Paulie directly and Tessio indirectly betrayed Vito

Paulie was a buttonman, not a capo.

Tessio indirectly betrayed deceased Vito by directly betraying the living Michael?

T
You could say that. Tess disobeyed Vito's command (in the fishtank scene) to "be a friend to Michael." But, he waited until after Vito died to make his deal with Barzini.

Michael's no betraying like Paulie and Tessio

Don't know Turnbull I reckon he went straight to Barzini from the fishtank scene and made his deal before Vito died

Michael's Frankie Pentangeli and Willie Cicci betrayed Michael but they showed cause!

I too believe Tessio had made his deal with Barzini when Vito was alive
Barzini and Michael's meeting to straighten any of their problems out! was already arranged before Vito's funeral

Breaking the peace?
What is our take if Vito hadn't died when he 'conveniently'! did?

If Michael would have still gone ahead with the Great massacre, Tessio-Barzini deal / Barzini-Michael meeting becomes moot and Tessio is off the hook....

Vito was expecting Barzini-Michael meeting to take place regardless of whether Vito was alive or not? Vito to Michael: Garden scene

Tess may have decided at the fishtank scene that he would go against Michael because he thought Michael was soft on Barzini. BUT: Barzini didn't make his move against Vito--he waited until after Vito died. I think Tess probably contacted Barzini right after Vito died, and cemented his plan (a meeting with Barxini where Michael would be "safe") at the burial.

Certainly Vito was expecting Barzini to move against Michael, but not him (Vito). Barzini figured Michael was weak, and would be weaker without Vito's guidance and counsel. That's why he waited until Vito died before he made his move--and why I believe Tess didn't approach Barzini right after the fishtank scene (see above).

Here's the thing though if Vito hadn't died when he 'conveniently'! did?

Are you saying Tessio-Barzini deal / Barzini-Michael meeting were all arranged and cemented only between Vito's death and funeral

Barzini didn't wait until Vito died before He moved against him when he was alive
1. sanctioning killing him
2. killing Sonny
3. car bomb attempt on Michael
4. chiseling Tessio's territories
5. backing Moe Greene

Maybe so but they didn't set him up to be murdered

I'm surmising that Tessio had made up his mind not to go with Michael after the fishtank scene. I don't believe he would have approached Barzini with a plan until Vito died. Tess may have had scruples about loyalty to Vito. He may have hoped that Vito might still take his side and influence Michael. Or, more likely, Tessio, "always smarter," would have seen that it would be dangerous to approach Barzini before Vito died--what if Barz thought it was a plot by Vito (a la Luca/Tattaglia) to suss out Barz's intentions? An approach after Vito died, with "weak" Michael in charge, would be less suspicious.

1,2 and 3 all happened before the Commission meeting and the peace agreement. 4 was not covered by the peace agreement. Nor was 5, if it was even true that Moe "talked to Barzini."

Good point about before and after events of the Commission meeting and the peace agreement

As regards Tessio-Barzini plot (a la Luca/Tattaglia) would Vito be "ridiculous" and “incredibly stupid” again?! Surely not!
[borrowing from waynethegame Ref: Michael and Pentangeli's conversation]

and "always smarter," Tessio should have had more faith in his Don and "be a friend to Michael."
[borrowing from mustachepete Ref: Corleones destiny “Characters have to be credited with free will” to mess up! “or there's no story to tell”]

As such, Tessio's betrayal was pivotal in the massacre....All the other Dons were completely relaxed and confident that Michael was on his way to his death and were going about their routine as normal and made fairly easy targets for Michael's men
They were all taken by surprise as the Corleones had intended Perfect!

Tessio didn't have Michael's brain -- uh -- for big deals

Michael immediately quizzed Tessio “You talked to him”? [Barzini] when Tessio told Michael at Vito's burial, Barzini wants to arrange a meeting to straighten any of their problems out....

Tessio/Barzini meeting

Therein lies the issue?

Any move against Michael after their "Commission meeting and the peace agreement" is a move against Vito unless Barzini "waited until Vito died before he made his move--"

However neither Tessio nor Barzini could have 'known' when Vito will die even with "The Godfather's sick, right"?

