We are going to take a look at pure king and pawn endings where each side has an equal number of pawns. If there are no passed pawns or pawn majorities which can create passed pawns, then the endgame is almost always drawn. However, it is possible such an ending can be won if one side blunders or if other immediate tactical situations (such as a bad king placement) are present. Consider:
8/8/4k3/2p2p2/4p3/4K3/2PP2P1/8 b
Black to Move and Win
If White's king were on, say, a1, then the position would be drawn. But the king is badly placed in front of a Black pawn steamroller. Play begins: 1. ... f4+. White has two squares to retreat to. Let's look at each:
2. Kf2 e3+ 3. Kf1 (forced) e2+ 4. Ke1 f3 5. gxf3 c4 6. c3 Kd6 7. d3 cxd3 8. c4 Kc7 9. c5 Kc6 10. Kd2 e1=Q+ 11. Kd3 Qe4+ and Black mates with the queen.
2. Ke2 f3+ 3. Ke1 f2+ 4. Kf1 Kf5 5. g4+ Kf6 6. d4 exd3 e.p. 7. c3 c4 8. g5 Kf7 9. g6+ Kg7 10. Ke2 f1=Q+ and again Black mates with the queen.
Black's success in the above position was his ability to create a passed pawn. In equal pawn endings, when one side creates a passed pawn, the other side can invariably create one too. The goal is to get the more advanced passed pawn. So, the rule of thumb is: advance your own passed pawn as quickly as possible and use your king to block your enemy's passed pawn as far from queening as possible. These principles are displayed in their pure form in the following diagram:
8/8/2k5/2P5/5p2/5K2/8/8
Whoever is to Move Loses
In this position, the pawns are blocked an equal number of squares from queening. Thus, whoever has to give way first will lose. For example: 1. ... Kd7 2. c6+ Kc7 3. Ke2 f3+ 4. Kf2 Kd8 5. c7+ Kc8 6. Ke1 f2+ 7. Kf1 Kd7 8. c8=Q+ and the White queen will mate. Black could have survived a bit longer by connecting kings instead of retreating to the back rank. But White would still win. See "King and Queen vs. King and Pawn" for the winning technique.
Did you notice the little zigzag pattern the kings were making in the above line of play? It is a typical pattern performed so as not to lose another tempo. Let's see another ending featuring the above ideas:
1k6/1p6/8/1PP5/8/4p3/4K3/8 w
White to Move Wins
Here, White has blocked Black's passed pawn 2 squares from queening and is about to get a passed pawn of his own. White's goal is to get his passed pawn one square from queening before it is blocked, since if Black blocks the passed pawn two squares from queening, transferring the move to White, White will lose just as Black did in the above example. White must be careful here, since 1. c6?? loses to 1. ... bxc6 2. b6 Kb7. The correct way to proceed is: 1. b6! Kc8 2. c6 and now both 2. ... Kd8 3. c7+ Kc8 4. Kd1 e2+ 5. Ke1 and 2. ... bxc6 3. b7+ Kb8 4. Kd1 e2+ 5. Ke1 are winning for White.
Here's another ending where White wins by a tempo:
8/k7/P6p/8/8/8/2p2p1P/2K2R2 w
White to Move Wins
Here, White's rook provides him with an opportunity to lose a tempo (transferring the move to Black). But timing is everything. For example: 1. Rxf2?? h5 2. h4 (2. h3 h4 is even worse) Kb8 3. a7+ Ka8 and Black wins. White wins like this: 1. h3 h5 2. h4 Kb8 3. a7+ Ka8 4. Rxf2 Kb7 5. a8=Q+ etc.
