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H. G. Muller wrote on 2008-11-09 UTC
David Paulowich:
| There may be some forced checkmates that involve a Bison leaping 
| over one of the Kings, but I assume that a Falcon can still force
| checkmate, possibly taking a few moves longer.

The patented Falcon is actually 100% equivalent to the Bison in the KBiK end-game, because of its multi-path character. No Falcon move can be blocked on a single square; at least 2 blockers are needed. But the blockers wil then always have to be on adjacent squares, and two Kings a never do that. So KFK can be played aexactly as KBiK.

In end-games with more than 3 pieces this is no longer true, and a Falcon might be weaker than a Bison. In KQKBi, KCKBi and KAKBi this is of no importance, as they are aready lost for the Bison, and can only be more lost for the Falcon. KRKBi is a dead draw, and downgrading the Bison to a Falcon does not change that: KRK is only marginally won, and only by virtue of zugzwang. Any extra piece for the defender spoils the zugzwang, and thus make the K+R attack on K unsuccessful. And a Bison is far too agile to be hunted down by K+R. Even KRKN is almost always draw because K+R cannot get a Knight. The other way around, a Rook can defend quite easily against Bison by cutting off the opponent King from your own.

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