Green’s Dictionary of Slang

fast one n.

[orig. milit. use, to malinger]

1. [1920s] any scheme seen as amoral, corrupt, underhand.

2. a lie, a spurious story.

In phrases

pull a fast one (v.)

1. [1920s+] (also spring a fast one, pull a fastie, work..., pull a fast switch/shuffle) to get away with something, usu. a slightly nefarious scheme.

2. [1930s] to stage a crime, e.g. a hold-up.

3. [1930s] to make an escape, to run away.

slip a fast one (over) (v.) (also put over a fast one) [orig. used in cricket/baseball ]

[1920s+] to take advantage of someone by trickery, to hoodwink.