Ok, going to mostly comment on wording and any obvious issues this run through ...
Sprawl - $6
Victory
4 VP
If the game ends due to three cleared piles, 7 VP instead.
I'm not sure if there's a difference between "7 VP instead" and "+3 VP," at least practically, but feel free to disprove me.
+VP is generally used to refer to what happens when you play a card like Monument and gain points in the form of VP tokens. If you were to actually get 3 VP tokens at the end of the game due to a card being in your deck, I would find that ... weird. For a card that has two possible VP values depending on an end-game condition, check Distant Lands:
Worth 4VP if on your Tavern mat at the end of the game (otherwise worth 0VP).
Also, in terms of making the game tempo interesting, I'd like to see what happens if it goes the other way around (because you might try to use your big spends to buy this rather than Provinces, only to see your opponent stop buying Provinces and start emptying piles).
I'll get to the other criticism later, but I ran some math and theory in my head for Sprawl in a head-to-head.
Note: I managed to mix up cost and VP value while I was making this card, so the cards were technically balanced for a 5 VP Duchy and an 8 VP Province. The intent was that Sprawl was always worse than Province, VP-wise, but you should be able to stay ahead by having more Sprawls than Provinces. Nevertheless, I'll just theory out the card as written and in reverse, as suggested.Other Note: Throughout this, I will sometimes say you need X Y's to win. That really means you need an advantage of X in Y's, but I'm writing this after I wrote much of this and I'm lazy.Card as Suggested7 VP if ends on three-pile, 4 VP if ends on ProvincesIf you think the game will end on Provinces, buy Provinces (6 vs 4). If you cannot afford a Province, buy Sprawls (4 vs 3).
If you think the game will end on three-pile, you need six Sprawls to match seven Provinces. (If your opponent gets eight Provinces.... the game is over on Provinces.) If you take one Province, you need five Sprawls to beat six Provinces; however, that makes it more likely that the game will end on Provinces.
Card in Reverse4 VP if ends on three-pile, 7 VP if ends on ProvincesIf you think the game will end on Provinces, and you buy no Provinces, your opponent will end up with 48 VP. You need at least seven Sprawls to be ahead at 49 VP.
If you are competing for Provinces, are ahead in by at least 2 points (1 if you have turn advantage), and have tempo, buy Provinces. The game will be closer to ending on Provinces and your opponent will be unable to catch up.
If you are competing, are behind or tied, and have tempo, buy Sprawls. You will gain more points if you trade Sprawls for Provinces. If your opponent buys Sprawls as well, you delay the endgame so you can catch up. It is also easier to gain two Sprawls in a turn than two Provinces.
If you do not have tempo but are competitive in points, buy Sprawls. Similar logic.
If there are no more Sprawls and you have more, buy Provinces to end the game faster.
If there are no more Sprawls and they split 4-6 against you, you can come back if you have three more Provinces. Otherwise, aim to three-pile.
If there are no more Sprawls and they split 3-7 against you, you need a five Province advantage.
If they split 2-8, you must have an eight Province advantage.
If they split 1-9, you cannot come back on Provinces alone. Either stall for time or aim to three-pile. If you try to force a three-pile too late, however, your opponent will simply gain an insurmountable lead in Provinces anyway.
If you think the game will end on three-pile, and you buy no Provinces, your opponent can have, at most, 42 VP. Even if you have all ten Sprawls, that is still only 40 VP. If your opponent buys six Provinces, you need to have at least four more Sprawls than he Provinces. If your opponent buys five, four, or three; you need three more. If your opponent buys two, one, or none; you only need one more.
If you are competing for Provinces, you need at least two Sprawls to overcome a 3-4 split in your opponents favor.
If you are competing for Sprawls, it is wiser to attempt to end by Provinces if your opponent cannot gain a Sprawl advantage of more than two in the time you can gain a Province advantage of four. (Technically, you only need three, but an advantage of 5-2 still leaves one Province left.)
You can also try to gain eight Provinces for six Sprawls. This is too easily blocked, however.
That's... a lot of math. And I'm not even done thinking.