I remember encountering the phrase when I was a kid, not knowing the context, not being able to get a satisfactory answer from the adults, and figuring I'd discover it when I was older.
Now it's 700 years later and I'm re-watching the Scorsese film, which is loosely based on the novel of the same name, and realizing I still don't know what the phrase means.
I do have this vague feeling that the phrase pre-dates the novel, but obv could be mistaken.
So, why is this book called "The Color of Money"?
I feel I should explain why I accepted an answer with so few votes in comparison to the others. I don't think I've ever agonized so much over an SE answer.
I think it's a coincidence that both pool tables and currency notes are green. At best a happy one, at worst a superficial one whose obviousness threatens to obscure more meaningful readings. Moreover, the table doesn't have to be the same color as currency for the author to say that a pool hustler looks out over the baize and metaphorically sees the riches he hopes to win on that battlefield.
I think Tevis riffed an idiom that pool gamblers use to demand proof of value because the characters in his story are very concerned with whether they and each other are actually in possession of what is required to make their scheme work. It's all a big gamble built on top of many smaller gambles, and their overarching concern is with the color of their own money, so to speak. And to resort again to hypotheticals, if it were common for gamblers to say "let me heft your coinpurse," I think the book would be titled "The Weight of Coinpurses" or somesuch.
Many thanks to everybody who contributed to the discussion.