What the best orders for command cards?

Don't have a source for it but I remember reading someones calcs that unless its a quick chain always put the quick card at the end as the loss to damage/np gain from not having arts/buster as the first card isn't worth it compared to how few extra stars having the quick card first generates.

In general, if its damage you're after put buster first, so BAA, BBB, BAQ.

Also depends on the servant. I've found that the arts buff from putting the arts card first on a servant with really bad NP gain usually isn't worth putting it first over a buster card for the extra damage.

https://pastebin.com/raw/TP1wHpZE

Card selection is quite variable to different servants. Generally put Quick card as 1st place is not recommended, but that depends. Also NP card cannot be ignored.

https://grandorder.gamepress.gg/combat-mechanics

Here are the actual percentages to do the math with. I think BQA gives the best damage since the first card bonus attack up will have more effect on the Art than Quick

Buster lead gives the whole chain 50% bonus.
Art lead gives whole chain 100% NP generation bonus.
Quick lead gives whole chain 20% star generation bonus.

BBB gives 20% additional bonus to each card.
QQQ gives 10 flat stars instantly for you to spend next turn.
AAA gives 20% flat NP gauge.

Buster/Quick/Art Brave also makes the Ex do 350%, instead of 200%.

Almost always, B lead gives you the most damage for that turn. Of course if you hyper buff a servant's Q or A, it might differ. That I can say definitely.

However, servants have wildly different generation rate and hit counts to say for sure what gives you more NP. You'll need to check wiki on the hit counts and play more to figure it out. For servants like Jack who has high counts on Q, but low counts on A, it would be better to AQQ. But for servants like Caster Gil, who only has 2 on Q but 5 on A, it would better to QAA. It all depends.

Occasionally you'll see servants that are abnormal, boasting high hitcounts on B. Scathach, Kiritsugu and Summer Kiyo are like that. Their B can be placed at the end of a chain with Q/A lead, to generate sufficient amount of stars and/or NP respectively.

Never start with Quick, unless you are going to do a QQQ brave chain. Or if it's a NP.

It depends on the hitcounts, in the end of the day. Kiyolancer will generate more NP with ABB instead of AQQ like the vast majority of the cast, for her buster hitcounts. Note that the majority of the servants has 1 hitcount on buster, thus not good for stargen or np gen.

If you only want dmg, start with Buster.
BBB=the best ofc
BAB=2nd best dmg, but BBA will give some extra NP gain at cost of some less dmg
BQA does more dmg than BAQ