two or three initial moves = win? you have to play a game with the following rule : white can initially play two moves, then one move each side as usual, and a draw counts as a victory for black. Which side do you choose ? (say differently, do you think this variant favors white or black ?)

Same question with three initial moves for white. Maybe this is already solved?
Since I'm a 1.d4 player, my first two moves as White would be 1.d4 and 2.c4. After that position, Stockfish gives an evaluation of +0.59 if Black plays ...e6. I would definitely enjoy playing this as White since the threat of playing e4 at any time prevents the Nimzo and Dutch. Black best option is to settle for a QGD one tempo down by playing ...d5 on the next move, but this would be very comfortable for me. So I'd probably choose White, but it's not an easy decision.

That being said, it's not close to winning for White. An extra move just guarantees a pleasant edge.

With three initial moves, I would go for 1.e4, 2.d4, 3.Nf3. Stockfish gives a +0.99 evaluation, and it would be very tough for a human to defend as Black in a practical OTB game. This seems on the verge of winning for White, but still not a definite win.