So, at the climax of TTT, Kellhus is down in the depths with his father. The Holy War is locked in its ultimate clash with Fanayal's final army. The Scarlet Spires and the Cishaurim are annihilating one another.
And Conphas is coming up behind the Holy War with a fresh army, and the Imperial Saik.
As we all know, they blunder across Achamanian, and then Saubon rolls up in the confusion and kills Conphas, taking command of the army (and the Saik), and bringing them in on the side of the Holy War.
Fundamentally, this is the conclusion of the battle, as the Saik are the only School left on the field, and they annihilate the Fanim just as they did the Scylvendri at Kiyuth.
The thing I want to point out is...this seems like total luck.
Like, Conphas's downfall is the result of several elements in sequence, each seemingly unconnected to Kellhus's machinations.
1: He splits the Saik up, leaving them unable to defeat a Mandate Schoolman.
2: Akka (owing to his feud with Iyokus) ends up behind the main battle, in prime position to spy the incoming Nansur force and take them on
3: Saubon rolls up immediately after Akka starts throwing down.
If any of those things go differently, the whole thing fails.
If Conphas has the Saik gathered together then they murder Akka, then Saubon.
If Akka isn't present then the Grandmaster of the Saik kills Saubon
If Saubon shows up earlier then the Grandmaster kills him
If Conphas is still in control of the Imperial force then the Holy War is massacred, as a School and an army show up behind it. That leaves Kellhus in a position where conquering the Three Seas seems like a pipe dream, as he is the loathed False Prophet who led the Holy War to damnation, defeat, and death.
So, do y'all think that Kellhus planned the foiling of Conphas and the suborning of his army, or do you think that was just a lucky break (ie: Kellhus doesn't know anything about the Nansur, his plan was just Holy War > Fanim, with him finishing off any Cishaurim who happened to survive)?