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Bingo is a slang term used in Scrabble for a play using all seven of one's tiles. A player who does this receives 50 points in addition to what the word would normally score. In the United Kingdom, this is more often called a bonus (the term sanctioned by Mattel, the game's manufacturers there), but is occasionally called a bingo.
Bingos are an important part of achieving high scores in Scrabble. While a beginner might be lucky to score even one during a game, experts frequently score three or more. Much advanced strategy revolves around making bingos: blank tiles are hoarded, unwelcome letters are played even for a low score, and flexible letter groups like AEINST (a six-letter stem which anagrams with 23 letters -- all but J, Q, and Y -- to form nearly 70 bingos) are built up until a bingo is formed. This strategy is often at direct odds with that of placing high-value letters on premium squares.
A common misconception is that the bonus received for using all seven tiles is multiplied if a double-word or triple-word score is used. This is not the case: a 9-point word using seven tiles played across a triple-word score is worth 77 points (3 times 9 plus 50 points for the bonus).
These facts are according to the SOWPODS lexicon as amended in 2006.