3+ then if 43.Kd2 Nb4 (Both 43...Nxe5? 44.Rxe5 and 43...Rb4? 44.Rxb4 Nxb4 win for White) we have this position:

Black could draw IF the K was on the f-file and it was his turn but it’s not so the position is lost.  Back to the game:

43.Bc3 Nc6 [Not 43...Na2+?? 44.Kb1 Nxc3+ 45.bxc3 wins] 44.Rb6 Ne7 45.Rd6 [45.Kd2 was probably better because it improves the position of his K. 45…Ke8 46.b4 Rg6 and now, not 47.Rxg6 because once again, White keeps winning chances by keeping the R’s on 47…Nxg6 Draw] 45...Rg6! Hoping he takes the bait.

46.Rxg6? He did!  He should have tried something like 46.Re3 and be prepared to slog it out another 50 moves or so, but he trusted his engine. 46...Nxg6

The engines favor White by 1–1/2 P's but that is because, due to their horizon effect, they can't see the draw...it's too far away. The interesting thing is that if White’s K were anywhere on the 2^nd rank in the final position he would win.