Was the destroying of the Ring lucky?

[Telcontar_Dunedain]

Some people that I have talked to have regarded the destroying of the Ring as LUCKY. I disagree with this and this is why.

In the chapter Mount Doom on page 922 Frodo says to Gollum

'"Begone, trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire Of Doom"'

Then what happens. Frodo claims the Ring for himself, Gollum bites off his finger and has the Ring. Then he falls over the edge in celebrating that he finally has his precious back.

For didn't Frodo say in The Two Towers

'If I were to put the precious on and command you to cast yourself over the precipice of fire you would do so'

For Gollum was held to the promise he made when Frodo & Sam found him or when he found Frodo & Sam might be more accurate.

'"We promise, yes I promise," said Gollum. "I will serve the master of the Precious. Good master, good Smeagol, gollum, gollum."

What do you guys think. Was it luck or did the command of Frodo and promise of Gollum work against him.