Por que o One Ring traiu Isildur?

It wanted to stay hidden until the proper time

Most of this is synthesis on my part, as there are no detailed writings concerning the Ring's intentions.

If the Ring is a mostly dumb object, the answer could be that it não plan ahead: "I am on Isildur's finger, Isildur is not my master, therefore I must slip". It could also have been a random event, as Bilbo mentions that it "might suddenly slip off a finger where it had been tight".

If the Ring is less dumb, it could be that it wants to hide because Sauron is too weak. It only reappears when Sauron becomes strong enough to call for it.

However, if we assume the Ring is inteligente and can make decisions on its own, then we can come up with a couple of reasons.

A Ring of Power looks after itself, Frodo. It may slip off treacherously, but its keeper never abandons it.

^{The Lord of the Rings: The Fellowship the Ring, The Shadow of the Past, p. 73}

Sauron is gone

Sauron's physical form was destroyed at the end of the War of the Last Alliance by Elendil, father of Isildur, and Gil-galad.

Then Sauron was for that time vanquished, and he forsook his body, and his spirit fled far away and hid in waste places.

^{The Silmarillion, Of the Rings of Power, p. 353}

He would not reappear for a thousand years.

It's not clear what would happen if you put the Ring next to his disembodied spirit. Because the Ring is a physical artifact, a body could be required to use its powers. Sauron did bring back the Ring from Númenor in spirit form after the island's destruction, but whether it helped him get a body back is unclear to me.¹

Assuming he can't use it, it is useless for the Ring to immediately try to get back to Sauron. If Sauron poderia use the Ring, then it may be that it doesn't know where he is or how to reach him. In both cases, secrecy would be more important.

Isildur doesn't trust it anymore

Isildur is coming to his senses and wants to give the Ring to the "Keepers of the Three". At this time, this was Galadriel, Círdan and Elrond:

"I cannot use it. I dread the pain of touching it. And I have not yet found the strength to bend it to my will. It needs one greater than I now know myself to be. My pride has fallen. It should go to the Keepers of the Three." [...]

"My King," said Elendur, "Ciryon is dead and Aratan is dying. Your last counsellor must advise nay command you, as you commanded Ohtar. Go! Take your burden, and at all costs bring it to the Keepers: even at the cost of abandoning your men and me!"

^{Unfinished Tales, The Disaster of the Gladden Fields, p. 354-355}

The Ring would slip from his finger minutes later. Getting picked up by an Orc or even being lost in the river would be a better fate than ending up with some of Sauron's most powerful enemies.

Others want to destroy it

There are many people who are aware of Isildur having the Ring. Among them are Elrond e Círdan, two of the most powerful Elves at the time, who urged Isildur to destroy the Ring. The longer the Ring stays with him, the more likely it is that someone will take it and attempt to destroy it. At the time, Mordor is basically destroyed after having been under siege for seven years. The journey to Mount Doom would be a walk in the park.

"But few marked what Isildur did. He alone stood by his father in that last mortal contest; and by Gil-galad only Cirdan stood, and I. But Isildur would not listen to our counsel." — Elrond

^{The Lord of the Rings: The Fellowship of the Ring, The Council of Elrond, p. 319}

It doesn't want to make someone else também poderoso

If Isildur is able to keep the Ring, he could end up being a very powerful man. He is not on the level of a Maia like Gandalf, but he is still a Númenórean at a time when they are at their most powerful: a little more than 100 years before, an armada of ships from Númenór had invaded Valinor.

Isildur being in full possession of the Ring could mean that he would become too powerful even for Sauron, in the event of his return. It also means he would likely become a subject of intense scrutiny from anybody else in a position of power. If knowledge of the Ring and its powers were to become public, it might have even more trouble returning to Sauron.

Why did it wait so long?

The Istari

Sauron is first seen taking a physical form around the year 1050 of the Third Age, a full millennium after Isildur's death. He takes over Dol Guldur in the forest of Mirkood. The Ring might have thought of leaving its hiding place, but the Istari were sent by the Valar at the same time. The Ring might have felt that Sauron was not in a position where it would be safe.

And [Saruman] deemed that the Ring, which was Sauron's, would seek for its master as he became manifest once more; but if he were driven out, then it would lie hid.

^{The Silmarillion, Of the Rings of Power, p. 362}

Indeed, Sauron would wage war by proxy, using the Nazgûl to destroy the northern kingdom of Arnor and capture Minis Ithil, which would become Minas Morgul. In 2063, Gandalf would drive Sauron, who was still only known as the Necromancer, out of Mirkwood. Had the Ring worked its way towards Sauron, it might have been found or perhaps Sauron would not have been strong enough to protect it against the Istari.

Out of hiding

It was only 400 years later, in 2460, that Sauron would come back in strength to Dol Guldur. At the same time though, there was a lot of activity in the Gladden river:

[Saruman] set a watch upon the Gladden Fields; but soon he discovered that the servants of Dol Guldur were searching all the ways of the River in that region.

^{The Silmarillion, Of the Rings of Power, p. 362}

The Ring might have decided that its master was ready or perhaps it became concerned that it might be found by the wrong people. It may have been forced to act quickly. Three years later, two Stoor Hobbits by the name of Sméagol e Déagol would find it.

O resto, como dizem, é história.

