The SET game works with a deck of $81$ cards. Each card contains a set of symbols with four attributes: color (red, green, purple), shading (empty, striped, or solid), shape (oval, squiggle, or rhombus), number of symbols (one, two, or three). All the cards are unique. A SET occurs when three cards satisfy the following property for each of the four attributes: The attribute on each card is the same, or the attribute on each card is different.
Two players play a game with the 81 SET game deck. The game starts when first player selects 12 cards from the deck and puts them on the table. Then there are rounds where first player removes a SET (3 cards) from the table, and second player replaces the 3 cards by cards from the deck. First player wins, if after 27 rounds he ends up with 27 SETs. Second player wins, if in some round the 12 cards on the table contain no SET.
Who wins, first player or second player with the optimal strategy?