at the drop of a hat
at the drop of a hat {adv. phr.}, {informal}
1. Without waiting; immediately; promptly.
If you need a babysitter quickly, call Mary, because she can come at the drop of a hat.
Compare: ON THE SPUR OF THE MOMENT.
2. Whenever you have a chance; with very little cause or urging.
At the drop of a hat, he would tell the story of the canal he wanted to build.
He was quarrelsome and ready to fight at the drop of a hat.
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Source: A Dictionary of American Idioms