How is water drained from the poop deck?

I'm wondering about wooden tall ships, particularly from the 16 and 1700s, I understand that water which doesn't exit through the scuppers will collect in the bilge. But surely water from the poop deck wouldn't be allowed to drip into the captain's quarters where there may be maps, paperwork, etc. And other rooms like the magazine and pantry would have to be kept dry as well. How is water kept from draining between the planks on the poop deck? And how are the important rooms kept dry?