The Black Mage Rotations

[PessimiStick]

So rather than do a ton of trials to weed out RNG, I figured we can just theorycraft this since it's pretty straightforward.
I'm going to ignore the cast time of the initial F3 here, and assume F3 is always cast from UI3
Hardcast F2 = 1.2 GCDs
Hardcast Flare = 1.6 GCDs
Everything else is 1 GCD to cast

Rotation #1: F3 --> Flare --> Transpose --> B2 --> B2
1 + 1 (doubledip) + 0.7 (average time you expect to wait for a mana tick after transpose -- 1/2 GCD + transpose animation delay) + 1 + 1 = 4.7 GCDs
220s * 0.7 + 260 * 1.8 + 0 + 100 + 100 = 154 ST and 668 AE Potency
32.8 ST P/GCD, 142.1 AE P/GCD

Rotation #2: F3 --> F2 x3 (this is what I can always cast) --> Flare --> Transpose --> B2 --> B2
1 + 1 (doubledip) + 1.2 + 1.2 + 1.6 + 0.7 + 1 + 1 = 8.7 GCDs
154s + 180 + 180 + 180 + 468 + 0 + 100 + 100 = 154 STP and 1208 AEP
17.7 ST P/GCD, 138.9 AE P/GCD

Pure Flare seems to be the clear winner, plus you get cooler animations.
Also, for the purposes of WP, rotation #3: F3 --> Flare --> B3
1 + 1 + 0.5 + 1 = 3.5 GCDs (The 0.5 is from the expected time for a mana tick from Mage's Ballad so that you can cast B3)
154s + 468 + 154s = 308 STP, 468 AEP
88 ST P/GCD, 133.7 AE P/GCD

In order for this to be better than Rotation #1, you'd need to have Ballad tick in less than 0.3 GCDs. I don't actually know whether that's realistic or not, would require a LOT of in-game testing with video/stopwatch, since I don't think the Combat Log has enough granularity to tell otherwise (if mana gain is even shown).