Hello!
Please just ignore this (somewhat stupid) comment in #137! This is really ridiculous. I never meant it with arrogance. If it sounded so, I'm sorry, I'm not a native speaker. Please read my words only, not between them, ok? But I think that you like some discussion about your studies. Otherwise you would't have presented them in this forum but elsewhere where you're not assumed to response to comments I think. The position is full of subtilities, thats the reason why I didn't give concrete lines, but only a plan. But if you want to challenge me, we can try some lines:
Ok, indeed after
1.Nxf7 Qh4
2.Nd8 Qg5
3.Rxe6+ Kf8
A) 4.Rf6+ Ke8
A1)
5.Nc6 Qf5+! with the perpetual idea along the b1-h7 diagonal (b1,f5,h7) is very strong and after the try
6.Kb7 Qb1+
7.Kxa7 the white king is really misplaced and cut off along the b-file!
A2) The same problem seems to occur after
5.Rd6 (to cut off the black king along the d-file first) because of 5...Qg4+!
6.Kb7 Qb4+ attacks the a5-pawn.
B) This is the reason why I think in this particular case its better to deal with the pin after
4.Nc6! Qf5
5.Kd7 and now:
a) 5...Qf7 6.Re7!
b) 5...Kf7 6.Kc7!
c) 5...Qg4 6.Kd6 and then Re7 and Kc7 and again White can reach his "dream position" (Kc7,Nc6,R goes to f6 or d6!, pawns e5 and a5 protected). Then play from the "dream position" starts with the double threat of pushing the e-pawn and collecting the a-pawns without becoming cut off with the king.
Hope I didn't overlook something important.
Anyway, it's a very interesting ending!
Would you really bet I would never win this position against an engine? Even if this quesion is completely irrelevant, you should not go for this bet. I think I would win this in a corr game with some intensive work in a few weeks! Even if it would be draw theoretically the engines would make mistakes probably for sure.