I always used to hate playing as black. But recently, I have used gambits more, and I feel it's so powerful, e.g. the 1... d5 response to 1. e4. Most of us know that white has a statistical advantage (about 10% more), so it seems that only through gambits can black have a chance.
But what is the best gambit to white starting with 1. d4? A gambit by black here seems iffy.
You ask whether gambit play is the main way for black to play for a win, but instead of gambit play specifically, the issue is more generally one of unbalancing the position (and this is true regardless of which color one has). Sacrificing material for some other type of compensation is certainly one way to do this, but it is only one of many. Generally speaking, the more unbalanced a position is, the more easily either side can end up playing for a win.
Consider the following two somewhat extreme positions. Position A arises in the Exchange Variation of the Slav Defense after the following moves:
[FEN ""]
1. d4 d5 2. c4 c6 3. cxd5 cxd5 4. Nf3 Nf6 5. Nc3 Nc6 6. Bf4 Bf5 7. e3 e6 8. Bd3 Bxd3 9. Qxd3 Bd6 10. Bxd6 Qxd6 11. O-O O-O
Position B arises in the Sicilian Dragon:
[FEN ""]
1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 g6 6. Be3 Bg7 7. Qd2 Nc6 8. f3 O-O 9. O-O-O
Note that material is entirely level in both positions, yet Position A is much more drawish than is Position B. In my database, 1264 out of the 1285 games which reached position A ended in a draw, or 98.4% of them! At the same time, only 2829 out of 10788 games reaching Position B ended in a draw, a mere 26.2%.
The reason is that in Position A everything is level: equal material, identical pawn structures and piece development, same-side castling, etc. In Position B, despite the material equality, the position is more unbalanced, in particular via the opposite-side castling, the differing pawn structures, and the fact that each side will need to develop pieces for defensive purposes near its own king and offensive purposes on the other side of the board.
In sum, I think it's a mistake to think that gambits are necessary in order to play for a win with black, any more than it's necessary with white, and instead one should strive to unbalance the position in order to create greater winning chances. But as with gambits, while unbalancing the position can decrease the likelihood of drawing, this is usually by increasing both of the individual likelihoods of your winning or your losing. So by upping your chance of winning the full point, you are also taking on greater risk yourself.
With that in mind, one should always take one's particular opposition into account. For instance, if one player is significantly stronger than another, he or she might even aim for something like Position A (maybe not quite that, but something like it) with every intention of playing for a win, and counting simply on greater skill and the opponent's inevitable mistakes in order to have very high winning chances without taking on any of the the risk of Position B, wherein the stronger player could have a bad day and make a mistake that, in that position, could be serious enough that even the significantly weaker player could then carry the day from the point when the mistake was made.
Even more to the point: despite what I wrote above, it's important to be aware that at the amateur level, absolutely any result can come out of absolutely any opening, no matter how crazy or how lifeless it may seem (or even objectively be). Almost every game at lower levels will involve swings back-and-forth throughout the game, in terms of where the objective advantage lies, as both players make mistakes. So whatever the outcome of the opening phase may be, the game is still there to be had in the middlegame, and then again in the endgame if it gets to there. Thus what is most useful in opening play at the amateur level is aiming for positions that you understand, and that you are comfortable with, as this makes it more likely that you will do better in the middlegame.
No, the best way to win as black is to play better moves that white does. Know your openings, be reasonably booked up, and follow established principles. There's no reason to take unnecessary risks in the opening.
Now if you like taking risks, that's a different story. But you don't have to in order to have a decent chance of winning with the black pieces.
When playing Black, you should mainly "take what White gives you," to quote Vince Lombardi the football coach. That is, you should wait for White to make a mistake, then try to take advantage of it.
It is when you are White that you can try to "force" errors, which of the leeway your first move gives you. But if you are Black and undertake a failed initiative, you've really put yourself at a disadvantage.
