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H. G. Muller wrote on 2019-05-31 UTC

Well, it is difficult to asses whether this capability for a pair to statically create an impenetrable barrier for a King is really important. Actually I think that Wizards can just do it (on 8x8), when standing next to each other in the center. But very often pieces can inflict a 'dynamic confinement' on a King. As long as you have to spend fewer moves to maintain it than the King needs to escape, you have moves to spare for other pieces to approach. Besides, FAD complement each other in a different way: standing next to each other the completely cover a 5x6 area, As a result they can drive a King to the edge with checks, and checkmate it there, without any help. This makes them very, very dangerous.

Even a King + Bishop can dynamically confine a King on boards of any size. The King has to cover the hole through which the opponent threatens to escape, and has to follow the bare King as long as it keeps running in the same direction to renew the escape threat. But when it reverses direction, to try an escape on the other side (which he eventually must, as he bumps into the edge) you have one free move. Therefore a Bishop can checkmate together with an arbitrarily weak piece (as long as that can go everywhere) on boards of any size.


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