ditto 

The following position is taken from Rechel-Hebden, 02-03-2008.
I think it nicely illustrates the discussion and the general principles listed in this thread.



38.Ke3                   
White starts to improve his king position
38......., Nd5+
Black seems to violate a principle here, and commit a common error.
He checks but at the same time allows white to improve his king position even further. But there was a deeper thought behind this:
Black wanted to keep his a-pawn on a6 rather than have to move it to a5, where it is vunerable to Kd4-c4-b5
Still, black can draw this position with more conventional play
         38........Ke7 39.Kd4, g5! (following the principle to move your potential past pawn first).

39.Kd4,Nc7!
The indicated defence.
40.Nb7
Opening a path for the king to the queenside
        After 40.b4,Ke7 41.Kc4,Kd6 42.Nb7,Kd7 43.Kc5,g5!
        black still draws.
40......,Ne6!
Black prevents Kc5 making it difficult for white to make progress
41.Kd5, Ke7
If white had tried to invade the queenside with 41.Kc4, black would
have set his kingside in motion with g5.



An important position. White now offered the exchange of knights,
and black evaded it. We'll come back later to the pawn endgame.
Let's first convince ourselves that white couldnt make much progress by other means.
(a) Invading the queenside with his king
42.Kc6, g5! 43.Kb6,h5! 44.b4,f5 and black's counterplay on the kingside is in time to hold the balance.
(b) Creating a passed pawn as soon as possible
42.b4,g5! 43.Nd6,Nf4 44.Kc6,Nd3! and white cant make progress either.
42.Nc5, Nxf4?
A decisive error, the pawn endgame would have been drawn.
43.Kc6!, Nxh3
Under the changed circumstances white's king invasion is decisive.
After 43...g5 44.b4,h5 45.b5,axb5 46.a5! black's counterplay comes to late.
44.b4, 


There is no longer a defence against the manoevre 
45.b5,axb5 46.a5! creating an unstoppable passed pawn.

Let's get back to the pawn endgame that could have occured after
42...Nxc5! 43.Kxc5



43....g5!
Again the important principle to move your potential passed pawn first
43.....f5? 44.h4! would have lost:
            (a) 44...a5 45.f4! (now blacks pawn majority is rather useless) 45...., Kd7 46.Kb5 and white wins.
            (b) 44...Kd7 45.b4,g6 46.Kd5! white wins using his queenside pawns as a decoy.
44.b4
White must be attentive as a king invasion may now even lose:
44.Kb6,f5!
    (a) 45.Kxa6,h5! 46.a5, g4 47.fxg4,fxg4 48.hxg4,h4! black wins
    (b) 45.Kc5,h5! 46.b4,g4 (46.Kd5,h4! whith the breakthrough g4 coming)
45.Kxa6??, h5

44....., h5
45.Kd5,f5
46.Ke5,g4
drawn

If there is some interest, I can elaborate on this endgame as there is much more to learn.

To sum up, if we are going to generalize, it seems that at least three variables are important:

1) The position of the kings
2) The size of the majority
3) Whether the majority is a strength or a weakness

Also, I'd add a fourth (rather obvious) one:

4) How advanced the majority is

Of course, this gets more complex the more variables we add, but then again, chess is complex and every position must be considered separately. Looking at these variables, it should be no surprise that a queenside majority is often preferred. In most cases, both kings are on the kingside, and often, variables 2 and 4 also count in favour of the queenside (players are more reluctant to move the kingside pawns if the kings are positioned there). Thus, the most important question is perhaps whether the majority is a strength or a weakness. After all, in many positions, the assessment depends on the answer to this question: "Is the passed pawn weak or strong?"

As for the case where kings are on opposite wings, I'd add that even if you do reach an endgame, it's impossible to generalize at what side you want your majority - if you have the majority on the same side as your king, your opponent will as well.

chk wrote on 05/15/08 at 11:00:08:

I think you underestimate the center pawn. In many endings in the CK (in particular the Smyslov variation) it is that e-pawn which gives black pieces and king more room than the whiteys. Plus while it is true that a q-side majority is useful it is also more difficult to defend, precisely because the king is on the other side.

thanks everyone! so to make sure i understand it, basically most people are saying that the pawn majority on the side opposite of the king is abit better because it could help get a passed pawn to force the other king to chase it down, however it won't always be certain. In a rook endgame you are basically going to draw and the majority won't matter much. When the king is on opposite sides, an endgame is less likely as it is much more attacking and aggressive. In some cases a kingside or queenside pawn advantage won't matter.

I agree that in a pure pawn ending with Kings on the same side, the side with the distant majority (i.e. away from the Kings) may have a better chance.

With a pair of Rooks on, it's a lot more drawish, but the side with the distant majority may still hold the advantage, unless it ends up with a passive Rook.

However, with more pieces on (and I'm still concentrating only on the endgame), the majority that is actively supported by its King, may be able to advance faster and prove to be a decisive advantage, especially if it can be combined with mating threats and / or an attack on the enemy King.

For example take a position that arises a lot from the Sicilian, the QG and many other openings:
White's pawn sceleton: h3/g2/f2 & a2/b2  - the King sits at g1
Black's pawn sceleton: h6/g7/f7/e6 & a7  - the King sits at g8

- with no other pieces on, White may be winning
- with one Rook each added, possibly winning for White, but a lot more drawish
- with, say, White having R+B+N and Black having R+2B: Black has most of the chances imo. His majority will be the more mobile one (his King and the Bishop pair will help for that) and could also use threats against Kg1 to gain tempi.
- with R+B against R+B things seem complicated to me: it mostly depends on who will progress more before exchanging to a more elementary position (like the ones mentioned above).

Hope my logic makes sense. I would also like to hear about other players opinions as these are just my thoughts and I could be wrong somewhere or simply forgetting sth..

It is indeed a complex matter.  Having a majority on the side where your opponent castled could provide you with/increase your attacking chances in the middlegame, for example.  There is also something to be said for the fact that in the most common kingside-versus-queenside majority structures, the side with the kingside majority also has a central majority (as in having an e-pawn versus no central pawns for the opponent).  Traditional theory might hold that such a central pawn [majority] lessens in importance as the endgame approaches, and that the side with the queenside majority (assuming both sides castled short) should then get an advantage.  Daniel King (an English GM) wrote an article/book chapter taking issue with that, contending that the side with the central/kingside majority is usually at least not worse even in the endgame.

If you have a pawn majority away from both Kings you have the advantage to get a passed pawn there. Then the opponent King has to march there and you may have a chance to grab the pawns which are left on the other side of the board. The advantage is biggest in pure pawn endgames and in endgames with knights. If other pieces join the party things get a lot more complicated. But its always the real position with its specific tactical and strategical aspects that counts - chess is a game of exceptions and surprising features, therefore we play it. If it would be so easy - "get a queenside majority and win" - then the game would certainly not be played anymore.