A contract settles at a die roll, doubled if a coin lands heads, plus 5 if a drawn card is red. Quote it, then decide whether to trade with a bot showing 9.5 bid, 10.5 offer, and whether to make or take.

Fair value is 7.75, so sell to the bot at 9.5: take its bid, do not join its market. The die is worth 3.5, the coin's doubling 1.75 and the card 2.5. The bot's bid is 1.75 rich, about 0.43 standard deviations of the outcome per contract. Even a coin that always landed heads would only make the contract worth 9.5, so only a stacked deck could justify the bot's price. Sell the 10 offered and re-quote around 7.75.

Break it into pieces and use the fact that expectations add. The die averages 3.5, heads adds another 3.5 half the time, worth 1.75, and a red card adds 5 half the time, worth 2.5, so fair value is 7.75. The doubling is the only step that needs care: it multiplies the die, so its value is the die's average times the chance of heads, which works because die and coin are independent. A shop running a festival offer, double points on weekends plus a flat bonus for paying by card, prices it the same way: average base, plus average uplift, plus average bonus.

Centre on 7.75 and set the width from the risk. Of 24 equally likely outcomes, the settlement runs from 1 to 17 with a standard deviation of about 4.07. A market of 7 at 8.5 is tight enough to show you know the value and wide enough to protect you if the interviewer knows something, such as which card is on top. In a game with no informed counterparty you can quote tighter; if they hint that they have peeked, widen and lean.

Sell to it, and take rather than make. Hitting the 9.5 bid earns 1.75 a contract in expectation, and posting your own offer at 8.5 would let the bot buy from you a whole point cheaper. Joining its market at 9.5 at 10.5 would mean offering at a price where no one rational buys. Selling all 10 lots earns an expected 17.5, against a standard deviation of about 12.9 on the position, so the trade can still lose: the contract settles above 9.5 in 8 of 24 outcomes, 33% of the time.

Before you sell, ask the one question that could make the bot right. Is the deck full and the coin fair? Even if the coin landed heads every time, the contract would be worth 3.5 times 2 plus 2.5, exactly 9.5, so the bot's bid needs either a coin that cannot land tails and a deck that favours red, or rules you have misread. Saying this out loud shows the interviewer you checked whether the price is information before treating it as a gift. Then trade, and as the die, coin and card are revealed, reprice each piece and update your quote.