## Digression: Second Thoughts: What About Pinning Power?

"More directions means more forking power", I said in the previous section. What About Pinning Power?

The calculation we've been using for the mobility of runner pieces assumes that their influence ends where they are blocked. But if you have a Pawn on a2 and a Rook on a1, does the Rook really have no effect on a3?

Runners can pin pieces, and of course there are variations on the pin (one is often called the x-ray attack or skewer attack), variations of attacking more than one piece with a unidirectional move; the point is always that one piece is directly attacked, but if it runs away the piece behind it will be attacked instead.

Runners can also give discovered check, where a friendly piece that's blocking an attack moves away. Again, it's the same principle of finding two targets lined up.

Perhaps the Queen is more valuable than the separate Rook and Bishop for some other reason than her greater forking power (as per the previous section), and perhaps forking power is no stronger than the pinning powers of the Rook and Bishop.

If you have a Pawn on a2 and a Rook on a1, does the Rook really have no effect on a3? Well, let's see.

A Rook on a1. With the usual 70% chance of a square being empty, we see that a2 has a 30% chance of being occupied, half of that friendly, half the friendly pieces are Pawns (on average...).

If there's an enemy piece on a2, there's nearly a 50% chance that it's subject to some sort of pinning attack (88% of the time, there will be some other piece on a3, a4, a5, a6, a7, a8; half the time, that piece is friendly; once in awhile, a piece is pinned against an empty square by something like Ra1-a8 mate).

If there's a friendly piece on a2, there's nearly a 50% chance that if it can move away it will unmask a discovered attack from the Rook.

If there's a friendly Pawn on a2, there's a large chance that it can advance and profit from the Rook's support.

If I had some time, I could try to calculate the Rook's indirect influence on the squares beyond it. Meanwhile, I think this offers another explanation of why the R3 is weaker than its mobility.

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