They believed it was round, just like any other person of their time. (I notice you didn't specify a time period, but it's been known since antiquity that the earth was round.)

https://www.reddit.com/r/AskHistorians/comments/4n981p/how_common_was_the_knowledge_that_the_earth_was/

https://www.reddit.com/r/AskHistorians/comments/a1me78/did_a_significant_amount_of_people_actually_think/

https://www.reddit.com/r/AskHistorians/comments/3uufv2/when_did_people_understood_the_concept_of_time/

https://www.reddit.com/r/AskHistorians/comments/56no2h/did_people_who_traveled_long_distances_in_ancient/

Even in antiquity, the world was known to be round. Additionally, pirates would have personal experience with the roundness of the earth for two reasons.

First of all, navigation at sea requires you to take into account the geometry of the earth. Second, arguably the best demonstration of the Earth's shape is the fact that the bottom of a ship disappears below the horizon before the mast. This would've been readily visible to pirates. The very fact that they utilized crow's nests is evidence that they knew the earth was round. On a flat earth, height wouldn't matter at sea for seeing distance, as nothing would be in the way of vision. This obviously is not the case on a round earth.