"The name of the game is Petals Around the Rose, and that name is significant. Newcomers to the game can be told that much. They can also be told that every answer is zero or an even number. They can also be told the answer for every throw of the dice that are used in the game. And that's all the information they get."
Also found: "You can use any number of dice..."
These are your clues to solving the mystery!!