There are essentially two directions you can take.
First, you can try to power out a quick victory, overwhelming the deck's ability to keep the board under control. This means aggressive starts, dealing damage as quickly as possible, and casting multiple spells in a turn to push through the counterspells in the deck. Since this archetype is so reactive, if you can create more threats than your opponent can keep up with, you can secure a quick victory and essentially render all of the milling effects meaningless. Unfortunately, this requires a pretty aggressive build as well as a good opener, and such a start may not even be possible for many of the popular archetypes. Which is where the second strategy comes into play.
You see, you need to realize that any Mill archetype is playing an entirely different game. Rather than trying to reduce your life from 20 to 0, Dimir Mill is trying to reduce your library from 60 to 0. This means that anything you can do to keep more cards in your library is ultimately going to be good for you.
Furthermore, the strength of this deck is also its greatest weakness. Both Pilfered Plans and Thassa's Bounty take as many cards from your opponent's library as they do from yours. The only way the Dimir Mill deck has to get ahead in total cards remaining is to cast Psychic Strike and Grisly Spectacle. But your opponent can only cast these two spells if you allow them.
So the second strategy is this: refuse to play into Dimir Mill's strengths. Instead, play a different game entirely.
- Take your entire Sideboard, dump it into your Library, and Submit. Viola! You just boosted your "life total" from 60 to 75.
- Aggressively mulligan, even down to a single card, if that's what it takes to keep your library larger than your opponent.
- Don't cast any draw spells. Anytime you do this, you are reducing your "life total" by the number of cards you draw.
- Don't cast any creature spells either, and only cast other spells if you are certain your opponent can't counter it.
So, is there anything the Dimir Mill deck can do to counter this second strategy? That's what I'll cover on Friday. See you then.