The card game they are playing is named "Baccarat". It is also the same card game in the introduction of James Bond (Sean Connery in Dr. No).
"The Man Who Broke the Bank at Monte Carlo" (originally titled "The Man that Broke the Bank at Monte Carlo") is also a popular British music hall song published in 1891 by Fred Gilbert. The song remained popular from the 1890s until the late 1940s, and is still referenced in popular culture now.
Final film of Shirley Aaronson.