^{1 Sauron only needs 100 years after Númenór's destruction to get his new body and fight in the War of the Last Alliance. After losing the Ring, he requires 1000 years to first reappear in Mirkwood as the Necromancer.}

^{I'm not sure why there's a difference, but maybe there isn't actually one: "Sauron was, of course, 'confounded' by the disaster[...] He was attacked by Gil-galad and Elendil before his new domination was fully established." (Letters #211) So it may be that he seria have needed 1000 years after Númenór and that, Ring or not, Sauron generally needs a lot of time to get a new body.}

^{All citations from the Harper Collins editions}

The Ring was trying to get back to its master

It is true that betraying Isildur didn't turn out too well for the Ring and its master, but it would have been hard to predict that at the time.

The Ring wanted to get away from Isildur and so increase the chances of eventually getting back to Sauron. The fact that Isildur ended up dead in the process would also have been considered a plus. But as Gandalf tells Frodo

‘There was more than one power at work, Frodo. The Ring was trying to get back to its master. It had slipped from Isildur’s hand and betrayed him; then when a chance came it caught poor Déagol, and he was murdered; and after that Gollum, and it had devoured him. It could make no further use of him: he was too small and mean; and as long as it stayed with him he would never leave his deep pool again. So now, when its master was awake once more and sending out his dark thought from Mirkwood, it abandoned Gollum. Only to be picked up by the most unlikely person imaginable: Bilbo from the Shire!

‘Behind that there was something else at work, beyond any design of the Ring-maker. I can put it no plainer than by saying that Bilbo was meant to find the Ring, and not by its maker. In which case you also were meant to have it. And that may be an encouraging thought.’

_{The Lord of the Rings - Book I, Chapter 2: The Shadow of the Past}

So the Ring did something that it seemed should further its goals, but in fact did not. And "some other power" influenced that decision. Gandalf doesn't name this other power, but refers to it more than once. I have always assumed it was Eru, although it could have been one of the Valar (perhaps Manwë).

Depending on which version of the death of Isildur you accept, it could be the ring knew it was at risk.

Unfinished Tales tells us that Isildur repented of his taking of the ring and intended it to go to the keepers of The Three.

‘Alas, it is not, senya. I cannot use it. I dread the pain of touching it. And I have not yet found the strength to bend it to my will. It needs one greater than I now know myself to be. My pride has fallen. It should go to the Keepers of the Three.’

^{Unfinished Tales | Disaster of the Gladden Fields}

This version then fits in with the idea that the ring knew it was a risk and left. It also makes Isildurs escapar a more noble reason.

Because staying with Isildur would be risky.

Yes, the ring is slowly corrupting one of the most powerful people, but it is a very bad time for the ring: Sauron is at his weakest point in history.

Sooner or later someone would notice that Isildur is acting strange and either would persuade him (or more probably use force) to drop it down Mt. Doom. And if the ring falls down the river... Well, the ring is patient, its master needs time to regain his strength, so hiding in the river until everyone forgets about its existence is a quite smart thing to do.

Maybe it just really didn't like Isildur.

It does have some desire to get back to its master, but the time when it intentionally left Gollum was "when its master was awake once more and sending out his dark thought".

At the time we are talking about, basic malice and revenge may have been the bigger consideration:

There the Ring betrayed him and avenged its maker, for it slipped from his finger as he swam.

^{The Silmarillion, Of the Rings of Power, p.354}

Sauron had no army ready at that time. And the ring was in the hands of the king. Signs of the influence of the ring on his human mind had already shown and it probably wont take long before Isildur would become a dictator of some sort. (See also the influence on Galadriel: "In place of a Dark Lord you would have a Queen!")

Adding the added longevity of Isildur it won't take long before people would understand that the ring is causing this. Which would probably lead to a risky war in winch the destruction of the ring would be the main goal. Better to go unnoticed until there is some defense layer at mount doom.

If you subscribe to this idea, it's quite a simple explanation, really: The Ring has a part of Sauron's soul inside it. Therefore, one could say that the ring is Sauron. Perhaps the ring achieves a mind of its own, but then again, if you split your soul into two different parts, would it still be connected into one soul or would each piece become its own psyche as each experiences two different existences at the same time? Yep, very philosophical when it comes to that. But nonetheless, the Ring is part of Sauron, and one could say that the reason why the Ring chose to fall off is perhaps because Sauron saw it fit. Why didn't the Ring stay with Isildur because he "saved" it? Well, Sauron isn't the kind that thanks people. He's out for himself; if you do something "nice" for him, don't expect something back. Besides, technically Isildur didn't "save" the Ring, his mind had already been somewhat corrupted by it; thus Sauron manages to indirectly save ele mesmo mais uma vez.

Also, Sauron is technically not, per se, the Ring's "master" (even though by referring to Sauron as its master skips some confusion in the long run... well, if you think of it, is your soul the master of your body? Technically. That's when things start to get weird and off topic. Anyway): he is the Ring, the Ring is Sauron. The Ring has influence and the ability to persuade because the part of his soul that Sauron put in the Ring contained most of his persuasion (which is more or less how it gets into peoples' minds- Sauron was able to trick entire populations without even touching them, so he has the capability). I'm fairly certain that there are quotes about this in some of Tolkien's books, but I admit that it's been a while since I've read them, but I vaguely remember this since I started writing about Sauron and the Ring in a paper, then scrapped the idea and analyzed Melkor, Feanor and Maeglin instead...

Sauron's Will is in the Ring. His WILL wanted to destroy any and all that wanted the Ring, and to be with Sauron and Sauron alone. His WILL is what made the Ring come off. "Letting" Bilbo come into possession was a way out of Gollum's cave, and then on it's way back to Sauron. To me the Ring isn't really "thinking" so much as the will wanting it's own way.