Bronze Dice appear in the second half of the Arqa Block in Tartarus, on floors 41F through 46F. They are the target of one of Elizabeth's subjugation requests. After accepting the quest from Elizabeth, they may drop Bronze Figurines upon being defeated. Five Bronze Figurines need to be collected to complete the quest.
Bronze Dice also appear later on inside the love hotel on Shirakawa Boulevard during July 7th's Full Moon Operation.
In The Answer, Bronze Dice will appear in the second and third section of Caina within the Abyss of Time.
Bronze Dice appear on floors 5 and 7 of Yukiko's Castle in the Midnight Channel. They will generally wait for a turn or so and use Last Resort, KOing themselves and inflicting heavy damage to the party and any Shadows remaining on the field.
Upon being defeated, they may drop Power String. Collecting 6 Power String items will unlock the Lion Happi male armor at Daidara, which is the best armor available to the protagonist and Yosuke at that point in the game.
Bronze Dice appears on the fourth, fifth, and seventh floors of Yukiko's Castle within the Midnight Channel. It may drop Blue Quartz when defeated instead of Power String. Selling 6 Power Strings at Daidara Metalworks will unlock the Lion Happi male armor in the shop.