Centre control - essential principle or just a dogma?

One way you can test for yourself is imagine / experiment with setting up a ^ shaped pawn formation in the opening against a v shaped pawn formation. (V shape gets space on both flanks while ^ shape takes central space). Both sides develop their bishops and knights. Now in the middlegame, what are some differences?

@23 Untrue for me except when saved by formulaic openings where the themes didn't change. Eg. Kid and najdorf English flank attacks

Doesn't this kind of situation happen all the time? And generally, I don't see that much of an advantage to either side. At the most, initial development would be dificult to make if the one side is really constrained. But, that wouldn't be the case in the scenario you described. And if there is a contraint, both sides would be constrained more or less equally in the scenario you described.

Hmm. Well a related idea is why is a queen worth 9, rook with 5, etc.? Why is a knight on the edge supposedly worse than a knight not on the edge (maybe this is not true either?)

In the v vs ^ formations both sides may be equally constrained, but will their pieces be worth the same? If your answer is "yes" that's fine, I'm just trying to provoke some ideas.

Perhaps addressing particular concrete positions would be more fruitful than discussing generally ie aimlessly.

Yep, another adage I think is silly is 'knights on rim are dim' or something of that sort. If the knights have to attack the rim, then they will on the rim. If they have are facing attack from the centre, then they will run to the rim. Why is it dim?

About the value of the pieces, its a debateable topic. I think its difficult to determine the value of activity of a piece (unless there is something very obvious going on in the position). Of course, the general value is fixed and I largely agree with it.

I guess so. But then a person could just one of the many examples of e.g. an opening where putting a knight on the rim is the best move.

For a general reason I think it's more useful to talk about it generally... like why, geometrically speaking, might one area of the board be more useful (like the center, or one of the flanks, the back ranks, etc).

So why is a rook worth more than a knight? In the opening especially, knights often do a lot more while rooks just sit passively in a corner... and even after castling they're usually stuck behind your pawns anyway.

I look at activity as attacking or constraining the opponent king or opponent pieces. The more you are in a position to attack or constraint the opponent pieces the better... especially the high value targets like King & Minister. So, those pieces that are attacking the opponent King or Minister seem to be of greater value than those pieces attacking lesser pieces. And those pieces attacking nobody are of even less value.

Rooks are more than horses in general because its just a more powerful piece than horse, not just in centre but anywhere. But, in terms of activity and position, sometimes Rooks maybe less than the horse. I agree that horse is more important initially. And the main strength of the horse is to navigate the closed positions quickly by jumping over the pieces.

One way I've seen teachers tell new players (and I know you're not new, this is just for example) is that if you put a rook on an empty board it controls 14 squares... no matter where you put it! The center, the corner, as long as it's an empty board it always influences 14 squares.

Then they do the same for each piece. I think they explain that the knight is worth the same as the bishop because it can hop over pieces and most of the time during a game there are plenty of pieces getting in the way.

So anyway, if the value of a piece is related to how many squares it can influence, then that's one argument for placing them near the center.

If the value of a piece is mostly related to threatening the enemy king, then after the enemy king castles, only pieces near the enemy king have high value (so we'd have to evaluate if the v or ^ shape is better in the opening.

Another idea not mentioned is pieces can be valuable for defending important squares too, like the squares near your king.

So far our ideal piece:
1) influences many squares
2) influences squares around enemy king (or high value target)
3) influences squares around our king (or high value target for our opponent)

Agreed. All I am saying is that influencing more squares is not the main criteria. Its desirable but not necessary. The main criteria should be the key squares. And the key squares would be around the high value targets on the board(kings & ministers). Similarly, key pieces would be attacking, constraining or defending high value targets on the board(kings & ministers).

I agree... but then why are rooks given a value of 5? Even in the opening you don't rush to sacrifice them... yet they often aren't influencing many squares, and aren't attacking anything. It's the knights, bishops and queen that can quickly attack from early in the game.

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So it's sort of an average... rooks are more likely to influence important squares (due to better mobility) at some point in the future. Centralized pieces are more likely to influence important squares (both defensively and offensively) in the future. They can more easily maneuver to either side. Other than the number of squares controlled, geometrically, the center is the area closest to all other points on the board.

In a V shape, to maneuver pieces from left to right you have to pass through the bottom point of the V where the pieces will become congested or through the center which will be contested by enemy pieces. In the ^ shape the bottom of the ^ is both your territory, and not contested by enemy pieces.

But, there is a difference in a piece and square. A square is fixed and cannot move. So, controlling the centre square for later use is different from saving your rook for later use. The rook is mobile and can go to any nook & corner while the centre square will remain in the centre.

Also, its really difficult for me to envisage a position where only one side is controlling the centre completely. Because the centre is under attack from all sides, it ends up being controlled by both parties unless centre has no value and both sides don't care about it.

Yeah, the square itself has no value, it's the consequence of occupying a central square vs an edge square, and the consequence of a ^ formation vs a v formation. Just like all pieces have the same capturing power (a pawn captures just as well as a queen) the only difference is mobility.

Here is an example of one side not contesting the center. Each side vacated 6 squares behind their pawns to be used by their pieces. I suppose the only difference is the white e+d pawns control 4 squares while the a+h pawns control 2.

Even this position looks broadly equal. The only critical point is that the high value targets are in the middle of the board, so controlling that space has higher value. If you put the king & minister in the corner, then it will be even more interesting.

Even then, central pieces are better.

White has 6 pieces that can quickly be brought to operate in the upper right quadrant.

Black has about 3 that can quickly operate in the lower right quadrant.

Also geometrically, white's pieces are on average closer to black's king.

Oh, and of course, centralized pieces can operate in attack and defense at the same time. Black's b7 bishop attacks, but does not defend for example.