Make a Market: Three Dice

Three fair dice are rolled face down. You are the market maker on their sum. Over three rounds the dice are revealed one at a time (none before round 1). Each round you state your fair value and quote a bid and an ask no more than 2 apart.

Counterparties arrive every round:

• Noise traders know only what you know. A noise buyer lifts your ask if it is at most (public expected value + their edge); a noise seller hits your bid if it is at least (public expected value − their edge). Edges are between 0 and 2.5.
• An informed trader knows the true sum and trades 2 lots whenever your quote is mispriced relative to it.

Your position is capped at ±10. At the end, your position settles at the true sum.

Goal: finish with a total score $\geq 0$ (score = PnL − inventory charge − fair-value error penalty; see the scoring rules panel).