The higher over 80% skill, the better your chance for getting a White Pearl. Some people say that if you wear Luck Pieces, then you have an even better chance, the higher your Luck is. It seems though that the Luck feature or Chance Roll is broken and has not been fixed yet.
As far as Serpents, you won't see one until you reach 90% and those will only have Level One Treasure Maps on them. At 100 or GM, you will start encountering Serpents with Waterstained SOS Bottles and of those 1 in 25 will be an Ancient SOS.