Why are 3 pawns stronger than 4?

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michaelbluejay

I just played a game where black had four queenside pawns to my three, which I thought should mean that s/he could have got one of them down to the 1st rank to queen.  But in fact, black's extra pawn is useless for some reason, which I can't quite put my finger on.  (I ran the position through a computer, and it doesn't find a way black to break through.)  Here's the position, I don't think it matters whose move it is, but it's actually black's.

I know my king is stronger, but just looking at the queenside pawns, my 3 seem to be able to ward off black's four.

Why is this?  I'm hoping to learn some general principle that I can apply to other, similar positions in the future, rather than having to calculate every possible pawn move by each side to figure out whether black can break through or not.  Thank you for any help you can provide.

EvgeniyZh

Fourth pawn is advanced which make it useless. You can see that d5 controls c4 and e4 squares, both of which are not important. And White pawns are more advanced than Black, which make thematic 3x3 pawn break winning for white, not black.

nuclearslurpee

Have you analyzed Ke5 if it is White to move? that may or may not be winning, I'm not certain. I can see that White and Black both queen (in that order) but since White queens first he may be able to force a trade and queen the remaining pawn.

Mika_Rao

Well, black can make a passed pawn easily.

But white's king is too close, so no dice.

Let me see if I remember a few other patterns of 1 less pawn stopping 1 more pawn though...

 



Mika_Rao
mashanator wrote:

A position like this will almost always be winning (or at least, a sizeable advantage) for the side with the outside passer (in this case, the g5 pawn), because the side who has it can use it as a decoy while the King destroys the whole other side. Unless your pawns are ridiculously advanced, or you're up two pawns over there, you're pretty much screwed. Even if the d5 pawn was on, say d6, it's as good as irrelevant:

 



Q+p vs Q is a fairly easy draw when the defender's king is in front of the passed pawn.

michaelbluejay

Thanks everyone for the ideas.  I think this is my conclusion:

(1) As mashanator showed, black *can* make a passed pawn in at least a couple of ways.

(2) But, that fails because either:

   (a) white can also make a passed pawn, which is much closer to queening, or

   (b) the white king can take out black's passed pawn.

So, I guess the general rule is, don't just look at the number of pawns on each side, look at how far advanced they are, and how easy the respective kings can get to those pawns.