Cast lots - Idioms by The Free Dictionary
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To decide something by picking an item, often a slip of paper, at random. Let's cast lots to decide who will go first—it's the only fair way to do it.
cast/draw ˈlots (for something/to do something) decide who is going to do something by using a method in which each person takes a piece of paper or a stick and the person who has the paper with a special mark on or the shortest stick is chosen: They drew lots to see who should speak to the parents.