Hmm sorry to but in but its not allowed to double post.
Anyway, seeing as no one else has replied to your post which has been up for several days I will take the liberty to do so
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Psycannons versus the new Eldar avatar are useless as he has a MEQ save aside of his ++ save meaning that he will just take his normal save.
Now, I don't know about the stern thing, I don't think so as the GM and termies are one unit and stern is a IC. Even so you DON'T want to use him. His strands of faith [or whatever its called] is just a major advantage for your OPPONENT. [Ow lets see, a pen 2 for your dread, lets reroll that one shall we?] not to mention the Greater Deamon of Tzeench
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For a sidenote the avatar DOES count as a Deamon, it always did.
Now with the new rules eldar are rather toned down versus GK in comparison to first, their star cannons don't fire allot anymore and allot of players tend to give preference to the scatter laser which has a fixed number of 4 shots a turn. [The amount of high S shots makes up the AP] Eldar are more insane then ever, being able to lay down TREMENDOUS amounts of high S firepower which ranges between 4/6.
What kind of opponent are you facing? MEQ? What kind of units does he likes to use? The Eldar are able to vary so much that I can't really help you if you ain't able to point out what kind of lists he plays. *prays he ain't using banshees with a farseer which casts doom on your termies before charging in.*