1839, American English, poker term, perhaps from Dutch bluffen "to brag, boast," or verbluffen "to baffle, mislead." An identical word meant "blindfold, hoodwink" in 1670s, but the sense evolution and connection are unclear; OED calls it "one of the numerous cant terms ... which arose between the Restoration and the reign of Queen Anne." Extended or figurative sense by 1854. Related: Bluffed; bluffing.
"broad, vertical cliff," 1680s, from bluff (adj.) "with a broad, flat front" (1620s), a sailors' word, probably from Dutch blaf "flat, broad." Apparently a North Sea nautical term for ships with flat vertical bows, later extended to landscape features.
1844 as an alternative name for poker; from bluff (v.). As "an act of bluffing" by 1864.
Expose someone's deception, invite a showdown, as in I don't believe they have enough capital; I'm going to call their bluff. This term comes from poker, where bluffing (pretending) that one has better cards than one's opponents is an intrinsic part of the game, and calling someone's bluff means forcing them to show their cards. By the late 1800s it was being applied to other enterprises. Also see show one's hand.