A Market on Unseen Dice

Four players at a table each shake a sealed cup holding $6$ fair six-sided dice; nobody, including the shakers, has seen any face. You must make a market on the grand total of all $24$ dice. (a) What is fair value, and what would you quote to open? (b) A confident counterparty sells you $10$ contracts at your bid of $82$ — how do you adjust your quote? (c) One cup is lifted and its $6$ dice show a total of $15$. What is your new fair value?