oh, he's turned down for a new policy. that makes sense. sort of.
The thin man is an insurance agent for ship captains and he's crooked.
The wager:
A ship captain pays the thin man.
If the ship captain dies, the thin man pays his family lots of money and thin man "loses" the "wager." If the ship captain lives, the thin man "wins" the "wager" since he collected the insurance premium.
The scene is confusing for a number of reasons - you have to realize that there are TWO ship captains the scene refers to.
The thin man sold insurance to a ship captain (who you do not see in the scene) and when that ship captain died, the thin man simply chose NOT to pay the captain's family.
From the 'Hardhome'
script:
JAQEN: The man is a gambler. He wages that his sailor's ship will make it to its destination. It is a strange wager for the captain. He only wins if he loses his life.
ARYA: So why would a captain make the wager in the first place?
JAQEN: A girl tells a man that she has seen.
ARYA: If the captain dies, the thin man pays his family a lot of money.
JAQEN: But perhaps the gambler loses his bet and decides that he doesn’t have to pay after all. A destitute woman and her small child, what can they do to such a man if he keeps their money for himself? To whom can they turn for recourse?
Arya looks to see a man praying on the floor.
So it is assumed that the unseen captain's surviving wife came or prayed to the Faceless Man for help.
The captain that is *actually* shown in the scene, goes to the thin man to buy another insurance policy for his next upcoming trip. The money on the table is the insurance premium, but the thin man refuses to sell him a new insurance policy because after looking at the documents of the next planned trip Thin Man determined that it was too risky despite the ship captain's safe track record up to this point.