Oct 08, 2026 by Offer

Optiver Probability Interview 2027: Fair Price Dice Game

The Optiver probability dice game fair price answer: odd faces pay face value (1, 3, 5), even faces pay double (4, 8, 12) — summing to 33 over 6 faces, so fair is 5.5. Buy below it; demand a discount for variance. Commonly reported by candidates.

What This Question Assesses

This tests clean expected-value computation plus the trader's follow-up: fair price is not the same as a good trade. The interviewer wants the arithmetic done flawlessly and aloud, then the discussion of edge — at what price below 5.5 would you play, considering variance and bankroll? Candidates who compute correctly but cannot discuss the trading decision show calculation without judgement.

Optiver Probability Dice Game Fair Price: How to Answer

Step 1 — List payoffs per face. "Faces 1 through 6. Odd faces (1, 3, 5) pay face value: 1, 3, 5. Even faces (2, 4, 6) pay double: 4, 8, 12."
Step 2 — Compute the expectation. "Sum: 1+4+3+8+5+12 = 33. Divide by 6: 5.5. So the fair price — the price at which the game has zero expected profit — is 5.5."
Step 3 — State the trading rule. "I would play at any price below 5.5 and sell (offer the game to others) at any price above it. At exactly 5.5 I am indifferent on expectation."
Step 4 — Add the practical overlay. "In practice I would want a margin below fair value — the edge must compensate for variance and the fact I only get limited plays. I would also consider my bankroll: even a +EV game is a pass if the stake risks ruin."

An example line: "Odd faces pay 1, 3, 5 and even faces pay 4, 8, 12 — that sums to 33, over 6 faces gives 5.5, so fair is 5.5; I would buy below that and want a discount for variance, since one play at full Kelly on a single die roll is not a trade I would take."

Optiver Probability Dice Game Fair Price: Common Mistakes

Arithmetic slips. The most common error is mis-doubling an even face or mis-summing. Slow down, list all six payoffs explicitly, and add them visibly.
Confusing fair price with a buy price. Fair means zero edge — a trader needs edge. Saying "I would pay 5.5" reveals you do not understand why the firm exists.
Ignoring the sell side. A market maker quotes both sides. Mentioning you would offer the game above fair value shows you think like a trader, not a gambler.

Simple EV questions are accuracy tests with a trading discussion attached — nail the number, then show the judgement.

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FAQ

What does "fair price" mean exactly? The entry price at which the game's expected net profit is zero — here 5.5. It is the indifference point, not a recommendation to play.

How much below fair value would you play? It depends on variance, bankroll, and repetition. In interviews, the key is showing you require a discount for risk — the exact margin matters less than the reasoning.

What is the variance of this game? Compute E[X²] − (E[X])² from the six payoffs: it is a moderately high-variance game relative to its EV, which is why bet sizing matters even with an edge.

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