More fully "one-and-thirty bone ace". A form of the card game thirty-one, in which the third card dealt to each player is turned up, and the player who holds the highest wins a prize, variously stated to be either a counter or the ‘bone’ (that is, half the stake). Also: the ace of hearts or diamonds, designated as the highest card in the game.
Early 17th century; earliest use found in John Florio (1553–1625), author and teacher of languages. Apparently from bone (although this is first attested later) + ace.