When American and Pakistani agents captured Abdul Ghani Baradar, the Taliban's operational commander, in the chaotic port city of Karachi last January, both countries hailed the arrest as a breakthrough in their often difficult partnership in fighting terrorism.

But the arrest of Mr. Baradar, the second-ranking Taliban leader after Mullah Muhammad Omar, came with a beguiling twist: both American and Pakistani officials claimed that Mr. Baradar's capture had been a lucky break. It was only days later, the officials said, that they finally figured out who they had.

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