Make a Market on the Sum of Private and Community Cards

In a second one-hour online market-making round, which the report says relies more on fluency with market-making concepts than the first, players trade a contract on the sum of the values of several playing cards. Each player holds private cards that only they can see, and there are shared community cards. You make two-sided markets (a price at which you buy and a price at which you sell), trade with the other players, and answer quick arithmetic along the way. The report gives no deck rules, card counts or settlement details, so settle them with the interviewer first. ### Clarifying Questions - Which cards does the contract settle on: every player's private cards plus all community cards, or only some of them? - How are cards valued (ace as 1 or 14, face cards as 11 to 13 or as 10), and is it one standard 52-card deck dealt without replacement? - How many players are there, how many private cards does each hold, how many community cards are there, and are they revealed during the game? - Are there position limits or a maximum spread, and what is the contract worth per point? ### Part 1 — Fair value from what you can see Using your own cards and any revealed community cards, estimate the expected settlement value and how far the true total may lie from it. Show how both change when a community card is revealed. ```hint Unseen cards come from what is left The expected value of each card you cannot see depends only on which cards you can see. ``` #### What This Part Should Cover - The expected total from the known cards plus unseen cards drawn from the remaining deck - A quick estimate of the spread of the total - An exact update when a card is revealed ### Part 2 — Quote, trade and manage your position Make a two-sided market on the total, react when other players buy from or sell to you, and keep your position under control. ```hint Price the people, not only the cards Think about why the width of your market should depend on how much the other players know that you do not. ``` #### What This Part Should Cover - Placing quotes around fair value, with a width justified by uncertainty and by what others know - Profit and loss of trades against the final settlement - Skewing quotes and sizing to manage inventory and limits ### Part 3 — Learn from the other players The other players see their own private cards. Explain what their quotes and trades tell you, and update your fair value accordingly. ```hint What would they have to hold? If a player keeps buying at prices well above your fair value, ask what their own cards would have to be for that to make sense to them. ``` #### What This Part Should Cover - Inferring a player's private cards from their quotes and trades - Combining that inference with your own information without overreacting - Adverse selection: when being filled is itself bad news ### What a Strong Answer Covers - Correct expected values and spread estimates for sums of cards drawn without replacement - Markets centred on fair value, with widths and sizes that reflect what others may know - Exact, fast updates as cards are revealed - Sensible inference from other players' behaviour, allowing for the possibility that it misleads - Clear communication of prices and reasoning under time pressure ### Follow-up Questions - You are already long several contracts when a low community card is revealed. Walk through your new fair value, quotes and position. - One player quotes much tighter than everyone else and trades in large size. What could explain it, and how do you respond? - How would your approach change if the contract settled on the highest single card instead of the sum?