Hard · Market Making & Trading Games · Market making · ~15 min · #20

Make a Market: Five Cards

Five cards are dealt face down from a standard 52-card deck (Ace = 1, ..., King = 13). You make a market on their sum over five rounds; before each round after the first, one more card is revealed. Your quotes can be at most 4 wide and your position is capped at ±12.

Because the cards are dealt without replacement, each revealed card also changes the expected value of the cards still hidden.

Goal: finish with a total score $\geq 2$ .

Scoring rules

Each round you enter a fair value, a bid and an ask (ask − bid ≤ 4). Then the round's counterparties arrive in a fixed, seeded order:

12 noise traders, each with a random edge between 0 and 4. A noise buyer lifts your ask if ask ≤ public EV + edge; a noise seller hits your bid if bid ≥ public EV − edge. Size 1.
One informed trader who knows the true value: buys 2 at your ask if ask < true value, or sells at your bid if bid > true value.
Fills that would take |position| above 12 are rejected.

After the last round the position settles at the true value.

Score = PnL − 0.15 × Σ|position after each round| − 0.5 × Σ|fair value − public EV|

PnL = spread edge (earned versus the public EV) + information PnL (position × (true − EV) at each fill). Target score ≥ 2. The same seed and the same quotes always produce the same result; the final score is recomputed on the server.

Seed 2024Round 1 of 5Counts toward this problem

0 of 5 revealed

Position

Cash

Mark @ EV

Max width

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Concepts

Conditional expectation without replacementAdverse selectionInventory skew

Relevant for

Quant TraderDesk Quant

Make a Market: Five Cards

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Worked solution

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