[clause],偏偏 + [clause]
[subject] + 偏偏 + [verb phrase]
[subject] + 偏偏 + 要 + [verb phrase]
偏偏 marks an outcome that runs against what someone wanted, usually with annoyance. It goes after the subject, or before the subject when it covers the whole clause. It is spoken.
With a person as subject, often with 要, 偏偏 says they insist on doing the opposite of what they were told.
偏偏 can single out the one person or thing that breaks a pattern: everyone else did, only this one didn't.
偏 alone does the same when someone insists, and is a bit blunter.
偏偏 brings frustration. For a happy outcome you'd waited for, use 终于; for a surprise either way, 竟然.