Sometimes, because of events in other parts of the board, pawns are left on their own against the enemy King. When this happens, knowing one single rule will be enough to decide the game.
The Rule Of The Square
How can you tell if the enemy king can catch your pawn? One way is to calculate in your head, from the positions below:
"If I move my pawn to e6, then the king moves to c6, my pawn to e7, the king to d7, my pawn to e8 and I get a queen, but then the king takes my queen."
This works, as you see, but it's long and gives you too many chances to make a mistake. A second way is to count moves:
"Let's see, my pawn on e5 queens in 3 moves, while the king on b5 requires 3 moves to get to the queening square."
This is simpler, but you can still get confused. If both numbers are the same, as in the first example below, the pawn can't queen. But what if the pawn is one move closer than the enemy king? Will it still win? Look at the second position below and work it out for yourself. (Answer: only if it is the pawn's turn to move; if the King moves first the queen will not survive.)
There's an even simpler method, though. One that doesn't involve either move calculation or counting. Draw an imaginary line coming out of the front corner of the pawn's square nearest the enemy king, continuing forward and to the edge of the board, to the square with the white "X", in the example positions below.
The pawn's square and the square where that line ends will form the corners of a larger square. If the enemy king is in that square, or can move into that square, the king can catch the pawn.
In this position, the enemy king is inside the box, so no matter who is to move, the king will catch the pawn.
In this position, the enemy king is not inside the square, so if it is white to move, the pawn will queen. But, with Black to move, the king can move to b5, which is in side the square, so the pawn would not be able to queen safely.
This rule is even more useful when you have more than one pawn, because you can use that rule to protect your pawns when your king is away from them. For example, when pawns are connected, the forward pawn is obviously protected by its partner but what can protect the backward pawn? Even alone against a king, the forward pawn can protect its partner:
So we see the pawn on d4 cannot be captured, even though it seems undefended, because to capture it the king would have to move out of the square of the e-pawn, and the e-pawn would then win the race to queen. Even though the d-pawn seems to be undefended, the Rule Of The Square defends it.
Neither of these pawns can force their way through to queen on their own, however. All the enemy king needs to do is move back and forth from d5 to e6 and back, and neither pawn can move without being captured. But this isn't always the case.
In the next position, the two pawns are one square apart. Usually, this makes them weaker, as neither pawn is obviously protected. But when facing a lone king, these pawns are protected, by the Rule Of The Square:
This technique can also be used to promote pawns that are farther away from the queening square, so long as white's king has a free square to move to:
Note pawns that are separated are only protected if the king cannot get in between them. The above example works only because the enemy king cannot get to a square on the b-file between the pawns. Separate the pawns by another file, and they will only be successful on their own if they are close enough to the queening square:
One final note about the Rule Of The Square. It works all the time, so long as the enemy king has an unimpeded path to the queening square. But if you can arrange to block the path of the enemy king, you can force it to step outside the square, and queen your pawn: