lottery vs luck of the draw

lottery

noun
  • Something decided by chance. 

  • A scheme for the distribution of prizes by lot or chance, especially a gaming scheme in which one or more tickets bearing particular numbers draw prizes, the other tickets are blanks. 

luck of the draw

noun
  • The random production of favorable or unfavorable results; chance. 

How often have the words lottery and luck of the draw occurred in a corpus of books? (source: Google Ngram Viewer )