Draft

Draft or Card drafting is the process where players pick cards from a limited subset, such as a common pool, to gain some immediate advantage or to assemble hands of cards that are used to meet objectives within the game.

Description
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Games where cards are simply drawn from a pile are not card drafting games - drafting implies that players have some sort of choice.

The most commonly known draft format in Magic: The Gathering is Booster Draft. But there are many casual variants, as well. Examples are Auction Draft Flavor Draft and Chaos Draft.

Draft matters
Conspiracy Draft has a "draft matters" theme.

Draft stamps
At most high level draft events (Players Tours, Grand Prix, etc.), the organizers stamp the cards used in each draft with a unique stamp. This prevents players from cheating by swapping cards from outside the draft into their decks. Different symbols and stamp colors are used for each different draft round. The positions of the stamps on the cards are also significant, and allow the organizers to recreate the draft from scratch if necessary.