
Out of a/the hat
Random Decision
Used when a choice seems to have no specific system or reason.

We couldn't decide on a restaurant, so we picked one out of a hat.
No Preferences
Suggests all options are equally likely or acceptable.

Any of these plans could work, so let's draw one out of a hat.
Luck-Based Choice
Emphasizes the role of luck or chance in making a selection.

Who will go first in the game? Let's choose out of a hat.
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