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SKA: I think one kind of strategy is to kill your player's king fast enough to win.
Right, as opposed as the strategy of say, Logic, where the strategy is not to be fast enough to win. Sorry, but "achieve the goal of the game fast enough to win" isn't strategy - that's what the game is about.
As whether or not Behemoth has a mate, that depends on your definition of mate. If you define mate as "a situation where the player is in check, and the player does not have a move to get out of check", then, sure, Behemoth does have a mate. I don't really know how else to define mate.
Could you care to elaborate on the There are so many ways to win? Person mention a handful?
(kaŝi) Se interesas vin la progreso de turniro en kiu vi ludas, vi povas diskuti pri ĝi kun viaj kontrauŭloj en la forumo de la turniro. (HelenaTanein) (Montri ĉiujn konsilojn)