Good question. The fact is, Accardo had the power to exile Giancana, to murder Giancana, and in my opinion, most tellingly, phase Giancana out and give more and more power to a successor of his choice, Teets Battaglia. Accardo's ultimate power was retaining sole rights to who gets to wear the 'boss' title. Giancana was somewhere between Front Boss and Street Boss. Accardo would have the public believe Giancana was the boss, while in reality he only handled the day to day affairs. Murder contracts had to go through Accardo first, while Accardo was able to order a string of 11 murders without Giancana's say. Something else to consider, Jackie Cerone was Giancana's Underboss, yet in later years he would be part of the plot to murder him, so again, Accardo was at all times the ultimate power.

Just for the record, Giancana earned his promotion because he was a good and creative earner. He took notice of the African-American policy racket and came up with a plan to take it for himself and the rest of the Outfit. Seriously impressed Accardo.