Not just gambling, but prostitution and narcotics. There is a long history up till after WW2. The real Racket boss was actually Warren Diamond, who was a mentor to Binion, that committed suicide in 1933, which allowed the Italians to gain more in the gambling scene. Diamond empire fractured.
Back on Binion. He split from Diamond in 1926 or 1927 and joined Salvatore Lopiparo son of Tony, and Ray Laudermilk to start up Southland Hotel which was owned by Sam Maceo of Galveston, with Tony Lopiparo overseeing it. This also about the time that he started to have a solid friendship with deputy sheriff Bill Decker which would lead him to having a friendship with Sheriff Schmid. Sam Murray was a former Diamond Lieutenant who operated on his own and was left alone. This act is said to have started the hatred between Binion and Joe Civello. Finally Murray started to muscle in on Binion's and the Dallas mobs number rackets. So Binion sent Ivy Miller a new face to dispatch Murray. This murder would set off a war in Dallas. Herbert Noble who was Murray Bodyguard would eventually take over Murray rackets after two more killings, was able to get Ray Laudermilk to switch to his side. When Laudermilk was killed the war stopped when Noble discontinued his Policy games. After that Binion became the top gambling boss in Dallas. During WW2, he moved in on Fort Worth and gave free rent to the gamblers of the city. Near the end of WW2, Chicago was interested in Dallas and used Big Phil father of Joe Civello to start the ball rolling. Binion did not like it was pouring money to both the Sheriff and DA races. When he his choices lost, he moved to Las Vegas. There he met Bugsy, Bones, and other Jewish gangsters that would eventually lead to him meeting New York, Cleveland, and Detroit higher ups in LCN. He met with David Berman after Bugsy was killed, weather it was an approach to run the Flamingo or not is unknown. Binion would meet Frank Costello who helped start up The Horseshoe with Binion doing as he pleased as long as he kicked up tribute, the casino had Genovese, Cleveland, and Dallas interests in it. Binion and Costello got along well, but Binion and Nobles fued stopped Costello from pumping money to Texas gambling operations.