There should be a deterministic way to get items from the vault. Now not saying that you should get this specific trinket guaranteed, but like, pay 3k gold per vault slot to guarantee that this will be a random trinket and nothing else.
Do it thrice, and you’d see 3 trinkets, one of which might be what you need.
That’s one way to make this casino minigame more useful. Otherwise it’s only handy at the start of the season and it’s a pain to get what you still need, like I too would rather have better trinkets, or a belt.
As for the RP setting behind it? The vault warden is underpaid and wants some side cash, and in return he gets you what your heart desires. Simple as that.