Shady games that separated suckers from their money spawned this expression. At 16th-century English village fairs, unscrupulous game operators would coil a belt on a table in such a way that a gullible player believed he could stab it with a skewer as it was unrolled. But the operator would pull the belt from the table before it could be pierced. The belt was not really fixed, or fast (as in "held fast"). It was loose. Nowadays, any trickster or con man who winks at principles can be described as "playing fast and loose," whether it's at the carnival, the office, or elsewhere.
This temporary state of confusion or disorder has its roots in a poorly plowed field. In ancient Rome, it was considered important that the lira, or furrows made by a plow, be straight and regular. A careless farmer who deviated from the straight line was said to be delirare, or off track. In the same way, a delirious person has thoughts that deviate from a straight line of thinking.
SOURCES: 'The Encyclopedia of Word and Phrase Origins' by Robert Hendrickson; 'Why You Say It,' by Webb Garrison; 'A Dictionary of Contemporary American Usage' by B. and C. Evans; 'The Story Behind the Words' by Morton Freeman.