It was shown in the chapter "King, Queen, and Pawn vs. King and Pawn" that the following position is won for White.
8/8/8/2p5/2P5/5QK1/6k1/8 w
White to Move and Win
One winning technique is to put the queen on e5 and then run up the "hole" on d5 with the king. The Black king will either follow up the hole and get caught in an explosion or it will stay behind, getting separated from the White king and mated by the queen.
Did you know that the following position is also won for White?
8/8/8/2p5/2P5/5RK1/6k1/8 w
White to Move and Win
In ICS rules (no check rules) this is obvious. The technique is the same as the position with the queen, since, with no check, the rook can beat the lone king. However, the position is also won under FICS rules as we shall soon see.
This brings up the question: If we move the blocked pawns to each of the other 40 different possible positions on the board, which positions would be won and which merely drawn? The answer is, surprisingly, that 34 of the 40 positions are won and only 6 are drawn. Even more surprisingly is that different won positions require different winning techniques.
The following diagram has an X marked where the White pawn is in each of the 6 drawn blocked-pawn positions.
Six Drawn Positions
Let's now begin to look at the winning blocked-pawn positions. First, consider:
8/8/8/8/8/p3R3/P1k5/2K5 w
White to Move and Win
White wins as follows: 1. Kb1 Kc1 2. Ka1 Kc2 3. Rd3 Kc1 4. Rd2 Kb1 5. Rc2 Kb2 6. Rc8 Kb1 7. Rc3 Kb2 8. Rxa3## [1-0].
The winning technique is similar whenever the White pawn is on the 2nd rank. Let's look at one more:
8/8/8/4k3/4KR2/3p4/3P4/8 w
White to Move and Win
Here is one sample line: 1. Ke3 Kd5 2. Kf2 Ke5 3. Ke1 Kd5 4. Kd1 Kc5:
8/8/8/2k5/5R2/3p4/3P4/3K4 w
White to Move and Win
Here, the White rook will force the Black king to the 1st rank: 5. Rb4 Kc6 6. Rb5 Kc7 7. Rb6 Kd7 8. Rc6 Ke7 9. Rd6 Kf7 10. Re6 Kg7 11. Rf6 Kg8 12. Rf1 Kh7 13. Rg1 Kh8 14. Rg2 Kh7 15. Rg8 Kh6 16. Rg7 Kh5 17. Rg6 Kh4 18. Rg5 Kh3 19. Rg4 Kh2 20. Rg3 Kh1 21. Rh3+ Kg2 22. Kc1 Kf2 23. Rg3 Ke1 24. Rf3 Kd1 25. Re3 Kc2 26. Rxd3## [1-0].
Besides catching the Black king in an explosion by taking the pawn, another winning technique that works in some blocked pawn positions is to separate the kings, force the Black king far from the pawns, capture the pawn, and then queen. This will work if the blocked White pawn is sufficiently far advanced. For example, if the White pawn is at least on the fifth rank, this will work. Consider:
8/8/3p4/3P4/5R2/5Kk1/8/8 w
White to Move and Win
Play begins: 1. Ke4 Kf3 2. Rf6 Kf4 3. Ke5 Kf5 4. Ke6 Ke5 5. Kd7 Ke4.
White has separated the kings.
Play continues: 6. Rf5 Kd4 7. Ke8 Kc5 8. Rf4 Kb5 9. Rc4 Kb6 10. Rc5 Kb7 11. Rc6 Kb8 12. Rc7 Ka8.
The Black king is cornered. Now White must get his king away.
Play continues: 13. Kf7 Kb8 14. Kg6 Ka8 15. Kh5 Kb8 16. Kh4 Ka8 17. Kh3 Kb8 18. Kh2 Ka8 19. Kg2 Kb8 20. Kh1 Ka8
White is ready to take the pawn.
Play continues: 21. Rd7 Kb8 22. Rxd6 Kc7 23. d6+ Kd7 24. Kg1 (not Kh2??) Ke6 25. d7 Kf5 26. d8=Q Kf4 27. Qd3 [1-0].
The same technique of queening works when the blocked White pawn is on a4 or h4 (but just barely). The technique does not work with the White pawn anywhere else on the 4th rank (or 2nd or 3rd ranks). Consider:
k7/8/1R6/p7/P7/8/8/7K w
White to Move and Win
A failed attempt is: 1. Ra6+ Kb7 2. Rxa5 Kc6 etc. (draw). Instead, White must gain a valuable tempo first: 1. Rb1 Ka7 2. Rb5! Ka8 3. Rxa5 Kb7 4. a5 Ka6 (4. ... Kc6 5. a6 [1-0]) 5. Kh2 (not 5. Kg1??) Kb5 6. a6 etc. [1-0].
So far, we've proven wins when the White pawn is on any of the following squares marked with an X:
If the White pawn is on b3, b4, c3, or c4, then White can win by forcing the Black king to the left edge of the board and catching it in an explosion when taking the Black pawn. The procedure is analogous if the White pawn is on f3, f4, g3, or g4. For example:
8/8/8/8/4R1p1/6P1/4kK2/8 w
White to Move and Win
The following line will illustrate the winning idea: 1. Kf3 Ke3 2. Kf4 Kd3 (2. ... Kf3 3. Kg5 Kf4? 4. Kh6+ [1-0]) 3. Kf5 Kc3 4. Rd4 Kb3 5. Rc4 Kb2 6. Rc1 Kb3 7. Rc2 Kb4 8. Rc3 Kb5 9. Rc4 Kb6 10. Rc5 Kb7 11. Rc6 Ka7 12. Ra6+ Kb7 13. Ke4 Kc7 14. Rb6 Kd7 15. Rc6 Ke7 16. Rd6 Kf7 17. Re6 Kg7 18. Rf6 Kh7 19. Rg6 Kh8 20. Kd4 Kh7 21. Rg8 Kh6 22. Rg7 Kh5 23. Rxg4##.
This leaves only the six squares a3, d3, e3, h3, d4, and e4 mentioned at the beginning of the chapter to be drawn. The four in the middle are drawn because the Black king cannot be forced close to them to catch in an explosion and the White pawn is too far from queening. The two on the edges are also drawn. They are clearly too far from queening and White cannot catch the king in an explosion due to stalemate. Consider:
8/1k6/8/8/p7/P7/8/2R4K w
White to Move. Game drawn.
An attempt: 1. Rc8 Kb6 2. Rc7 Ka6 (2. ... Kb5? 3. Rc6 [1-0]) 3. Rb7 Ka5 4. Rb6 stalemate.
There is no other way to win. So, six of the forty blocked pawn positions are drawn.