The interesting thing about these king and equal pawn endgames with passed pawns or pawn majorities is that virtually none of them are drawn! (I can imagine a situation where kings are connected and both pawns queen.) It's all a matter of who will queen first. When each side has a pawn majority on opposite wings, it is essential to have your king in front of your opponent's pawn majority, since it must be ready to stop the passed pawn as far from queening as possible. Consider:
1k6/pp5p/8/8/8/8/P5PP/1K6 w
White to Move Wins
Here, White has an easy win since his king is ideally placed in front of Black's majority and since the Black king must waste several tempi getting over to the king side to stop White's eventual passer. Even if White's king were on e1 and Black's were on d8, giving a symmetrical position, all White would need is the first move to win the ending. (I base this conclusion not on analysis but on the fact that since passed pawns are possible on each wing, someone has to win, and whoever moves first is closer to blocking the enemy pawns or advancing his own.) Let's see a sample of how the above position might play out: 1. Kb2 b5 2. a4! (better than 2. Kb3 b4! and now Black's a-pawn can dislodge the White king and when the White king moves the Black b-pawn will advance -- although White should still win). 2. ... b4 3. Kb3 and now White has done his job blocking the Black passer as far from queening as possible. Play continues: 3. ... Kc8 4. g4 Kd8 (in general, Black should keep his pawn on h7 to maximize the number of moves it will take White to create a passed pawn) 5. g5 Ke8 6. g6 hxg6 7. h4 Kf8 8. h5 Kg7 9. h6+ Kh7 10. a5 a6 11. Kc2 b3+ 12. Kb2 and how since both pawns are blocked two moves from queening and it is Black's move, White wins.
Actually, that was a little close! White won by only one tempo. He could have made a much more convincing win by leaving his king on b1 and pushing his majority immediately. Like this: 1. g4 Kc8 Black is forced to run his king over already (1. ... b5? 2. g5 Kc8 3. g6 hxg6 4. h4 and the White pawn cannot be caught). 2. g5 Kd8 3. g6 hxg6 4. h4 Ke8 5. h5 Kf8 6. h6 Kg8 7. h7+ Kh8 and Black barely stops the passer. Now White has a very comfortable win.
Note that these king and pawn endings are very common in games. Let's take a look at an instructive position from a game Rekursiv vs. Sordid:
3k3r/2R3pp/4p3/p4p2/P2P4/6PP/8/6K1 w
White to Move
Let's take stock of the position. Black is up a pawn, but White has a draw by repetition (1. Rd7+ Kc8 2. Rc7+ etc.) if he wants it. Actually, White can also recover his pawn with 1. Rxg7. However, looking at the pawn structure, White has no hopes of creating a passed pawn after trading rooks. White's d-pawn will trade with Black's e-pawn, and White's g-pawn will trade with Black's f-pawn, and the a and h-pawns will remain opposed. So, the position is drawn. However, White plays on to see if Black will make a mistake. First note that White doesn't have to recapture the pawn immediately with Rxg7 since Black has no way to save both the g and h pawns. For example, Black can't play Re8 because then Rc8+ would win. Play begins: 1. Kf2 f4!?. Black makes a risky move (without calculating it all out). He is giving White the opportunity to create mutual passed pawns by playing g4, bypassing the Black f-pawn. Then after taking the g-pawn (or h-pawn if Black moves g-pawn), White has a kingside majority. Of course, Black has the passed f-pawn. The question is: Who's passed pawn will queen?
Anyway, White has nothing to lose by advancing the g-pawn now and giving it a shot, since he always has the draw by repetition. So, without counting tempi, White plays 2. g4! . Black responds with the strange move 2. ... g5?. Now, natural would have been 2. ... f3, to get the passed pawn as advanced as possible before it is blocked. However, White has no time to play 3. Kf3 because then Black saves his pawn with 3. ... h5, after which White would have to settle for perpetual check. But Black's 2nd move proves to be a mistake because now White can recover his pawn and then win the queening race. I leave it as an exercise to decide whether 2. ... f3 would have changed the outcome of the game (think about it after reading the rest of this article).
Play continues: 3. Rxh7! Actually, if White was going to take on h7, he should have done it like this: 3. Rd7+ Kc8 (3. ... Ke8?? 4. Rd8+ Kc7 5. Rc8+ and the rook will soon explode the king) 4. Rxh7. Then, White would have deflected the Black king a little farther from White's promotion square. But all is well and there's not much time to think of such things since the time controls for the game were only 1 minute for the entire game with a 1 second increment per move!
