Control of the Center:
Part of the Advanced Beginner's Chess Guide (Section 1)

Control of the Center
Point Count Chess: [+]
[Vulnerability v. Control of a Square]

2. Vulnerability (of units involved)

At the very beginning of this article, we saw with Diagram 3, re-shown below, how two Pawns, due to their equally matched for strengths & weaknesses, could cancel each other out, when both are alone in attacking the same square(s).

Control of the Center, Image 3, Advanced Beginners Chess Guide
Diagram 3 (Re-shown): Both Pawns
share Control of d5 & f5.
The matter of Vulnerability comes into play with the mismatch in the relative worth of the Pawns and Pieces, respectively.

In relation to Pawns, Pieces are considered more powerful, having a greater range of movement, in their own unique ways. That's all well and good, when it comes to attacking the enemy units, or returning to defend one's own troops. However, when it comes to Controlling Squares, their higher perceived worth makes them more vulnerable to loss, when pitted against units considered to be of a lesser value (with Pawns being at the bottom of the pile). Because of this, Pawns gain in usefulness, as being agents deployed to restrict the enemy Pieces, keeping them out of critical squares, wherever they may be.

For instance, in Diagram 6, below, we've replaced White's Pawn for a Knight, while Black's Pawn is retained. Now, ignore the fact that a lone Pawn against a Knight would be quickly lost, and instead we're focusing solely on the two unit's abilities to protect squares.
Control of the Center, Image 6, Advanced Beginners Chess Guide
Diagram 6: Knight v. Pawn. Unopposed, White's
Knight Controls more squares.
Without having moved, White's Knight already displays superior range of movement, over Black's Pawn. Both adverse units target squares unopposed, but White manages to Control 3 squares, versus 2 for the Black Pawn.

White's superiority is further underlined, when it's moved to one of it's most-effective squares, as seen in Diagram 7, below.
Control of the Center, Image 7, Advanced Beginners Chess Guide
Diagram 7: White's Knight shows its superior
range of movement, compared to Black's Pawn.
In just one move, White's Knight has increased its range, to target an optimum eight squares. Such maneuverability is one of the main factors in making the Knight worth relatively more than a humble Pawn. However, in Diagram 8, below, this superiority is shown to have limits ...
Control of the Center, Image 8, Advanced Beginners Chess Guide
Diagram 8: Black's Pawn Controls d5, because
of the higher value, thus greater Vulnerability,
of White's Knight.
Moving one square forward, Black's Pawn relinquishes its guard of d6 & f6, to move within attacking range of d5 & f5, respectively. Remember back to Diagram 3, when it was the two adverse Pawns attacking the same square, that their equal value served to cancel out either's unopposed Control?

This time, in Diagram 8 (above), the higher, relative worth of the Knight serves to keep it out of the d5-square, unwilling to be captured by a unit of lower relative worth. It's because of this higher vulnerability factor that Black's Pawn is considered to be the unit that Controls d5.

Adding more Pieces, in Diagram 9, below, we can continue to see the impact of Vulnerability.
Control of the Center, Image 9, Advanced Beginners Chess Guide
Diagram 9: Black Controls d5, as White's Rook
is mis-matched and more Vulnerable against
Black's lower-value Pawn.
The two Minor Pieces (Knight & Bishop) are worth relatively the same, so they're matched up when it comes to a swap-off. That leaves the Rook versus Pawn for Control of d5, and, as before, the higher-value unit (Rook) has more to lose; it's kept out of d5 by the lower-value unit (Pawn), and so, in this situation, Black would Control d5, due to the Vulnerability factor taking its toll on White's army.

Moving On: Time v. Control of a Square (Page 4).

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