Basket Arbitrage

How it works

Each round shows a set of cards. Every card is a tradeable basket of commodities (gold, silver, platinum, copper, oil) with its composition listed, a bid (what you receive to sell one) and an ask (what you pay to buy one). You set a quantity from -3 to +3 on each card - positive means buy at the ask, negative means sell at the bid. The screen shows your live net inventory per commodity and your live cash PnL as you build the position.

A round only counts when you press execute with every commodity's net inventory at exactly zero AND the position cash-positive. Unhedged inventory is rejected as directional risk, and a balanced position that crossed the spread at a loss is rejected too. The structure is always the same trade: some basket card is quoted rich relative to the cost of replicating its composition from the component cards, so you buy the pieces at their asks and sell the basket at its bid (or the reverse when the basket is cheap).

A session is 20 rounds: 4 hand-curated levels, then 16 procedurally generated ones climbing from 2 commodities in play up to 8. The generator builds each basket as an integer combination of the component cards, so a zero-inventory, positive-PnL hedge always exists within the position cap. There is one shared clock for the whole set - 8 minutes across 20 rounds, running even while you read a round's result screen. When it expires, the session ends and unexecuted work counts for nothing.

How scoring works

A successful execution on round k (1-indexed) scores round(PnL in dollars times 10 times k) - the same dollar of locked-in PnL is worth 10 points on round 1 and 200 points on round 20. Failed executions score nothing, and rounds ended by the clock score nothing.

Your session total is summed across rounds, and your best session score is stored locally as a personal best.

Price by replication, always at the prices you actually trade

The core idea is the law of one price: two positions with identical composition must cost the same, or the difference is free money. To check whether a basket is rich, compute its replication cost - the sum, over component cards, of the quantity needed times the price you would actually pay. Buying components means paying asks; selling the basket means receiving its bid. The arbitrage exists only if basket bid minus component-ask cost is positive.

That asymmetry is the whole discipline. Mid prices are a fiction you never trade at; every leg crosses a spread, and the spread is exactly what makes most near-misses unprofitable. Beginners compute edge at mids, find phantom arbitrage, and then execute into a negative PnL - which this game explicitly rejects with 'you crossed the spread at a loss'.

Work composition first, prices second. Write down (or mentally tally) what combination of components reproduces the basket exactly - the curated levels teach the patterns: units versus multi-packs, a basket equal to two pairs minus a shared single, a bundle equal to a pack plus a barrel. Once the composition matches, the PnL check is a single subtraction.

Netting to zero is the hedge, sizing it up is the edge

Zero net inventory per commodity is what converts a price gap into an arbitrage instead of a bet. If you sell a rich basket without buying the pieces, you are short its commodities and exposed to their prices - the game correctly refuses to score it. The mental model is a vector equation: your action quantities times each card's composition vector must sum to the zero vector, while the cash leg sums positive.

Once you have one valid unit of the trade, consider scaling it. Doubling every leg doubles the locked-in PnL at the same zero risk, up to the per-card cap of 3 - level 3's explanation notes exactly this. Since points are PnL times 10 times the round number, sizing up a clean hedge is the cheapest score multiplier in the game. Check the binding constraint: the leg that needs the largest quantity (often the basket at -1 versus components at +2 or +3) determines how many units fit under the cap.

On the bigger procedural boards, exploit how the puzzles are built: the basket card is an integer combination of the components with small coefficients (1 to 3), and the intended trade is sell 1 basket, buy the components in those coefficients. Find the card whose composition spans several commodities - that is the basket - then match each of its commodities against the component cards one commodity at a time.

Pace the shared clock like an assessment battery

The 8-minute budget across 20 rounds averages 24 seconds per puzzle, but the value is heavily back-loaded: the round multiplier means round 20 pays 20 times more per dollar than round 1. Speed through the early curated levels - they are fixed, learnable patterns worth few points - to bank time for the later high-multiplier boards where an extra dollar of PnL is worth 150 to 200 points.

The clock runs while the result screen is showing, so tapping through reviews quickly is worth real points. Budget consciously: if the first 8 rounds take under 2.5 minutes you are on pace; if a mid-game board has you stuck past 40 seconds, take the smallest hedge you can see rather than hunting the maximal one - a scored dollar beats an unscored three.

Late boards with 7 or 8 commodities reward a scan order: start from the basket card, list its commodities, and for each one find which component supplies it. Because components touch only 1 or 2 commodities each, this is a fast matching exercise rather than a full linear solve.

A worked example

Level 3, the Tri-Commodity Index ETF. Cards: Alpha Pair (1 Gold + 1 Silver) bid 60 / ask 63; Beta Pair (1 Silver + 1 Platinum) bid 95 / ask 99; Single Silver bid 12 / ask 14; Index ETF (1 Gold + 1 Silver + 1 Platinum) bid 152 / ask 156.

Composition first: Alpha + Beta = 1 Gold + 2 Silver + 1 Platinum - one Silver too many versus the ETF. So Alpha + Beta - 1 Silver = 1 Gold + 1 Silver + 1 Platinum, exactly the ETF. The replicating trade is: buy 1 Alpha at 63, buy 1 Beta at 99, sell 1 Silver at its bid of 12, sell 1 ETF at its bid of 152.

Inventory check: Gold +1 -1 = 0, Silver +1 +1 -1 -1 = 0, Platinum +1 -1 = 0. Cash: -63 - 99 + 12 + 152 = +2. Balanced and positive, so it executes for +$2.00; at round 3 that is 2 x 10 x 3 = 60 points. Note the sizing lesson attached to this level: repeating every leg (2 Alpha, 2 Beta, -2 Silver, -2 ETF) locks in $4 at the same zero risk, still inside the +/-3 cap - always ask whether the hedge scales before executing.

Common mistakes

• Computing edge at mid prices. You buy at asks and sell at bids; an opportunity that only exists at mids will execute at a loss and score nothing.

• Executing with a small residual inventory 'because the PnL is good'. The game rejects any nonzero net exposure - it is a bet, not an arbitrage, and it scores zero.

• Taking one unit when the hedge scales. PnL times 10 times round number means an unscaled hedge on a late round can leave hundreds of points on the table.

• Lingering on result screens. The single session clock keeps running between rounds; review time is paid for in end-of-session rounds you never reach.

• Solving prices before composition. Matching the commodity vectors first turns each board into arithmetic; starting from prices turns it into guesswork.

Why interviews test this

This is a direct training ground for trading-firm assessment batteries (the Optiver-style '80 in 8' format the session clock deliberately mirrors) and for interview questions on the law of one price: ETF create/redeem arbitrage, index versus basket pricing, and triangular consistency between related instruments all reduce to 'replicate the package, compare at tradeable prices, keep zero net exposure'.

Interviewers also probe the execution details this game enforces: which side of the spread each leg crosses, what residual inventory does to a 'riskless' trade, and how position limits cap the size of an edge. Being fast and exact on small integer replication arithmetic under a clock is precisely the skill being screened.