When I went to look up the original painting, I discovered there isn’t one: there are lots and lots of them. C. M. Coolidge seems to have made a career out of painting dogs playing poker. This is probably not what his parents had in mind when they named him Cassius Marcellus, but what can you do? A few pictures are especially well known, and A Friend in Need is one of the classics.
Not the rats you were looking for? You may be thinking of the similarly inspired picture by Jin Wicked. It’s a few years younger than mine—but definitely worth the wait!