For some reason while watching Ocean's Thirteen the one thing that jumped out at me was the repeated reference to shaking of Frank Sinatra's hand. This occurs earlier in the movie during a flashback with both Willy and Reuben shaking Sinatra's hand.
It also occurs near the end of the movie, when Daniel Ocean states to Willy Bank "You shook Sinatra's hand - you should know better."
It's not well-explained in the movie. However, it implies a sort of 'gentlemen's agreement,' an unbreakable code between the members of an exclusive group of businessmen who have been operating in Las Vegas since the days when (Frank Sinatra) was a Vegas performer and a man's word was his bond. The inference is that one does not attempt to fleece another member of the group. Clearly, Bank screwed over Reuben by making him sign over his investment for a small cash payment. Incidentally, Frank Sinatra played the role of Danny Ocean in the original Ocean's Eleven movie.
In part, it was also a nod to Frank Sinatra being an actor who played in the original Ocean's Eleven back in 1960.
Danny Ocean, played by George Clooney, was originally played by Frank Sinatra. Having Clooney say this was not only a reminder of the gentleman's agreement, but also a nod to the late Frank Sinatra who was a major figure in Vegas back in those days.