Nelson Algren (1909-1981) wrote about this advice in A Walk on the Wild Side (1956):
 
“Never eat at a place called Mom’s. Never play cards with a man named Doc. And never lay down with a woman who’s got more troubles than you.”
 
“Never play pool with a guy named Fats” is often assumed to Algren’s, but it’s not. “Minnesota Fats” was a pool player in Walter Tevis’s fiction The Hustler (1959). The musician and actor Tom Waits probably invented the line when he said in an interview in 1979:
 
“Never sleep with a girl named Ruby, never play pool with a guy named Fats.”
     
 
Google Books
Saturday Review
Volume 49
1966
Pg. 206:
Actor Bob Lieb says that when a show is on the road he always follows ancient thespian law: “Never play pool with a man named Slim,” and “Never go out with the character woman.”
 
Google Books
Hollywood Tragedy
By William H. A. Carr
Greenwich, CT: Fawcett Publications
1976
Pg. 104:
“Never eat at a place called ‘Mom’s’; never play pool with a man called Pops; and never go to bed with anyone who’s got more troubles than you do.”
 
Media Burn
Tom Waits 1979
“Never sleep with a girl named Ruby, never play pool with a guy named Fats.”
Hear this and more advice from Tom Waits in this 1979 video shot by Chicago-based filmmaker Phil Ranstrom in Carbondale, IL.
 
19 August 1999, Daily Herald (Chicago, IL), “College-bound sons offered advice—free” by Bill Page, sec. 1, pg. 20, col. 5:
Never play pool with a man named “Fats” or poker with a woman called “Ma.”
     
Google Groups: alt.politics.bush
Ashland Henderson
11/21/02
> Never eat at a place called Mom’s, never play cards with a man named Pops,
> and never believe anything you read from the Washington Times…
Right on. Don’t forget to never play pool with a man named Fats either.
 
26 December 2003, Chicago (IL) Sun-Times, ‘Astrological Forecasts for 2004—Pisces” by Georgia Nicols, pg. 24:
(And never play pool with anyone named Fats.)
     
Harmony Central Forums
muel
02-22-2010 08:45 PM
I think it was Tom Waits who said “Never play pool with a man named Fats, poker with a man named Slim, or sleep with a woman named Ruby.”
   
The Huffington Post
Never Have an Affair With…
Susan Silver
Posted: 11/15/2012 11:31 am
You know those old sayings, “Never play cards with a guy named Doc,” “Never play pool with a guy named Fats” and “Never eat at a place called ‘Mom’s’”?