What the audience sees is largely just one side of a chess match. I think that until deep into the movie, the Ola-Fredo phone call is the only thing that overtly shows who is on the other side.* I think that all we're left with is that Michael is reading the people around him and has decided on Roth because of the audacity of the attempt, and also because Roth has just made a friendly concession to Michael.

*There's also the bizarre presence of the Senate lawyer with Roth in Havana.