The giant "Joker" playing card in the Batcave is a trophy of one of Batman's early adventures. It's one of the three biggest constant items in the Batcave, alongside the Giant Penny and Batman's T-Rex.
The giant playing card was a constant feature in some of Joker's various hideouts, but there were usually different models on each place. The white card that is now part of the Batcave was also part of one of Joker's lairs and was later used on one of Joker's schemes in which he used oversized models of casino games including dice, cards and pinballs. When Batman defeated Joker on his own game, he took back to the Batcave a couple of giant dice and the Joker playing card.
The card was eventually moved along with other trophies to the second Batcave, which was located underneath the Wayne Foundation building, but when Bruce decided to move back to the original place, all trophies and mementos were moved back as well, including the Giant Joker Card.
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