Time to take stock of the position again. First note that the d and e pawns are "dead." They will play no role in counting tempi because whoever advances their central pawn, the other player will take it, and each player will have expended 1 move, perfect balance. White's h-pawn will move forward and Black will have to either trade its g-pawn for it or count on blocking it on the h-file with his king. There are two moves Black should consider here: 3. ... f3 and 3. ... Ke8. Both turn out to lose: 3. ... f3 4. h4 gxh4 (4. ... Ke8 5. h5 etc. loses for Black too) 5. g5 Ke8 6. g6 Kf8 7. g7+ Kg8 and since White's pawn is further advanced, he wins. Or: 3. ... Ke8 4. h4! (not 4. Kf3?? Kf8 5. h4 Kg7! 6. hxg5 (6. h5 Kh6 0-1) Kh6 7. g5+ Kg6 0-1; a general principle is: pushing your own passed pawn takes precedence over blocking the opponent's early) and now either 4. ... gxh4 5. g5 Kf7 6. g6+ Kg7 7. Kf3 1-0, or 4. ... Kf8 5. h5 Kg7 6. h6+ Kh7 7. Kf3 1-0.
But Black chooses another death, with the dumb-looking 3. ... Kd7?, which does not get closer to blocking White or closer to advancing his own pawn. White now won easily: 4. Kf3 (4. h4 is more exact and wins by more tempi -- there's that general principle again of pushing before blocking). Play continued: 4. ... e5 5. dxe5 Ke7 6. h4 Kf7 7. h5 Kg7 8. h5+ Kh7 and White went on to win because his pawn is further advanced.
Let's end this chapter by taking a look at a minor paradox. In equal pawn endings with passed pawns or potential passed pawns, a player has two goals: block the enemy passed pawn as quickly as possible; and, push your own passed pawn as quickly as possible. However, in a very close race, you actually don't always want to win, sometimes you want to lose the race by a tempo! Recall the crucial position:
8/8/2k5/2P5/5p2/5K2/8/8
Whoever is to Move Loses
If you block the enemy pawn before he blocks yours, then it will be your move in the above position and you will lose. Let's back up a move. Consider:
8/2k5/8/2P5/5p2/8/5K2/8 w
White to Move Loses
Here, White to move loses. For example, 1. Kf3 loses to 1. ... Kc6 and 1. c6 loses to 1. ... f3. Even worse is 1. Ke2 f3+ 2. Kf2 Kc6. Let's back up another move:
2k5/8/8/2P5/5p2/8/8/5K2 w
White to Move Loses
Again, White to move loses. This is because 1. Kf2 is met with 1. ... Kc7, reaching the same sort of position just discussed, and 1. c6 is met by 1. ... f3. So, paradoxically, making progress is causing White to lose. White can't do any fancy side-stepping either: 1. Ke2 f3+ 2. Kf2 Kd7 3. c6+ Kc7 0-1, or 1. Ke1 f3 2. Kf2 Kd7 3. c6+ Kc7 0-1. Let's back up yet another move:
2k5/8/8/5p2/2P5/8/8/5K2 w
White to Move Loses
Again, White to move loses, and again it is because this position reduces to the previous position: 1. Kf2 Kc7 0-1 or 1. c5 f5 0-1. Also, other first king moves lose to Black pushing his f-pawn (analysis left to you). This can be backed up even further. Let's put the pawns on their original squares:
2k5/5p2/8/8/8/8/2P5/5K2 w
White to Move Loses
White to move loses again. Any "progress" made by White is simply mirrored by Black, reducing to previous analysis. For example, 1. c3 is met with 1. ... f6, 1. c4 is met with 1. ... f5, and 1. Kf2 is met with 1. ... Kc7. What if White tries something like this?: 1. Ke2. Then, instead of mirroring, Black can win with 1. ... f5. For example: 2. c4 f4 3. Kf3 c7 4. c4 Kd6 5. c5+ Kc6 0-1. The trouble with moves like 1. Ke2 is that they give the Black pawn the potential to check the White king.
The above examples might lead one to believe that all symmetrical pawn endings with passed pawns or pawn majorities favor the side who doesn't have the move. This isn't true. Consider this simple example:
8/8/k7/5p2/2P5/7K/8/8 w
White to Move Wins
Here, White wins like this: 1. c5 Kb6 (forced because 1. ... f4 allows White to queen first) 2. c6+ Kc7 3. Kg3 f4+ 4. Kf3 1-0.
More analysis is needed to analyze exactly when symmetry favors the side to move and when it doesn't.