We're including cards as a symbol, but we expected a lot more joker imagery from someone who calls himself Joker.
Early in the movie, Grissom makes a couple of comments about cards to Jack Napier, like this one:
GRISSOM: Don't forget your lucky deck.
And this one:
GRISSOM: My friend, your luck is about to change.
Oh that Grissom. He's such a card. (Ugh. Sorry. We couldn't help ourselves.)
As for Napier himself, he plays with a deck of cards while Grissom is trying to figure out who the double-crosser is. (Hint: it's Napier, the wild card.) Napier turns up a Joker, and within twenty minutes, he's calling himself one.
This scant imagery is easy to dismiss, except for one factor: luck. Luck factors into Napier's transformation into Joker. In a struggle with Batman, who's a wild card in Jack Napier's life, Napier falls into acid and becomes the Joker. You could trace back all the "random" events that led to this happened, but you would drive yourself crazy and end up like him.
So all we'll say is this: luck is not in his favor.