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They actually get 24 skills but 6 of them are redundant (Fire/Ice/Thunder 1 and 2) and 3 of them are from the Archer class that give a physical power booster, a physical accuracy booster and a threat reducer for physical damage. So, that brings us to the following 15:
|Transpose||4||Buff Switch||12 sec|
|Surecast||8||Interupt Prevention||30 sec|
|Sleep||10||Single Target CC||2.5 sec|
|Scathe||15||Instant DD||2.5 sec|
|Swiftcast||26||Next Spell Instant||180 sec|
|Convert||30||Health -> Mana||180 sec|
|Fire III||34||Main DPS||2.5 sec|
|Freeze||35||AOE Root||2.5 sec|
|Blizzard III||38||Secondary DPS||2.5 sec|
|Apocatastasis||40||Magic Resistance Cooldown||120 sec|
|Manawall||45||Defensive Cooldown||120 sec|
|Thunder III||46||DoT||2.5 sec|
|Flare||50||AOE DPS||2.5 sec|
|Aetherial Manipulation||50||Port to Friendly||180 sec|
This is an acceptable DPS rotation for lowish level Thaumaturge:
Always make sure your Thunder DoT is up
Spam Fire until mana runs out
Use Transpose to switch your buff to ice
Spam Blizzard until mana fills up
Use Transpose to switch your buff to fire
**In light of more information regarding the BLM mechanics, I'll be posting a more solid priority based rotation for endgame coming up. I'm actually starting to get really interested in the class mechanics as I learn more.
Besides that you have some solid CCs in Sleep, Freeze and Lethargy. Sleep is a single target 30 sec CC that breaks on damage and Freeze is an AoE root that lasts for 10 seconds. Lethargy is a mediocre snare that lasts 12 seconds and is on a 30 second cooldown.
Your defensive cooldowns are Manawall and Apocatastasis. Manawall makes it so that you don't take damage for the next two attacks. Apocatastasis is usable on party members and reduces elemental damage taken by 30%.
Convert trades health for mana and is on a 3 minute cooldown.
Swiftcast is on a 3 minute cooldown and makes your next spell instant and is best used with long cast times like Flare (4 second cast) or Freeze (3.5 second cast). Surecast makes your next spell uninteruptable and is on a 3 minute cooldown.