The first time through, he allied with his brother.
Ozai hadn't always known he was destined for greatness. He had always thought well of himself, as befitted royalty, but with role models like his father and older brother running around, who wouldn't feel a little healthy inadequacy? Still, that all changed when Ozai was fifteen, on the day he first harnessed the power of lightning-bending. He was younger than both Iroh and Fire Lord Azulon had been, the first time he'd done it, and that realization gave Ozai an inkling that he might just be better than everyone else after all.
He dedicated himself to his training, both physically and mentally. He learned the ways of the court and the battlefield, of alliances and death duels. Always, he worked on his lightning. By the time his brother Iroh returned from Ba Sing Se, Ozai could generate the 'cold fire' faster than anyone alive (or even dead, in father's case). The price of that mastery was a certain sense of detachment that Ozai could no longer turn off at will, but he didn't consider that a liability at all.
On the contrary, it quickly became a benefit.
When Iroh arrived back at the palace, the older man was grief-stricken over the loss of his son. Ozai feigned sympathy, and made himself indispensable to his brother. Slowly, he began whispering of vengeance, and a return to greatness. Iroh was equally slow to accept such ideas, due to some set of mysterious scandalous experiences he had on the way home, but as the time came for Iroh to take up the crown of Fire Lord, his old sense of vision began reviving.
One thing could be said for Iroh. Fool that he was, once he dedicated himself to a mission, he put his all into it, and had a subtly effective style.
Even so, it all ended in ashes. On the day of the Comet, as the two brothers went out to incinerate the entire Earth Kingdom with their unmatched Firebending power, they were met by a young Air Nomad who claimed to be the Avatar, surrounded by old masters from across the world. The grumpy Waterbender was an unknown old man, but the Earthbender met descriptions of Mad King Bumi, and Jeong-Jeong and Piandao were of course well known to Ozai.
When it all ended, Iroh was dead, and Ozai stripped of his Firebending by some horrid magic of the Avatar's. He died forty years later, alone in a cell.
When Ozai awoke to find himself fifteen again, he was thoroughly unbalanced, but that did not keep him from re-discovering the lightning, nor from making many of the same mistakes.
It ended no better, the second time, nor the third, despite his best efforts. After the fourth, he realized that Iroh was never going to be strong enough to win.
Ozai had never been quite sure what to think about his wife. Descended from Avatar Roku, with the appropriate distant blood ties to the Royal Family, she should have been the strongest woman in the Fire Nation. Yet, she frequently disappointed Ozai in unexpected ways. The coddling way she treated their children was a perfect example; she just couldn't summon the proper sense of detachment required for greatness.
Still, Ozai didn't have many other choices, when it came to allies. She turned out to be a better killer than he expected, given the proper coaching and motivation, but wound up performing no better than Iroh at the end. That the Avatar had a different set of allies, this time, surprised Ozai. A strong Water Tribe Chief who couldn't bend, a bald but gray-bearded Earthbender with a deep voice and unconquerable spirit, and Admiral Zhao (of all people) united to stop both Ozai and his wife, and then the Avatar stripped them of their bending and locked them away on opposite ends of the Fire Nation.
He should have seen it sooner. Zuko was Ozai's spitting image, and so eager to please. All it took to wipe out that weak streak (undoubtedly inherited by his mother) was the right kind of attention. Even so, Zuko was never much of a Firebender; he never even managed to generate lightning before any of Comet arrivals, despite Ozai's best efforts.
Zuko always died, in the end. Even against the children the Avatar brought against him.
Just as Zuko was Ozai's image with his mother's spirit, Azula was Ursa's reflection with all the killer instinct that her father had been looking for. She was loyal, and powerful, and vicious, and clever. With Azula, after only a few tries, Ozai came closer than ever to winning.
She killed all of the Avatar's allies- the stupid Water Tribe boy who reminded Ozai far too much of 'Chief' Hakoda, the loud blind Earthbender, the self-righteous Waterbender girl, and Zuko.
Of all people.
Despite this, Ozai still couldn't win. The Avatar always defeated father and daughter, and took their bending away, except for the last time. The last time, Ozai had the Avatar at his mercy, injuring him too badly for the Airbender boy to even move out of the way of the final blow, but before he could strike, there was a powerful hit to his back, and a cold pain, and his daughter's ecstatic laughter.
Ozai gave up on Azula, after that.
No, in the end, the problem was clear. No matter how many times he went back to his fifteenth year, and rediscovered the lightning to his father and brother's amazement, he would never find the right combination of allies and actions that would give him the world.
In the end, it was obvious. Why had it taken Ozai so long to realize that he could only rely on himself?
Iroh, Ursa, and Zuko were all ignored; they would never be of any use. Azula became a tool, trained in a regime honed over multiple lifetimes, and then discarded before she could prove her unreliability.
Ozai went alone to burn the Earth Kingdom, and knew that victory was at hand.
The Avatar had come alone to face him.
Ozai couldn't help but smile. He had all the power in the world, and with no one to hold him back, he would surely triumph over this mere boy. This time, there would be no one to save him. The Last Airbender would finally fall.
His destiny was finally at hand!
Afterward, Ozai lay in his cell, once again robbed of his bending. It took many years of thought, but he finally realized the problem. After lifetimes beyond count, he couldn't help but accumulate a little of Iroh's brand of wisdom, and it led him to one inescapable conclusion. One conclusion born out by experiments beyond count.
Ozai was the only common factor in all those failed ploys.
He was the weak one.
He was the failure.
When his life ended, that last time, it was followed only by oblivion.