A shop with two price tags

Making a market means offering to buy at a bid and sell at an ask at the same time, both centered on your estimate of fair value. Interviews run this game live: the interviewer names a quantity such as the sum of two dice, a card total or an estimate, you quote a bid and an ask, and they trade against you and reveal information. Fair value for two dice is 3.5 + 3.5 = 7, so a quote of 6.5 / 7.5 earns 0.5 per unit on either side. When a die is revealed, fair value moves at once, and so must your quote. Width trades confidence against adverse selection: tighten when you are sure, widen when you are not.

Words you need

Expected value (EV): The average result if you could repeat the bet many times: each outcome times its probability, added up.e.g. A die pays its face in dollars: EV = 3.5.
Edge: Your expected profit per trade or bet. Positive edge means you win on average.
Bid and ask: The bid is the highest price a buyer is offering right now; the ask (also called the offer) is the lowest price a seller will take. To sell immediately you sell at the bid; to buy immediately you buy at the ask.e.g. A market '99 at 101': bid 99, ask 101.
Quote (making a market): Stating a bid and an ask together, as 'bid at ask'. You promise to buy at the bid and sell at the ask.e.g. '99 at 101' means I buy at 99 and sell at 101.
Market maker: A trader who keeps quoting both a bid and an ask and earns the spread when others trade with them.
Fill: Your order actually traded. 'My bid got filled' means someone sold to me at my bid.

Why it works

If you buy below fair value and sell above it, each fill has positive expected edge. Edge per fill equals the distance from your price to the true fair value, so a wrong fair value or a better-informed counterparty can turn it negative.

bid = fair - h; ask = fair + h; edge at the ask = ask - fair; edge at the bid = fair - bid

Spot it: An interviewer asks you to make a market on dice, cards or an estimate.

Technique reference and sources

A market maker is a shopkeeper who posts one price to buy goods and a higher price to sell them, both around what the goods are really worth. The gap is the shopkeeper's cushion. A customer who knows the goods are worth more will buy from you at your old price, so when you learn something you must change the tags before anyone else uses it. Two dice are worth 7 on average. Learn that one shows 5 and they are worth 5 + 3.5 = 8.5.

When this method fits

An interviewer asks you to make a market on dice, cards or an estimate.
You must update a fair value after a reveal and re-quote.
You need to decide how wide to quote when the counterparty may know more than you.
You practice in Figgie or the tradermath.org market games and want to know why your quotes lose.

Compute fair value. Add the expected value of each unknown piece. A fair die contributes 3.5, a known die contributes its shown value.
Choose a half-width. Pick h so that bid = fair - h and ask = fair + h. A smaller h wins more trades; a larger h protects against being wrong.
Post both sides. With no inventory adjustment, center a symmetric quote on your conditional value estimate. Inventory and other constraints can shift that center.
Update on every reveal. When new information arrives, recompute fair value and re-quote before anyone trades against the stale prices.

Fair value of dice: Fair value is the sum of the expected values: 3.5 per unknown die, face value per revealed die.

3.5 + 3.5 = 7
3 × 3.5 = 10.5
5 + 3.5 = 8.5

Quote around fair value: Bid is fair minus the half-width and ask is fair plus the half-width.

7 - 0.5 = 6.5
7 + 0.5 = 7.5
8.5 + 0.5 = 9

Edge on a fill: Edge at your ask is ask minus the true fair value; edge at your bid is fair value minus your bid.

7.5 - 7 = 0.5
7.5 - 8.5 = -1

Common traps

Keeping the old quote after a reveal. A reveal changes fair value immediately. After one die shows 5 the fair value is 5 + 3.5 = 8.5, so 6.5 / 7.5 is stale and loses 1 per unit at the ask.

Centering the quote on where you think the price is heading instead of on fair value. A market maker is not betting on direction. Center the quote on fair value and let the spread earn the edge.

Quoting very tight against a counterparty who may know more than you. Edge per fill is your price versus the true fair value. If they know the die shows 5, a tight ask below 8.5 loses 1 per unit in expectation. Widen when you are unsure.

Reading the spread itself as your profit. Your edge on a fill is half the spread only when your fair value is right. With a wrong fair value the same fill can lose money.

Another example: Minimum ask with nonnegative expected edge

Informed fair value: 5 + 3.5 = 8.5
At ask 7.5 the expected edge is 7.5 - 8.5 = -1, an expected loss of 1 per unit
At ask 8.5 the expected edge is 8.5 - 8.5 = 0, so you break even in expectation even against them
Guaranteed nonnegative settlement profit on every roll would need ask at least 5 + 6 = 11; ask 9 still loses up to 9 - 11 = -2 when the hidden die shows 6

Source notes

These explanations and questions are written for QuantArc. Links show the underlying mathematics and learning design.

Figgie (Jane Street)
Landing page checked: Jane Street's card game that simulates elements of markets and trading, with rules, a tutorial and a learning mode. Practice companion only; its rules and strategy tips were not reviewed against these lessons. Lesson examples are original.

tradermath.org market games
Listing page checked: browser games including market making on dice, a card market-taking game, Fermi estimation and a trading game. Practice companion only; game content was not played or reviewed against these lessons. Lesson examples are original.

IES: Organizing Instruction and Study to Improve Student Learning
Supports worked examples, retrieval, explanations and spaced study. Does not establish QuantArc's exact lesson length, mastery threshold or review intervals.