the map nobody has seen
Tap any square still under fog and dig it for 0.0005 ETH. The block after your dig decides what was there. Nothing is buried in advance, so nobody can read the chests out of the contract, the captain included.
The chance is simply the chests left over the squares left, and it's written in the margin. Every square of sand makes the next dig likelier. A chest pays 8% of the pot. The fifth and last chest on an island pays 20%, and then a new island rises out of the fog. One sand square in eight has a loose coin in it: half a percent.
Holders of $DIG get a second look at one empty hole per island.
On day 3 the tide goes out for an hour and every dig is twice as likely. On day 7 the voyage ends and whoever found the most chests keeps what's left. Each dig sends 80% to the pot and 20% to buying $DIG and burning it.