Much as I love organized crime stuff, I won't use the word "greatest" to describe people who were parasites on society, and who inflicted untold death, hardship and corruption. Instead, my view of the most successful Mafia leaders:
--Carlo Gambino was undoubtedly the most successful modern Don. Never convicted of a crime since the Thirties. Built the largest and most powerful Mob family in the US. Lived modestly, was virtually immune to arrest. De facto Boss of Bosses. Died peacefully (I give lots of weight to that factor!).
--Charlie Luciano: Sicilian-born, but the first truly American Mafia Don. A modern businessman in every sense--in effect, a captain of (criminal) industry. Formed and led the Commission, which, while never as effective as most people would like to believe, was a tremendous innovation and improvement over the "Moustache Pete" era. Reached out to and used (to good advantage) non-Italian gangsters. Even in prison, ruled by force of character. Shortcoming: not low-profile enough to escape arrest, prosecution, conviction and exile.
--Frank Costello: "Prime Minister of the Underworld". Iron hand in velvet glove. Political powerhouse--no judge was made in NYC without "Uncle Frank." Nationwide leader (with Meyer Lansky) of big-time gambling. Only Mafia guy who was seriously interested in Vegas in its early days. Retired successfully and got revenge on his replacement. Died peacefully.
--Tony Accardo: Brought order out of chaos in Chicago after Capone's conviction, Nitti's suicide and Ricca's short-lived transition. Your basic thug who succeeded by recognizing the power of brains, and letting brains overcome violence (but never letting go of violence when needed). Amazingly long reign, which extended even after he "retired." Never let The Law get to first base.

Those were real Mafia guys. Probably the richest, and most all-powerful American gangster was Louis (Lepke) Buchalter. He wasn't a Mafia guy, and he was the only mob boss who died in the electric chair, which disqualifies him (IMO) from my "success" definition. I will post a biography of him in the next few days.


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E nun me mporta si ce muoru accisu...
E s'iddu muoru e vaju mparadisu
Si nun ce truovo a ttia, mancu ce trasu.