Comments (3)
No. 1-3
  1. Kb2 Kb6 2. Kc3 Kc5 3. Kd3 Kb6 4 Ke3 Kc7 5. Kf4 Kd7 6. Kf5 Ke7 7. Kg6 Kd8 8. Kf6 Kc8 9. Ke6 Kc7 10. Ke7


I will just note that the study from 3 days ago is quite similar to this one, but Dave didn't finish it off- it has all the same themes seen here, including, in the most important line, the tactic of going around to the other side of the pawns from where the two kings started.



It can also be noted that black draws with 1.Kb1 Kb7 and 1.Kb2 Kb6/b8 taking the direct long distance opposition across an odd number of squares in those instances.

The question, then, comes down to whether white can win with 1.Ka2. On 1.Ka2, black doesn't have a direct opposition available since the king is on c7, but then you have to know that the equivalent opposition tactic is the long distance opposition across an odd number of squares and across one file (a long distance diagonal opposition). In other words, after 1.Ka2, black would draw if he could play 1....Kc6- the kings would be separated by an odd number of ranks and separated by the one file (the b-file). But black has no access to c6, so my first thought is that white will win this, so.....

1.Ka2 Kc8

The alternatives are no better, but 1....Kc8 at least makes white think a bit more. If black had tried 1...Kd7, white can take the long distance diagonal opposition across 3 ranks and one file with 2.Kb3 (also 2.Ka3 denies black the opportunity to take such an opposition because of the d5 pawn again). On 1...Kb7, white just takes the direct opposition across 3 ranks with 2.Kb3. On 1...Kb6, white takes the direct opposition across 3 ranks with 2.Kb2. On 1....Kb8, white just takes the direct opposition across 5 ranks with 2.Kb2. After 1....Kc8, though, white has to think one move further ahead to understand that black can't hold....


While being able to identify the effective oppositions that are available is pretty important in navigating these kinds of endings, it isn't everything- you have to be able look beyond them a move or two to. If all you are doing here is memorizing them, then you might object to 2.Ka3 in that black can take the long distance opposition across an odd number of ranks and across the one b-file, just like white was trying to avoid with 1.Ka2, but the problem isn't with black's second move, it will be that he can't translate that temporary opposition effectively because of that nagging problem with the c6 square.....

2..........Kc7 3.Ka4!

This is what you had to foresee.....that now black can't take the normal diagonal opposition from c6 after 3.Ka4, and has no direct opposition either because the white king stayed on the a-file. Really, all black has now is....

3..........Kb6 4.Kb4! Ka6

If black tries 4.....Kc7, white just takes the diagonal opposition with 5.Ka5. Continuing:

5.Kc4 Kb6 6.Kd4 Kc7 7.Ke3! Kd7 8.Kf4!

And white will win this, but it is instructive to work the rest of of it out because it reinforces the points I am laboring to make in this comment- that taking oppositions isn't always going to work if certain squares are unavailable later on. For a simple example from move 8, black can play...


but then white just follows with

9.Kf5! Kd7 taking the diagonal opposition, but then

10.Kf6! and black is lost because his own pawn prevents 10....Kd6.

In short, look for oppositions to take for yourself, how to deny them to your opponent, and then consider how the squares protected by your own pawns or protected by your opponent's pawns, or occupied by your opponent's pawns wille effect the play later on when trying to drive the enemy king backwards.