Why would Michael think the answer to “finding out who was the traitor in his family” was in Havana -- It was great drama indeed among others -

• Michael turning up in Havana without the $2 million
  Roth's gonna think his relationship with Michael is still good That's the key for him!
  Gotta keep Roth completely relaxed and confident, in their friendship
  No little gift for the President…. That would work!
• totally in the dark Fredo bringing the $2 million over
• Fredo denying knowing old man Roth and Ola
• Brothers having drinks together
• Fredo nearly confessing
• Roth's sixth sense
• Giddy! Fredo slipping up and revealing he is the traitor in the family
  We already knew Fredo is the traitor
• distraught Michael's devastation that the traitor is his own brother and crumbling to pieces
• You broke my heart
• Fredo and Michael, one with trepidation and the other broken-hearted
• Party in full swing but the brothers oblivious to the dancing -- uh -- everything
• No words spoken but what each brother is experiencing -- crystal clear