You should think of pawns not as individual units but as a group acting as one unit. If one pawn is one "point" then the entire pawn formation is 8 "points". This actually makes pawns one of the most powerful units in the game. The pawns are your front line and do an excellent job of defending each other in diagonal lines. If your ...
Preceding answers and comments make many good points.
Why struggle for a single pawn?
The simple answer is: Chess games are mostly won by material advantage!
Generally being up a single pawn in an otherwise safe position is a clear advantage, often a winning advantage.
In such a situation a GM analyst might say: And the rest is technique!
Of course there are ...
Another point which has not been raised by the excellent answers above is that pawns are easy to block. A pawn can be blocked by just one piece in front of it, and it cannot take the piece which blocks it. Contrast this with any other piece, which can take a piece which blocks its movement (barring other circumstances such as a pin).
This property means that ...
I'm not at all disagreeing with the existing answers - both sound. Indeed every pawn is a potential queen. However, one aspect of the question remaining is: why struggle for a pawn as opposed to a more decisive plan?
In the games that you are watching, if they are between capable and well-matched players, very often the game will be quite well balanced with ...
The answer by @Brian Towers is both beautiful and true, but not always true. It is perhaps true if you think of every pawn as a potential queen. However, in endings, especially in Rook endings, the textbooks will tell you not to be drawn into passive defence but to keep your pieces active, and counterattack. That being said, you may not have the choice. ...
As the old poem says:
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of the rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
Exactly the same principle applies in chess. ...
With such an overwhelming pawn advantage it should be easy enough to win.
What you said is definitely a good plan. You can push h5 and g5 to push the king back.
[fen "8/R4ppp/4pk2/1r6/8/5K2/6PP/8 b - - 4 38"]
1... h5 2. Ra4 g5 3. h3 Ke5 4. Ra2 f5
We can see here that black has an easy win. g4 is coming and once the pawns are traded, Black's two ...
My plan was to keep the Black rook on the 5th or 4th rank to cutoff
the White king and advance the h and g pawns. But then what?
Your plan is a bad one.
The general rule in rook and pawn endgames is:
Your king protects your pawns
Your rook attacks your opponent's pawns
You can add another one:
Push your passed pawns
As you can see your passed pawns are ...