[quote=@Disdain]
<Snipped quote by Threads of Fate>

Is there no way that bringing in outside help beyond the Codex will help raise our chances of victory? I don't want to be a gambler, especially not when all of Existence is at stake.
[/quote]

As I said, that falls under improbability.

[quote=@System]
<Snipped quote by Threads of Fate>

At five percent?
[/quote]

... 

At that low, we could just let the two fight in person, which means we have a sixty-seven percent chance of defeating the victor if it's Azathoth, and a sixty-one percent chance if it's Nyarlathotep. Specifically, though, the casualties would be immeasurable throughout all of Existence. Those two don't fight like you or I would. And even then that's assuming that all of their followers of note are outright killed before their confrontation. 

Otherwise... The only other option at that level that would increase our odds is to join one side outright, but then we're picking between two undesirable outcomes. We may as well just join Nyarlathotep and be done with it.