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There's a bug difference between a checkmate THREAT, and a Fool's Mate.
By definition, a Threat is : 'if you don't react accordingly, you're
lost'.

In RNBAQKMBNR , after 1.Mh3, which threatens mate, black is FORCED to
react. There are many ways, like moving a pawn around the King, which is
absurd; or advancing the King's bishop's pawn, which hardly a developing
move; or by 1.. Nh6 which gives white a very early pin, or 1..Mh6 which
leads to a very early exchange of Marshalls.

In Falcon Chess and Omega Chess, the threatened mate is a mate in 3, which
is less forcing than a mate in 2. It's easily refutable by very natural
developing moves that don't offend the sense of a chess player.

In chess, there's the famous Scholar's mate, which actually, with white
playing it, probably gives a weak position for white. While white moves
his queen around, black is developing, leading to a (=+) position.
Responding to 1.e4 e5 2.Qh5 doesn't offend the sense of the chess player
the way the above-mentioned Capa variant does.

A Fool's mate is hardly worth discussion at all.