When Vito returned home from the hospital, Sonny told him he’d arranged for Fredo to “learn the hotel business” in Vegas. We weren’t told that the Corleones had invested in Moe Green’s hotel. But they did: when Michael met with Fredo in Vegas, he said, “Now Moe Greene will sell us his share of the casino and the hotel so it could be completely owned by the Family.” And he pointedly reminded Moe that the Corleones had “bankrolled” his hotel.

So, when Fredo told Moe to expect a visit from his brother, Moe had to know that Michael was on a mission to buy him out. His response—“I tolk to Barzini. I can make a deal with him and still keep my hotel”—was a threat to Michael. If true, it would mean that Barzini would provide whatever money Moe needed to keep his money-losing hotel afloat, presumably in return for some part of Moe’s share, and with Moe still in charge. That would put Barzini eyeball-to-eyeball with Michael, in the same property, in newly wide-open Vegas—a new battleground.

In the previous scene, Tessio complained that “Barzini's people chisel my territory, and we do nothing about it. Pretty soon there won't be one place in Brooklyn I can hang my hat!” Barzini “chiseling” by opening betting parlors or loan shark operations in Tessio’s territory was one thing. But, Barzini supporting Moe against Michael by buying into Moe’s hotel and enabling Moe to stay in charge was quite another, vastly more provocative, thing, especially since Vito was still alive.

My question: Do you think Barzini actually told Moe he would invest in his hotel and stand against Michael’s move to buy him out and move him out? Or do you think Moe, “headstrong, talking loud, saying stupid things” (Roth in II), was shooting his mouth off and bluffing Michael?

No, I don't think Moe was bluffing. I think he really did make a deal with Barzini.

In the scene with Michael, Moe makes clear that he's very contemptuous of the Corleones in general: "The Corleone family don't even have that kinda muscle anymore..." and Michael specifically: "I made my bones when you were going out with cheerleaders!" Moe could see that a showdown was developing between Michael and the other New York families, Barzini in particular. Barzini was making it clear to Michael that there wasn't room for both of them in New York anymore. Something had to give. Moe could see this. Like Tessio, Moe believed the showdown would end with Michael's defeat and death. This was why he allied with Barzini. Wrong choice. But that's the risk you take in this business.

Moe's and Barzini's opinion of Michael was similar to how Khrushchev viewed Kennedy before the Cuban Missile Crisis--they saw him as a lightweight. Like Kennedy, Michael proved himself equal to the challenge before him.

"I talked to Barzini", was a stupid remark of Moe ("talking loud, saying stupid things”). On one hand he tries to show what a tough guy he is ("made my bones".) On the other hand he looks like a young boy who's "gonna tell my brother".

So, what would Moe be bluffing about? If he wanted Michael to believe that Moe was under Barzini's protection and thi was not the case, Moe would only gain some time, because it was clear that soon Michael or Tom would be able to verify/falsify that statement.

I think, Moe really lost his nerves. He felt his status being attacked by a young man. Same mistake as Woltz. But Moe had no horse to sacrify. Woltz was still useful as a film producer. Moe was skimming off the top. And he was foolish enough to admit it.

Moe was very similar to Sonny in style and temperment. As stated above, Moe took sides with Barzini and in our little plot line we know Michael out-smarted and out-muscled all of them.

I believe Barzini was using Moe for his own gain. Barzini was similar to Michael in his business acumen. Barzini would have kept Moe as an ally. I don't think Moe was looking to expand and conquer. Just give him the casino life and he was happy.

I don't think Moe was bluffing. I think that Barzini and Moe had come to an understanding. As others mentioned Moe would have been incensed that a punk kid (Michael) was coming to Moe's area of expertise and making demands and accusations.

I agree. Moe Green made a stupid mistake. He underestimated the Corleones, figuring that they weren't as strong as they had been some years earlier, and he figured that they were being pushed out of New York. His remark to Michael was made out of some false sense of security (having Barzini backing him).

I believe Moe did tok to Barzini, and I have no doubt that Barzini promised him he could make a deal and allow Moe to still keep his hotel. The "talking loud and sayin stupid things" aspect of Moe exemplified here was his telling this to Michael in thr first place.
I think the more significant question is whether or not Brzini intended to keep his word once he bankrolled Moe. I think he would have moved in on his hotel as well.