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Try to empty their library before they kill you. If a player can't draw a card because his library is empty he looses the game.
Not the most effective strategy unless you use a combo like Brain Freeze or Grindstone andpainter servant.

Most deck will use cards like

Glimpse the Unthinkable
Hedron Crab
Traumatize
Archive Trap
Mind Funeral
...

And try to mill you slow, such decks need to divide their card slots between mill cards like the above and cards to control the board so they won't get killed by creatures before their opponent gets milled. Board control cards are cards like Doomblade (= spot removal) and Damnation (= board sweeper)
Some also run counter magic like Counterspell and the likes as protection.


Combo decks are far more competitive because they are fast or very well at protecting their combo. They use a combination of cards to end the game in one critical turn.

Painterstone combo plays Painter Servant naming any color (usually blue because they play red elemental blast as a counter and spot removal) and Grindstone. Once both cards are on the battlefield you activate Grindstone and mill the entire library unless your opponent runs anti mill cards like Emrakul, the Aeons Torn which makes milling more difficult. (They play Tormod's Crypt to solve that problem but it slows down their deck as they have to wait until they draw into crypt)

Brain Freeze is a storm card. Basically decks that play it are mono blue and play High Tide in combination with cards that draw cards and cards that untap their land. This way they generate a lot of mana and play a lot of spells and then brain Freeze their opponent for far more cards then he has in his library.

mill decks are usually very casual in nature.

Thank you for the explanation but I was looking forward to see some decks. Competitive decks if possible.

These are the two most competitive mill decks in legacy:

Imperial Painter: http://www.mtgdecks.net/decks/view/21247

Mono red Combo Mill deck using Grindstone/Painter Servant combo. It's very good against multicolored decks using a complex manabase. It's avery good deck but Imperial Recruiters make the deck very expensive.

Spiral Tide: http://www.mtgdecks.net/decks/view/24374

Mono blue combo mill deck