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The  manacost can be tough to grasp—there haven't been a huge number of tournament staples like it—but your up-front deal (most often  for 2 damage's worth of [card]Flame Wave[/card]) isn't usually all that bad in the matchups you want it.

After Archwing Dragon and its story, this part also made me realize what I like about this game is that you guys dig deep. You have extensive memory of what cards there, which have been great, and which have been subpar. Then you seek out to give an old dog new tricks, but make sure that one isn't strictly better than the other-- each card has their applications. The new one may be arguably better, but rarely do you make cards that are strictly better in every way to another. I appreciate that level of research and the explanations for the costs of new cards.

Burn at the Stake

I love reading "three times", "deals damage to target creature or player equal to three times..."

Descendants' Path

Fantastic story.

Avacyn Restored Limited features several powerful Equipment, and this card was originally envisioned to offer a narrow but potent solution to those. With Standard being defined, to a degree, by certain other fliers wielding certain other Pikes and Swords, I expect this card to make at least a few sideboard appearances.

1) I don't get this limited tool, TBH. It just doesn't do anything narrowly. It's flying hate, that's what it's for. It's unbelievably rare that I have trouble with both a nasty creature and a nasty equipment. The reason? Because the "several powerful equipment" you mention don't exist. Equipment is kind of rare, even in sealed. There are two situations:
...a) Moonsilver Spear . I need to deal with the equipment. Did they put it on a flying creature? Probably not... I can handle the Thraben Valiant on my own; I need Demolish

...b) A nasty flyer needs to be answered. Probably not even equipped. Maybe a Voice of the Provinces with Bladed Bracers ? I need an answer to the flyer... I mean, thanks for the narrow incremental advantage interaction, but Thunderbolt would've been just fine.

2) Constructed? Possibly. Delver. Aha. Ahaa. It's awful. Delver equipped? Yeah that happens almost never. You know what's equipped? Traft or Stalker ... good luck with that. Well, maybe it's on a token! Again, thanks for the incremental advantage on that token... CVines is just better .

Somberwald Sage

Go for t3rd GaGa .

Ulvenwald Tracker

Fight is a good solution to green's problems. Although, it needs more so it has reasonable solutions to fliers. The situation is nothing like blue, who solved bad creatures by making under-costed Clones and the best creatures mana can be spent on.