Hoover knew about the Mob,but he didn't go after them because he didn't want his agents to be corrupted by the huge amounts of money that the Families could spread around. He was more concerned with public relations,and so he went after famous bank robbers,kidnappers,auto thefts ,and of course Communists.

He was reputed to have told Frank Costello at the Stork Club,"just stay out of my bailiwick". Gambling busts were not Hoover's priority,and as a result he failed to understand that after Prohibition ended,gambling became a huge contributor to the Mafia's power and influence.

When the Apalachin bust occurred,Hoover had to cover his ass,so to get around having denied the existence of the Mafia for so many years he created a new term. That term was La Cosa Nostra.
Now Hoover could say "Oh no, these weren't Mafia guys that got arrested,these were members of the Cosa Nostra,and of course we've been investigating them for quite a while.

As far as the horse racing,Hoover would get tips on fixed races from Walter Winchell,who got them from Frank Costello,who got them from bookmaker Frank Erickson. Hoover would let himself be seen at the $2.00 window,while one of his agents placed the real bets at the $100.00 window.
Hoover would claim that as a student of horse breeding, he only went to the track when one of his friends was racing a horse that he owned, and he would make small token wagers so as not to embarrass his hosts.