Juicylettuce, that increases the player chance. From what I have seen, when it hits 0, it means that no further improvement can be done.
So I assume that your Player chance in that port should be already at 100%.
You need to ask the quarter master to increase the player max.
I have been playing around this feature for all this time now so i think I can share a little guide which might be helpful to get you started (just stay off my treasure you scurvy pirates).
I think that the
best strategy (right now - it is still early, we might find better later) should be to ask the locals of each port (and only the locals). Do this till you can find a sizeable Port Max treasure. You need to keep asking the locals till you can not increase it any longer. About 25 millions is good.
Then will be the time to invest the first serious batch of turns; explore the port. Best is to take this to 100%. I noticed that this will get your success chances to 80%.
Don't go for player treasure right away. I suspect there is a little trick to take the Success chance to 100% but I am not sure (I have not done it yet, I am trying to do it though). Don't ask the head explorer at all, leave the chances at 50% - 50%. Don't even try to consult the Quartermaster - leave it at zero.
Go for the NPC treasure first: This can pay off your exploring costs
NPC treasure does not need many turns. I am not yet sure if you can take the max with 1 turn. I think you can't; You need something like 20 turns. Play around this as I have not done so yet. I have focused on player treasure all this time - I just came down to the conclussion that NPC treasure should be first priority in the first attempts.
Once you get a NPC chance like 15-20% then it is time to ask the head explorer and make that chance 0%. Time to go just for player treasure.
You MUST also ask your quartermaster. Player max can get as much as port max.
Then it is trial and error. It depends how deep the other player has dug. Just remember that with 2000 turns (this is why I mentioned 25 millions is good) you can find any treasure that has 2000 turns or less invested. If you invest 1900, you get a chance to treasures that have up to 800 turns. So if you get that far, consider going a bit deeper. Of course, 2000 turns is 12 days work so you realize here that this is going to take some time.
You might get lucky with fewer turns too. It depends on your style.
DISCLAIMER: I do not guarantee 100% what is written here. These are my personal experiences and the early ones too.
If possible, I would like to ask if what i write about the 2000 turns is correct as there is some controversy from the way it is written.