Green’s Dictionary of Slang

a member of the poorest class of gamblers.

1859, 1860		Hotten Dict. of Modern Sl. etc.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 450/1: But the Little Nick is what we call only ‘brown papermen,’ low gamblers – playing for pence.
1873		Sl. Dict.
1936		H. Corey Farewell, Mr Gangster! 277: Brown paper man – a cheap chiseler.