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A Strategic Rule I've Never Seen Before

I never heard of this rule, but its a good rule, thanks for that!

a similar rule I found myself and read it nowhere: The knight is the best defender. If you are under attack and need to get a piece closer to your king, the knight is usually the best defender.

Other way round: if you consider an exchange sac, you want it to do against the knight (as it is the strongest defender).
Also, if there are 2 knights nearby to defend, you can look at concrete sac-possiblities, but not for too long - usually it is not worth it, 2 knights are just too strong defenders.

Another rule: for white aim for symetrical openings, for black seek assymetry.
Examples: 1.e4 e5 2.Nf3 Nf6 is statistically poor for black, whereas 1.e4 c5 is statistically quite good for black.

Another rule: if black plays in the opening ...e6, then the statistically most promissing reply is g2-g3 and fianchetto the Bishop on g2.

Or this one: an early ....Nf6 development is statistically poor, because it is often the target of attacks.
Example: 1.e4 e5 2.Nf3 Nf6(?) or the modern is much more promissing than the pirc. In the modern you delay the ....Nf6 development. Thus, strictly speaking, this is a poor approach, too (indian opening): 1.Nf3 Nf6(?) 2.c4! - why? because the black knight would want to jump to e4, but the d-pawn has not been played yet, so d2-d3 would attack a knight on e4. A few moves later you can move d2-d4.

in the KID black likes to attack a white pawn on e4. Avoid giving him this target. Either delay e2-e4 by playing e2-e3 first and consolidate, or play g2-g3 and Bg2 and do not place a pawn on e4 at all.

Many players might argue with these rules. However, if you look at various openings and their statstics, you will see, it is all true!
A lesson from Larry D Evans from ages ago: the queen is a lousy defender. But always look at the board because “ chess is concrete game” ( say it with a Russian accent).
I have heard this too, IRL from a Swedish GM (Lars Karlsson), even if phrased like "it is more economic to defend with a less valuable piece". I have not read it, but I would be extremely surprised if no famous book mentions it.

In the second position though, I wouldve regarded the overall danger as huge and I wouldve tried to trade queens w Qf3 Qf5 before f3 (and lost)
Exception to the rule: the king can block the opponent free passer better than a rook. However, a king is worth the whole game, whereas you can lose a rook and still play on.

But joking aside, a king has about the same power like a knight or bishop or a king can block 3 connected pawns (if they are not too advanced).
The rule of thumb is that generally you better move pieces up than backwards