Is there a formula to calculate the amount of gold that a top ten pirate will give you?

Solution 1:

I recently played this on the iPad and while I wasn't trying to do exact math, I seem to remember thinking I was getting about 1/10th of their listed value on the Top 10 page when I defeated them.

This FAQ seems to back the idea that you'll receive 10% of their listed value.

It is possible to predict how much gold capturing a pirate will get you. Just have a look at the Top 10 Pirates list, and have a look at how much gold they've plundered over their career. Exactly 10% of that will be on board their ship when you capture it. Pirate wealth (as well as their other stats) updates at the beginning of every month, so decide for yourself if you want to capture them early, or leave them be for a while so you can go after them later in your career and get more gold.