Leave without paying one’s bill; also, go for broke in card playing. The first usage dates from the first half of the 1800s and alludes to leaving in the dark of night (by moonlight). Richard Wheland had it in Robert Capa (1985), “They would occupy a hotel room for a few weeks, until they had stretched to the limit their excuses for not paying, then ‘shoot the moon’ and move on to new quarters.” The second usage alludes to the card game of hearts, in which players lose points for every heart they hold at the end of the game. But in one version, a player dealt the right cards can “shoot the moon,” that is, try to take all the hearts for a bonus. Here the phrase means to risk everything for the ultimate prize.