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Isn't the deus ex machina (used in Greek plays) the fall into Sammath Naur, in regards to Gollum? Don't some believe that it's the hand of Eru who gives him the nudge over the edge?

Today, being of different opinion, I think that Gollum is not nudged, and that Eru played no overt part in it. Gollum is a rogue, meaning, to me, the element of chaos. Good and evil can be balanced, yet every now and then the pot needs a good stir, some tension, to bring forth something new. Bilbo possessed the Ring, but did not follow Frodo. Sauron desired the Ring, yet did not search for it himself and thought more of war than just finding the Ring ("I'll crush the islands of Free Folk then continue the search."). Very unmoved - inactive - and very orderly and structured, respectively.

Gollum, though old, decimated, starving, tortured in mind and body, still goes after the Ring. He plays both sides, good and evil, and even has two personalities, but what joins them is the chaos.

What a show for Eru! It most likely sat on the edge of it's seat, waiting to see how the dice would come up. Frodo could not destroy the Ring; the Wise knew or at least suspected that. Would Sauron be able to get the Ring from Frodo? Surely he would - there's no betting on that outcome. So we have Gollum, who if he gets to Frodo sooner (i.e. with Shelob), the Dark Lord might recover the Ring and all is lost. If he gets to Frodo later, Frodo puts him down before he strikes (and still all is lost). but if Gollum goes after the Ring, like he does, when Frodo is still admiring himself, there's a chance that Gollum will succeed, lose, destroy the Ring (with or without destroying Frodo), etc. The outcome is less certain and therefore more interesting.

Ah chaos. Gollum could play either side, and more likely neither side, as he was neither good nor evil, but somewhat unique. The dice were tumbling, and how will they land?

Afterwards, when Gollum reclaims the Ring yet falls off the edge (chaos makes poor choices as well as better choices - at random), the game is over. Eru, pickled pink by the great show, sends the Eagles as a 'thank you' to the players Frodo and Sam.

Hope that this makes some sense.

Gods who know what will be must get bored.