Why did Frank Sinatra play the Villa Venice

Just before Christmas in 1962, Frank Sinatra, Dean Martin, and Sammy Davis jr., aka The Rat Pack, did a week-long engagement at a Northbrook, Illinois supper club called the Villa Venice. Outfit boss Sam Gianacana was the hidden owner of this high-end club. Why did this famous group play this unknown club in suburban Chicago for free? And what was going on in the Quonset hut in the rear?
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