Hi, so... Fa'Tafi heals herself for 1 the start of each turn, and she has Strangling Roots placed on her while she is at full health. 
At the start of my next turn, Strangling Roots deals 2 damage, but does her self-heal come before or after this damage?  Anyway, since she heals one health every turn, and I do two dmg only on my turn, the most damage I can expect to put on her is 1pt anyway, right?

Thanks for all your help, and apologies if this is redundant.  It was kind of hard to run a search with these parameters.

I'm almost sure that in the cases of that, healing happens before damage takes effect.

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"Insert witty remark here"

If multiple effects, such as start of turn effects, trigger at the same time, the active (turn) player adds all of his effects to the chain first, in whatever order he likes, then the non-active player adds all of his effects to the chain in whatever order he would like. So, the answer to your question depends on whose turn it is.

In the scenario you described, on your turn she heals one damage from herself. On your opponent's turn, the strangling roots trigger gets added to the chain first, and her heal goes on top. She heals for one (if she has damage) because the chain resloves from top to bottom, then takes the two-point ping from strangling roots.

Thanks!  This makes perfect sense.  I forgot to think about the turn player's priority when it comes to start of turn abilities.