White to Play and Win

Steven B. Dowd

1.e5! 

Mate in 32, according to the tablebases, but we should not feel bound to play like a computer. 
But this is actually the only winning move, all others draw. 

I.	1.Kg7?= Rb7+ 2.Kg6 Rb6+ 3.Kh5 Rb5+ 4.Kg4= 

However, move, from the original position, all White pieces one file to the left. 
In this position, both the pawn push and the K to the 7th win. The reason why is quite simple... 
Your computer will show you, but figuring out *why* is very important...(4.Kg6 is also=) 

1...Kb2 The tablebases "prefer" Rc8.. why? who knows? And that doesn't matter. 
What matters is understanding the winning method. 

2.e6 Kc3 3.e7 Kd4 4.Kf7 Rh8 5.e8Q Rxh7+ 6.Kg6 Ra7 7.Qd8+ Kc5 8.Kf6 

Do you see how White has made logical progress against the king? 
A computer in these positions will often find a way to hold the rook until near mate, 
whereas most humans will also overlook ways for white to part the rook from the king. 
These are usually 2-3 move combination involving consecutive checks. 
The opponent can also blunder quickly, for example, 8. ... Ra3?? 9. Qe7+ wins the rook, 
as does 8...Rh7 9.Qa5+ Kc4 10.Qa2+ Kd4 11.Qd2+ Ke4 (11...Kc4 12.Qc2+) 12.Qc2+. 
Players may have heard that the secret to lasting longer in these endgames 
(and hoping, of course, you die of a heart attack before the game is finished, 
or perhaps they don't wish you a physical death, but hope that you will allow some skewer 
of your king and rook) is to bring about broader separation between king and rook 
until the right moment; however, the human mind is more prone to miss a series of checks 
than is a silicon beast.

The general rules for these kind of endings are:

1.	Unconnected pawns, even with the king’s support, only draw. And they must be far enough advanced, 
typically past the sixth rank.

2.	If the enemy king can get in front of the pawns, however, it is a win for the other side. 
But in most practical endgames, as in the above position, we find the king on the last rank 
from where a pawn was promoted and the other side had to sacrifice a rook for it. 
Thus, these endings are often the outcome of rook endgames, the most common kind of ending.

3.	As John Emms notes in The Survival Guide to Rook Endings, "Often there’s only one tempo, 
or one slight error, between a draw and a decisive result" in these positions, 
as the study well demonstrates.