My take, for what it is worth!
I believe Roth was not a greedy man, for the Corleones' Nevada properties nor Michael's $2 million [Michael was all set to be murdered New Year's Eve with or without the $2 million] but of course if they fell into Roth's lap, Roth will take it Bonus! and added bonus Michael's own money paying for his own murder
Michael's greed, nearly undone himself with Roth [not just people like Paulie, Fabrizio and Tessio]
Roth only started plotting revenge on Michael when Roth felt Roth had to “gift” Michael
their Hotel, then to stop Michael “making [any] further inroads in Roth's Nevada holdings” and eyeing Roth's Havana business
In fairness to Michael, Roth was stringing Michael along among others “gifting”
their Hotel and pretending “to go along” instead if Roth had been honest perhaps Michael and Roth could have worked out some mutually beneficial arrangement not dissimilar to Roth's Havana business Then both Michael and Roth could live happily for a hundred years!
How'd Michael know it was Roth? I also 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
On the other hand, Michael, who could have used violence or murder against Roth, didn't--he was negotiating for the Havana properties. Roth, on the other hand, set up the machine gun attack at Tahoe, and didn't care if Kay was killed in the attack. Moral of story: No honor among thieves
