1590s, "pledge as a forfeit to another who makes a similar pledge in return," originally in the argot of petty criminals, a word of unknown origin; see bet (n.), which appeared about the same time. Intransitive sense of "lay a wager" is from c. 1600. Used since mid-19c. in various American English slang assertions (bet your life, 1848; bet your boots, 1856; you bet "be assured," 1857, identified in Century Dictionary as "originally California slang").
1590s, "the mutual pledging of things of value to be won or lost based on some future event," appearing simultaneously with the verb, originally in the argot of petty criminals, a word of unknown origin. Perhaps a shortening of abet or else from obsolete beet "to make good" (related to better). The original notion is perhaps "to improve" a contest by wagering on it, or to encourage a contestant. Or perhaps the word is from the "bait" sense in abet. Meaning "that which is wagered" is from 1796.