My take, for what it is worth!

Roth undoubtedly wanted Michael dead soonest but blinded by revenge, Roth outsmarted himself with the Tahoe shooting plan and messed up big time!
Originally Posted by Turnbull
Conversely, Michael saw very soon that Roth's prize was to hold onto his Havana empire and, over time, take over the Corleones' Nevada properties through his hold on Fredo and the almost certain chaos that would follow Michael's death and the struggle for succession. As Michael said to Fredo in Havana, "He thinks he's going to live forever."
I believe Michael understood that whilst Michael was Roth's successor, the heir apparent, Roth was always going “to hold onto his Havana empire” until Roth's retirement or death and at the time, Michael would inherit Roth's interests in the Havana operation

Hence
Anybody kinda rooting for Roth to beat Mike?
Originally Posted by Turnbull
On the other hand, Michael, who could have used violence or murder against Roth, didn't--he was negotiating for the Havana properties

I doubt Roth would want “his hold on Fredo” to get around, incriminating Roth in the process
Besides Fredo would have been totally in the dark about “the Corleones' Nevada properties” and a liability even if Roth wanted to “over time, take over”

I now believe Roth was not a greedy man, for the Corleones' Nevada properties nor the $2 million but of course if they fell into Roth's lap, Roth will take it Bonus!

Michael was disgusted with himself how he hadn't seen through Roth's deceit including Roth's blessing! for Michael moving Klingman out and taking over their hotel - Roth “acts like I'm his son -- his successor -- but he thinks he's gonna live forever and he wants me out”
Originally Posted by Turnbull
So, I'm guessing, he zeroed in on Roth during the train ride. He called on Pentangeli, I'm guessing, to put him to a final test--asking him to stick his head in the lion's mouth by meeting with the Rosatos. Once Frankie agreed, Michael was convinced it wasn't Frankie--it was Roth
I acknowledge it is guessing scenario however I believe Frankie was never a contender that Michael never thought Frankie had anything to do with the Tahoe shooting

I believe, the reason Michael sent Frankie to the Rosatos' meeting was to continue to appease and string Roth along including Michael had not twigged, it was Roth all along and also to find out the traitor in the family not “to put him [Frankie] to a final test” nor Michael needed to be “convinced it wasn't Frankie”

Sure thing Turnbull Michael initially believed it was someone inside, telling Tom “They [Tahoe assassins] are dead already, killed by somebody close to us – inside” it seems neither Pentangeli nor Roth were even suspected?