Closed Scrabble Boards

Most SCRABBLE crossword games end only after all 100 tiles have been drawn and one player has played out (used all the tiles in the rack). However, the rules say that the game may also end when all possible plays have been made -- when the players have created a closed board. Games rarely end in this manner, and when they do, the players have usually used nearly all the tiles. Just how few tiles are theoretically necessary, then, to close the board