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To pass on this gem with Carolyn Fern would just be Foolishness. This is so good on Carolyn with Peter Sylvestre in play. 2 resources every turn for 4 turns -- awesome. With Dr. Milan Christopher, this setup, Liquid Courage, and Teamwork, The Nerd Girl becomes killer support, and the bigger the group, the better. Before you know it, everyone's rolling in it. Have her hand a Dark Horsed Silas Marsh a St. Hubert's Key while you're passing out goodies, and they may as well start calling you Dr. Frankenstein, because you've just created a monster.
TL:DR, avoid like the plague unless your options are limited or your name is Agnes Baker.
The faction is one of the two most resource starved groups in the game (the other being ), powerful economy cards are great but their cost may just be too great for you to pay for. Forbidden Knowledge is one such card, for the vast number of characters the horror is just too great and they perish quickly, Agnes Baker however LOVES this card.
4 Resources is good, 4 horror is BAD, from what we can surmise at the moment two points of horror heal is worth a card and two resources, I.E the trade here is very inefficient, not to mention the greatly increased risks in the scenario. Almost no characters have the horror tank to endure this and those who do might want to look at other options, like Uncage the Soul and Emergency Cache, both of those grant similar resource benefits and at no horror cost.
Secrets rarely combo, there are just 2 cards in the game that interact with this resource type and those cards are bad on their own.
So, it kills you and compares terribly to other cards, so why does Agnes like it? Heck, this card might as well be her strength card, and a 2-off at that! The main reason Agnes loves it is the fact that she can trigger the trigger outside her normal turn. With generous application of spells and being buried in enemies something like this might happen:
Trigger Forbidden Knowledge in the Mythos phase, shoot something with Shrivelling and pull a , get punched in the enemy phase taking another horror. That's 3 triggers on her ability in one turn which is another 3 points of damage on top of her Shrivelling, enough to kill bosses in solo in one round! Of course, typically, you'll perhaps not draw a special token with the Shrivelling or draw horror inflicting effects in the mythos phase, Forbidden Knowledge is very flexible so you can usually adjust accordingly. To be able to pull off combos like these you absolutely need Fearless and might need to forego a copy, or even both copies, of Arcane Research.
Forbidden Knowledge is the definition of Risk-Reward that makes Mystic a tricky faction. 0 cost for 4 resources is great, 4 Horror is not so great. Agnes Baker can use this to her advantage by dealing damage when she receives Horror, but you are limited to once per Phase. During your investigation phase you can take a free resource, take a horror, and deal a damage. If you're in a really tight spot where you need to eliminate an enemy, you have a player window during the Mythos phase after encounter cards are drawn and immediately before enemies attack. That's a total of 3 damage dealt, 3 resources gained, but also 3 horror taken in a single round, without having to make a skill check.
This is a useful asset, but you should only use it when absolutely necessary, or you'll find yourself dropping out of scenarios from sanity loss. Unless you're with friends that can patch you up with First Aid, you're going to be saving your second copy for the Intellect icon, or replacing it with leveled up cards as a campaign progresses.
I can see the appeal of this card in a Carolyn deck running Peter, but even if you do include it, I think it's a card that's due to get replaced pretty quickly. Depends if you're planning to go with Ancient Stones. If you do, you don't need this card once Ancient Stones (Healing Horror version) is up and running by scenario 3. Which begs the question...if it's going to take up a slot, why not find something more interesting to put in there? You'll make money with Peter solo anyway in the meantime. And if you're running Painkillers, this makes this card even less appealing. Carolyn deck building can be tight, but I favour trying out some esoteric cards that could help now and down the road...maybe a True Grit for versatility or Inspiring Presence to heal up and ready Alice Luxley if she's in your deck. In short, this card feels like 'immediate gratification' and even a bit superfluous, and would be neat to try other strategies with Carolyn.