Don’t cross me Spragg. I do not get my info from cards. I get it from the source. Below is a card fax signed by Carter that show the initials G R K Carter. This is a pass for Inaugural Meeting of his dog Track in 1929. The opening of the pier was also that same year and was in full swing when the postcard below also was mailed showing the G as George. I have another source that I can not put my hands on right now that shows Carter operating R. K. Carter's The Saw Dust Casino but the casino on the pier was anything but and the name Billionaire’s Club would make a lot more sense with the name of the pier known as the Million Dollar Pier. Thus the Billionaire’s Club came first.
Carter also ran a casino in the Lummus building known as Carter's Gambling House which was raided and torn down. The only reference to the the pier having a Beach Club I have ever found what on the HUB mold card for the order sent to Leavitt in 1939.

Now let’s look at the Year 1929 on Miami Beach. You had the opening of the Floridian and the influence of Capone on the Beach. And you had the following other gambling Casinos: the Cinema Casino, The Deauville Casino, the Jungle Inn , Club Lido, the casino in the Lincoln Hotel, the Ocean Drive Casino, the Palm Island Club, the Roman Pools Casino, Smith’s Casino and the Beach and Tennis Club (Located on Lincoln Road aka 18th Street). Note the name of the last club running on the beach in that time period Leavitt would not have named his the same but you never know.