Take a chance

He took a chance by supporting the unknown artist.

He took a chance on me, gave me an opportunity to get into management, the opportunity I wanted, which could not have been an easy decision to make.

[…] say they will tend to play it safe, relying on sure-fire box-office hits and refusing to take a chance on experimental works, which almost are always box-office failures.

When we did not use the X-ray, if we broke a piece of root off in extracting a tooth, we took a chance, left it in, and expected it to work out.