Right, so you agree that the base play of the card with no other considerations is a $3.5, that's exactly where it wants to be, because you have to consider the potential of this card to be anything from discard 2 +5 cards to a straight +5 cards.
If I have to consider that the card could be stronger than it is, I also have to consider that it could be weaker. Be unplayable when you have too many card in your hand is a flaw and that's why DtX should be consider like I told previously.
If we take for exemple a good DtX from the base game: Cursed village is balanced even if you play it at the start of your turn: if we replace the "draw up to 6 cards in hand" with +2 cards, the card is still playable.
Btw; the power of the card is anything from nothing (if you draw it in a hand of 7+) to a straight +5 cards and not anything from discard 2 +5 cards to a straight +5 cards.
If you have any virtual coin or other non-draw actions, its not that hard to get to the point where you can have a hand of 2 actions you can play first (which villagers help you to do), play Biblio, discard the 2 junk left over in your hand, and draw 5 cards. In that case, its stronger than Embassy at $5, since it discards one less.
There is two affirmation here and I have to precise them both:
- There isn't a lot of of non-terminal stop cards in the base game; sure the villager overpay is probably a good way to solve this problem but the power gap is so hight between 4$ to 5$ and 5$ to 6$ that I think it's not enough so either it should give 2 villagers / overpayed coins; either the overpay ability should be used in a different way (like; while you have this in play, you may overpay when you buy a card for +1 Villager per $ overpay). These are two example but I think both of them are a fair way to improve the card.
- Embassy isn't weaker because discarding after drawing is always better than discarding then drawing. Embassy is better than "draw the 2 best of 5 cards" and Bibliotecary can't be consider as this type of cards. (it's a weak argument, in your example it's still better than embassy but not as stronger as it seem)
With a hand of 4 other actions you can play (or an action that can play treasures), Biblio is a straight +5 cards, which is easily a $7 cost card being better than Hunting Grounds.
I think the phrase should be more: "With a hand of 4 other non-terminal stop actions (or the incredibly rare actions that can play treasures), Biblio is a straight +5 cards."
In these types of hands, Library could ba a +7 cards +; something that should cost an incredible amount of money; probably more than 10$. So with your reasoning, library have a power between a smithy+ and a 10-cost cards so it should cost at least 6$. But at 6$ we agree that the card is bad so we can deduct than, if we've made a wrong deduction while having good information it's probably because the logic have a flaw right?
In short, you're right, when its weakest (being played at the start of your turn), then it is definitely weak for $4. But at its weakest it is $3 lets say, and at its strongest its $7, that makes a price of $4 fair I would say. If it drew one more, it would have to cost $5, and then the overpay would be too far out of reach.
DtX are in the weakest posiion not at the start of your turn but when you draw them with themself.
So, if these arguments aren't sufficient (wich is totaly possible, and that's probably what is expected here) I can only advice you to playtest the card in a randomly-generated kingdom, where a player play DtX and an the other a non-DtX engine then play with the same kingdom while swaping roles. This is especialy efficient with someone that have aproximatively the same level as you but if the swap clause is respected it should be fine. (Even if, in order to have a reliable result, a lot of these games have to be played. It take a lot of time so maybe randomise then just analyse the kingdom with few people could be more efficient, IDK)