White to move. This is a famous study by Troitsky in 1912 and is presented by Andreas. How should White proceed?
8/4P2N/1k1K3r/8/8/8/8/8 w – – 0 1
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I’m looking at:
1. Nf6! then if:
1… Rxf6
2. Ke5 and the pawn cannot be stopped
so if:
1… Rh8 then
2. Nd7+ (K- Moves)
3. Nf8 and the pawn, again, can’t be stopped. For example if:
3… Rh6
4. Ke5 Rh5
5. Kf6 Rh6
6. Kg5 (R-moves to a safe square)
7. e8=Q
Have I missed anything?
Brad Hoehne
1. Nf6! then if:
1… Rxf6
2. Ke5 and the pawn cannot be stopped
You’ve got the right idea, but:
1.Nf6 Rxf6
2.Ke5 Rf1
…draws.
1… Rh8 then
2. Nd7+ (K- Moves)
3. Nf8 and the pawn, again, can’t be stopped. For example if:
3… Rh6
4. Ke5 Rh5
4…Rf1 draws as above.
Google “Saavedra position” — what you see there will point you to the winning line(s).
”1. Nf6! then if:
1… Rxf6
2. Ke5 and the pawn cannot be stopped”
How about 2…Rf1 intending Re1+ ?
1. Nf6! then if:
1… Rxf6
2. Ke5 and the pawn cannot be stopped
Instead of 2. Ke5, you should play, 2. Kd5. Then 2. – Rf5+, 3. Kd4 – Rf4+, 4.Ke3 Hf1, 5. Ke2 – and white wins
And if Black refuses the knight:
1… Rh8 then
2. Nd7+ (K- Moves)
3. Nf8 and the pawn, again, can’t be stopped. For example if:
3… Rh6
… the straightforward:
4.Kc7 (or 4.Kd7) is good enough, e.g.:
1.Nf6 Rh8
2.Nd7+ Kb7
3.Nf8 Rh6+
4.Kd7 Rh1
5.e8=Q Rd1+
6.Ke7 Re1+
7.Ne6
… etc.
Ahh, thanks. I see why Rd5 instead of Re5 is best. The king walks down, preventing the rook from occupying any square that would allow a skewer after the queening or a simple taking of the pawn before that. Very cool. It’s good to learn something new.
Brad Hoehne
White wins two ways!
1. Nf6 is obvious, but there is exactly one other clear path here:
1. Kd5!
Jon Edwards from Princeton has a similar teaching Rook and Pawn versus Rook endgame on his website.
http://www.princeton.edu/~jedwards/cif/rook1pawn.htm
Enjoy!
Peter / chesstoplay
1. Kd5!
It’s true that 1.Kd5 wins, but it’s a blind alley that doesn’t actually make any progress. (Maybe a good idea if you don’t see the force win right away and need to gain clock time?!) Sooner or later, White has to retrace his steps back to the starting position and play Nf6!
What about 1.Ke5?
What about 1.Ke5?
1.Ke5 fumbles the win just like it does in posts 2, 3, and 7: 1…Rh1 with 2…Re1 next.
Analysis by Rybka 2.3.2a MP 64-bit 4CPU:
1. +- (#34): 1.Nf6
2. +- (#36): 1.Kd5
3. = (0.00): 1.Kd7
4. = (0.00): 1.Ke5
Here’s the entire solution after perfect play from both sides:
1. Nf6 {0} Rxf6+ {0} 2. Kd5 {0} Rf5+ {0} 3. Kd4 {0} Rf4+ {0} 4. Kd3 {0} Rf3+ {0
} 5. Ke2 {0} Rf4 {0} 6. e8=Q {0} Rd4 {0} 7. Qc8 {0} Rd6 {0} 8. Ke3 {0} Kb5 {0}
9. Ke4 {0} Rd1 {0} 10. Qg4 {0} Rd6 {0} 11. Qg3 {0} Rd7 {0} 12. Ke5 {0} Rd8 {0}
13. Qb3+ {0} Kc5 {0} 14. Qc3+ {0} Kb6 {0} 15. Qb4+ {0} Kc6 {0} 16. Qc4+ {0} Kb6
{0} 17. Ke6 {0} Rg8 {0} 18. Qd4+ {0} Kc6 {0} 19. Ke7 {0} Rb8 {0} 20. Qf6+ {0}
Kc7 {0} 21. Qe5+ {0} Kb7 {0} 22. Kd7 {0} Ka7 {0} 23. Kc7 {0} Rb7+ {0} 24. Kc8 {
0} Ka6 {0} 25. Qa1+ {0} Kb6 {0} 26. Qb2+ {0} Kc5 {0} 27. Kxb7 {0} Kd6 {0} 28.
Qb5 {0} Ke6 {0} 29. Kc7 {0} Kf7 {0} 30. Kd6 {0} Kf6 {0} 31. Qh5 {0} Kg7 {0} 32.
Ke6 {0} Kg8 {0} 33. Kf6 {0} Kf8 {0} 34. Qf7# {0} 1-0
If Kd5:
1. Kd5 {0} Rh5+ {0} 2. Kd6 {0} Rh6+ {0} 3. Nf6 {0} Rxf6+ {0} 4. Kd5 {0} Rf5+ {0
} 5. Kd4 {0} Rf4+ {0} 6. Kd3 {0} Rf3+ {0} 7. Ke2 {0} Rf4 {0} 8. e8=Q {0} Rd4 {0
} 9. Ke3 {0} Rd6 {0} 10. Qc8 {0} Kb5 {0} 11. Ke4 {0} Rd1 {0} 12. Qg4 {0} Rd6 {0
} 13. Qg3 {0} Rd7 {0} 14. Ke5 {0} Rd8 {0} 15. Qb3+ {0} Kc5 {0} 16. Qc3+ {0} Kb6
{0} 17. Qb4+ {0} Kc6 {0} 18. Qc4+ {0} Kb6 {0} 19. Ke6 {0} Rg8 {0} 20. Qd4+ {0}
Kc6 {0} 21. Ke7 {0} Rb8 {0} 22. Qd6+ {0} Kb7 {0} 23. Kd7 {0} Ka7 {0} 24. Qe5 {0
} Rb6 {0} 25. Kc7 {0} Rb7+ {0} 26. Kc8 {0} Ka6 {0} 27. Qa1+ {0} Kb6 {0} 28.
Qb2+ {0} Kc5 {0} 29. Kxb7 {0} Kd6 {0} 30. Qb5 {0} Ke6 {0} 31. Kc7 {0} Kf7 {0}
32. Kd7 {0} Kf6 {0} 33. Qh5 {0} Kg7 {0} 34. Ke6 {0} Kg8 {0} 35. Kf6 {0} Kf8 {0}
36. Qf7# {0} 1-0
1. Nf6 {0} Rxf6+ {0} 2. Kd5 {0} Rf5+ {0} 3. Kd4 {0} Rf4+ {0} 4. Kd3 {0}
Notice that 4.Ke3 is just as good: 4…Rf1 5.Ke2, etc. White can’t step onto the e-file any earlier, though.