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Modificications for Three-checks Chess Variant

This topic is for the discussions regarding
"Modificications Required for Three-checks Chess Variant"

Here in the following game, played with
Stockfish AI level 3 (1500)
en.lichess.org/MwZMdoSi/black#68

after 34. ... Qxg5 the engine shows #-8
indicating mate in 8.

Would it not be sufficient for the engine
to say "black wins soon" for
we need to check only three times
without burdening
ourselves for mating the king for this is a game of
"Three-checks Chess Variant"?
In 3 check, #X refers to either checkmate or winning by 3 checks, as you would see if you followed the line to completion
#1 How would that work if your opponent has a choice between either getting mated or getting three-checked?

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