I don't want anything to happen to him [Michael] while his father's alive!

This is a fascinating question and I don't know if it has been fully answered.

As Turnbull noted, the blatant acts of hostility occurred before the Commission Meeting. The acts that occurred after were not direct violations of the peace agreement.

So what would have happened if Vito had held on for another 10 years? His death was not seen as imminent, so for all anyone knew, that was a realistic possibility.

I could see Barzini continuing to chisel away at Corleone territories and assets in such a way that is not an outright violation of the agreement, but would try to get the Corleones to retaliate in a way that is a breach. Then all other families would join Barzini in outright war.

Of course, if I could see Barzini's gameplan, then Vito and Michael would too, but what could they do to stop or counter it?

I reckon not a lot in their weakened state and they could be annihilated or perhaps call for help from their friends in the business like the Molinari Family

They can win!

Clemenza and Tessio's crew were full strength, Rocco's secret regime even if it was not up to the desired level at that time, it is still extra, in addition to their existing muscle

I believe there is a lot the Corleones can do to "stop or counter" and win the Gangland war against even combined Barzini and all the other families

• Barzini outed himself as the puppeteer in this Sollozzo business and Sonny's murder, at their Commission meeting – not a smart move!

• Tattaglia is a pimp

• Cuneo and Strachi small potatoes

Obviously the “outright war” throws a spanner in the works regarding the Baptism massacre because the surprise element is lost and the Corleones' acting weak / weaker cover is blown

I might add, I can't see the Corleones asking the Molinari Family [or any other friends] for help
The Corleone pride, like they can't fight their own battles / war

What's our answer gonna be?

I don't want anything to happen to him [Michael] while his father's alive!

The timing of Vito's death was convenient to the script. But, I'm guessing that Barzini would have continued to wait until Vito died to move against Michael. I think he underestimated Michael, and believed that Vito was still in charge--the power behind the throne--and he didn't underestimate Vito. He may also have been mindful of Vito's threat at the Commission meeting that if anything happened to Michael, "that, I could never forgive." (Yes, that threat applied to interference with Michael's return to America, but Barzini might have feared Vito's revenge for any lethal move against Michael). I also infer that Barzini didn't have to rush to kill Michael because he seemed to be doing just fine, chipping away at Corleone territories just short of provoking retaliation. In his mind, he could afford to wait until Vito died, and "weak" Michael was deprived of Vito's council.

Sure thing Turnbull whilst “Vito's death was convenient to the script” Barzini can't afford “to wait until Vito died [not knowing when?!] to move against Michael” giving precious time to the Corleones to rebuild eg: Rocco's secret regime and get ready for battle
Gotta get Michael or Vito? That's the key for Barzini but Barzini was "chipping away at Corleone territories" small potatoes

It was pretty much common knowledge that -

Fish tank scene [private]

Moe Greene meeting [public]

The longer Barzini waited as Tattaglia said at the Commission meeting “as time goes by and his [Vito's] position becomes stronger....

Barzini and Tessio were slippin' and certainly underestimated Michael indeed - “weak” civilian Michael, killed Sollozzo and McCluskey single handed when “nobody has ever gunned down a New York police captain Never”!

As you always say [or similar] Trilogy theme – underestimating / overestimating Their Achilles heel

another fascinating question Why not get Vito?

People. The word is "counsel"

How to lure him out of the mall?

Evita, you know you surprise me -- if anything in this life is certain -- if history has taught us anything -- it's that you can kill anybody

Underestimating / Overestimating Trilogy theme

If Tessio had succeeded

Whilst Carlo is not in the muscle-end of the family....

Smug Carlo could have run to Barzini gloating that the Corleones have no idea it was Carlo who helped Barzini, set up Sonny's murder
The Corleones are fleeing to Nevada and Carlo's gonna be Michael's right-hand man The inside man, for Barzini

Barzini might, he just might....buy Carlo-Tessio-Barzini deal / Barzini-Michael meeting

The only Don material Sicilian member of the family Don Carlo!

Barzini wanted only one thing from Carlo: Set up Sonny to be killed. He wouldn't need Carlo after that.