As a community at large we tend to think of Dominion as having a first player advantage.
What if we thought about it the other way, allow me to elaborate.
WITH ROCK
Consider a board that has a rock-paper-scissors scenario. If player 1 opens rock, player 2 can respond with paper, if player 1 then changes to scissors player 2 can either switch to rock, or allow player 1 the switch, allowing the switch takes a whole reshuffle and your deck will be weakened by having cards from rock.
This means that as player 2 you have more of a job to play responsive to your opponent than in the player 1 seat.
NO ROCK
To an extent this is irrelevant if there is no Rock-Paper-Scissors on board, but not entirely. For this scenario consider BM-X with the base set. On an oversimplified board of Witch, Moat, Money. Another conception is that moat is generally weak but here Witch is a moat that gives a curse.
There are 3 ways to play this board. (I'm going on an assumption that BM (no terminal) is just bad here)
BM-Witch
BM-Moat
BM-Witch/Moat.
Let's just deal with 4/3 opens for now
If player 1 opens Silver/Silver you can conclude that they are going for a witch. As Player 2 you can react by opening Silver/Moat (NOT MOAT/MOAT).
Now player 1 has a decision, continue on the witch path, or audible to moat. If they audible to moat they are spending turns with MORE MONEY to buy moats, while as player 2 your spending turns with more money accruing more money. So player 1 probably wants to continue down the witch path, when you see player 1 buy that witch you can react and buy a moat. Now as player 2 your running the (normally ideal?) 2 terminals to player 1's 1 terminal. Not to mention your terminal stop the positive effect of theirs at a lesser cost.
If player 1 opens Moat/Silver. Player 2 has to follow suit. On the second reshuffle player 1 can buy more money in which case player 2 should buy a witch before the reshuffle, if player 2 buys another moat player 2 should stick to more money and if player 1 buys a witch player 2 can buy another moat to be in the same as scenario 1.
Now for the 5/2.
Player 1 buys witch here (I don't think that anyone would disagree?). Player 2 can open DOUBLE moat here. If player 1 hasn't played a witch player 2 doesn't play a moat if they didn't collide, if they do collide player 2 needs to play the moat to accelerate the reshuffle. If player 1 has played their witch player 2 plays all moats until they trigger a reshuffle, hoping to pass player 1 on the reshuffle to a more money filled deck because player 2 needs to hit green before player 1.
Anyways this is just a train of thought, I'm interested in hearing other peoples thoughts on the matter and different ways player 2 can capitalize on this knowledge in boards that DON'T have rock-paper-scissors.