bet: [16] Since its comparatively late arrival, bet has ousted the earlier lay, wager, and game as the main term for ‘risking money on an uncertain outcome’ (gamble is later still). It is by no means clear where it came from; the usual explanation is that it is short for the noun abet, in the sense ‘instigation, encouragement, support’ – that is, one is giving one’s ‘support’ to that which one thinks, or hopes, may happen in the future (abet itself comes from the Old French verb abeter, and is related to English bait).
It first appears in Robert Greene’s Art of Cony Catching 1592, which suggests an origin in the argot of smalltime Elizabethan criminals. => abet, bait, bite
1590s, as both a verb and noun, in the argot of petty criminals, of unknown origin; probably a shortening of abet or else from obsolete beet "to make good," from Old English bætan "make better, arouse, stimulate," from Proto-Germanic *baitjan, in which case the verb would be the original. The original notion is perhaps "to improve" a contest by wagering on it, or it is from the "bait" sense in abet. Used since 1852 in various American English slang assertions (compare you bet "be assured," 1857). Related: Betting.