Akuna Capital Expected Value 2027: Dice Question Explained
The Akuna Capital expected value dice answer: 7. Each die averages 3.5, and expectation is linear — so the sum's expected value is 3.5 + 3.5 = 7. Commonly reported by candidates, this tests linearity of expectation, the single most useful probability tool in trading interviews.
What This Question Assesses
This tests whether you reach for linearity of expectation instead of grinding through 36 outcomes. The interviewer wants the insight: E[X+Y] = E[X] + E[Y] regardless of dependence — and the follow-ups will test whether you know when that shortcut applies.
How to Answer: Akuna Capital Expected Value Dice
- Step 1 — One die: (1+2+3+4+5+6)/6 = 3.5.
- Step 2 — Apply linearity: E[sum] = E[die1] + E[die2] = 3.5 + 3.5 = 7 — no need to enumerate 36 outcomes.
- Step 3 — Note the power: linearity holds even for dependent variables — the key fact interviewers probe next.
- Step 4 — Contrast: E[X·Y] does NOT split this way in general — only for independent variables. Know the boundary.
Example: "One die expects 3.5, and by linearity of expectation the sum expects 7 — E[X+Y] equals E[X] plus E[Y] whether or not the dice are independent."
Common Mistakes on Akuna Capital Expected Value Dice
- Enumerating all 36 outcomes — correct but slow; the interviewer wanted the linearity insight.
- Forgetting linearity needs no independence — that is precisely what makes it powerful, and the likely follow-up.
- Misapplying it to products — E[XY] = E[X]E[Y] only under independence; conflating the two is a common trap.
Linearity of expectation unlocks half of trading-interview probability. Learn it cold — it is the highest-leverage concept in the packet.
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FAQ
Does linearity need independence?
No — that is the point. E[X+Y] = E[X] + E[Y] always holds.
What is the EV of the product of two dice?
12.25, since independent: 3.5 × 3.5. Independence is required here.
What about the expected maximum?
Harder — enumerate or use the CDF: P(max ≤ k) = (k/6)², then E = sum of P(max > k). A good follow-up to prepare.
Why do traders care?
Pricing is expectation under risk-neutral probabilities — EV thinking is the job, and this question is its simplest form.
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