Card breakdown
It costs you two mana and it doesn’t do anything when you cast it, you first need to wait a whole turn until it does something. If it survives though, it will let you see two more cards that turn and it lets you choose the best out of three cards. That’s pretty good, but is it worth going down a card to do so? Also, Natural Selection does the same thing except it cost one mana less, you can cast it at instant speed and it also lets you reshuffle if you don’t like the top three cards.
After the first draw however, Sylvan Library let’s you see one new card every turn and choose that one instead of the two remaining cards so it effectively can remove two bad draws which absolutely can be nice. So both cards have upsides compared to the other.
But back to Sylvan Library. After the first turn you only see one new card every turn, so if you didn’t like the other two it’s exactly as drawing one card every turn and the Library doesn’t actually do anything anymore. So to recap, it lets you rearrange three cards and negate two bad draws for two mana. I’m not sure that is actually worth spending a card on most of the time.
So when could that effect be good enough to spend a card on? I would say it’s good in a combo deck, as those decks usually just want to find a couple of specific cards and do not care about card advantage as much. This is why the ability to “dig” two cards deeper is good in a deck like that.
And then one last thing, the card is horrible in multiples so a deck can’t contain too many of them.
Life as a resource
But Sylvan has one more ability that we haven't touched on yet and that is that you can pay 4 life to draw a card. So for 4 life the card replaces itself and you get the other effects for "free". Now we’re talking! But 4 life can be a lot in some matchups so it’s not always a choice you can make. Against some decks though, you can draw even more cards and that’s when Sylvan Library really shines. The question is if it's worth a slot in every green deck just because it can be good sometimes against some decks?
After reviewing the card like this I do not think of it as a card good enough to be worth a slot in most decks. If you are looking for a specific card or want to use it in the sideboard against control to outdraw them for the win, then maybe.
Every day I’m shuffling, shuffling...