The black pearl really depends on the server. My wife has one white and now one black. I feel like if you watch the room and notice that no one else has ordered a pearl recently, just ask for a peal and not a black one. They will grab a black just to add to the show that is traders sam. Now if they are selling alot of them, its prob less likely they will pull out a black pearl as it wont add to the over all show up the room. We had a great server who was even nice enough to have my wife help her give out a second black pearl that night after Ryno and his group left. The table that came in after Rynos noticed my wife had a black pearl and mentioned to the server that a person there had 8 white ones. The server told them they should never ask for a black pearl and then grabbed my wife about 30 minutes later. Ask her to help give the table next to us a black pearl as well.
So she brought out a pearl under a napkin and put it on our table and then proceeded to do a magic trick with a white pearl under a napkin at the table next to us. She waved a wand and poof a white pearl. The guys face dropped in sadness and then of course the waitress showed the white pearl was empty did more "magic" and poof my wife reveals the now second black pearl on our table for the guy at the table next to us. It was fun and needless to say the waitress got a nice a tip.
So my rule of thumb for black pearls. Is dont ask for one, dont expect one and watch the room to see how many pearls are being ordered also of course play around with the room and always yell 2 shots of rum when the hippoto mi tais are ordered