“Fast and loose” was the name of an old cheating game, known in the middle of the sixteenth century at least.
The game was thus explained by James O. Halliwell in his Dictionary of Archaic and Provincial Words, Obsolete Phrases, Proverbs and Ancient Customs, from the Fourteenth Century (1847):
“A cheating game played with a stick and a belt or string, so arranged that a spectator would think he could make the latter fast by placing a stick through its intricate folds, whereas the operator could detach it at once.”
In fact, the game must have been known at a considerably earlier period, for the present phrase in a metaphorical sense, to say one thing and do another; to be slippery as an eel; to have loose morals, appeared in one of the epigrams in Totters Miscellany (1547):
“Of a new married student that plaied fast or loose”, i.e., was unfaithful.