These are
collectible trading card games organized as follows.
Each player pays an entry fee which covers several booster packs and an additional fee for the store. Then each player gets a booster pack. The players are seated in a circle, and each player chooses one card and then passes the pack to the player on one side of them. When the pack has circulated and no cards are left, a second package is given to each player, and after that a third. After that players may be given additional cards to fill out their deck, land in Magic the Gathering. The players then choose a subset of the cards they have selected to make a deck.
After everyone is playing with a full deck, physically at least the tournament is run pretty much like any other tournament. In addition to any prize, the players take home the cards they have 'drafted'.