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a promise that costs more to enter than to escape.

means A device, scheme, or situation designed to catch, ensnare, or deceive someone who steps into it unaware.

from From Old English 'træppe,' a snare for catching animalsrelated to words for stepping, since a trap is something you tread into. The sense widened from literal animal-catching gear to any clever device or deceptive arrangement that closes around the unwary. The slang for 'mouth' (as in 'shut your trap') is a much later, jokier extension of the same idea: an opening that snaps shut.

venus flytrapCounts to two touches before snapping shut
music genreNamed for the houses where drugs were sold
plumbingThat U-pipe traps water to block sewer gas
chessA losing move that looks like winning
lobsterMost caught lobsters could escape but don't
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