[The Might]

Okay...

"Many that live deserve death. And some that die deserve life. Can you give it to them? Then do not be too eager to deal out death in judgement. For even the very wise cannot see all ends. I have not much hope that Gollum can be cured before he dies, but there is a chance of it."

Seemingly Eru could, as he also seemingly planned the downfall of Sauron carefully.
But did he know what exactly was going to happen or as the Architect in the Matrix was sure that something was going to happen.
The Architect was certain that the desire to save the human race would be stronger then Neo's love for Trinity and he was wrong.
Did Eru think the same way and think that Frodo's desire to save m-e would be stronger then his own greed caused by the Ring?
What if he was wrong? What if Frodo did claim the Ring somewhere else. Would a hand then come out of the sky, pick him up and throw him in Orodruin? Would he give Eonwe a call and tell him it's 'bout that time again? Or would he let the people of M-e to their fate?

I find this quote quite interesting from Professor Tom Shippey:

However, ‘chance’ was not the word which for Tolkien best expressed his feelings about randomness and design. The word that did is probably ‘luck’....to ‘change their luck’, and can in a way say ‘No’ to divine Providence ~The Road to Middle-earth

especially together with these:

'Frodo had done what he could and spent himself completely (as an instrument of Providence) and had produced a situation in which the object of his quest could be achieved. His humility (with which he began) and his sufferings were justly rewarded by the highest hounour; and his exercise of patience and mercy towards Gollum gained him Mercy: his failure was redressed.''~Letter 246

’'But at this point the ’salvation’ of the world and Frodo’s own ’salvation’ is achieved by his previous pity and forgiveness of injury. At any point any prudent person would have told Frodo that Gollum would certainly betray him , and could rob him in the end. To ’pity’ him, to forbear to kill him, was a piece of folly, or a mystical belief in the ultimate value-in-itself of pity and generosity even if disastrous in the world of time. He [Gollum] did rob him and injure him in the end- but by a ’grace’ that last betrayal was at a precise juncture when the final evil deed was the most beneficial thing anyone could have done for frodo! By a situation created by his ’forgiveness’ , he was saved himself, and relieved of his burden."~Letter 181

Eru seemingly thought...'well, I've planned it all, now it's up to you. If you do your best I might give a little push in the end, if not, well then it's your own fault you'll live in a crappy world.'

And so comes his intervention:

"Frodo deserved all honour because he spent every drop of his power of will and body, and that was just sufficient to bring him to the destined point, and no further. Few others, possibly no others of his time, would have got so far. The Other Power then took over: the Writer of the Story (by which I do not mean myself), 'that one ever-present Person who is never absent and never named." - 192 From a letter to Amy Ronald 27 July 1956

All in all, for me it seems that within M-e you can change your luck, you can change your fate in moments as the one mentions above.

Again, Eru does the same thing with Gandalf. After the Valar's plan to overthrow Sauron by sending the wizards fails Eru repays Gandalf for his sacrifice and sends him back to finish the job.

"For in his condition it was for him a sacrifice to perish on the Bridge in defence of his companions, less perhaps than for a mortal Man or Hobbit, since he had a far greater inner power than they; but also more, since it was a humbling and abnegation of himself in conformity to 'the Rules': for all he could know at that moment he was the only person who could direct the resistance to Sauron successfully, and all his mission was vain. He was handing over to the Authority that ordained the Rules, and giving up personal hope of success.

That I should say is what the Authority wished, as a set-off to Saruman. The 'wizards', as such, had failed; or if you like: the crisis had become too grave and needed an enhancement of power. So Gandalf sacrificed himself, was accepted, and enhanced, and returned. [...]He was sent by a mere prudent plan of the angelic Valar or governors; but Authority had taken up this plan and enlarged it, at the moment of its failure."~Letter 156

Okay, so much for how it seems to work in M-e. But what if Tolkien doesn't really like it. Take a look at this:

There are, I suppose, always defects in any large-scale work of art; and especially in those of literary form that are founded on an earlier matter which is put to new uses – like Homer, or Beowulf, or Virgil, or Greek or Shakespearean tragedy! In which class, as a class not as a competitor, The Lord of the Rings really falls though it is only founded on the author's own first draft! I think the way in which Gandalf's return is presented is a defect, and one other critic, as much under the spell as yourself, curiously used the same expression: 'cheating'. That is partly due to the ever-present compulsions of narrative technique. He must return at that point, and such explanations of his survival as are explicitly set out must be given there – but the narrative is urgent, and must not be held up for elaborate discussions involving the whole 'mythological' setting. ~ Letter #246

Interestingly enough, the Professor doesn't mention the salvation of M-e. Isn't this in a way also cheating? Frodo failed and if things worked as in our world the Nazgul would have arrived, would have dealt with Gollum and the hobbits and would have taken the Ring back to Sauron. And all would have lived miserably ever after.
Isn't it somehow cheating that in M-e Eru pops up time and again and does some fine-tuning?

One could of course now argue that such fine-tuning takes place in our world as well, only that most don't see it or don't believe it happens. But that is another story and so I think we should stick to M-e for now.