1736 Canting Dictionary / D / DOCTOR [thing]
a false Die that will run but two or three Chances. They put the Doctor upon him; they cheated him with false Dice.
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Entry taken from 1736 Canting Dictionary, by Nathan Bailey.
Doctor in the 1811 Vulgar Tongue
Also see examples in Canting Songs and Slang Rhymes collected by John S. Farmer (1896).