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AkunaCapital·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Akuna Capital quant engineer interview had at least one math/probability problem that looked clean on the surface but had a few moving parts worth thinking through carefully.

Questions Asked (1)

Q1

Given a probability p for some event, treat 1/p as the fair decimal odds. What stake should you wager so that a win yields exactly $1000 in net profit? Handle edge cases where p is out of range.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The math itself isn't bad once you write it out.

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AI HintsAI Generated

Suggested Approach

First, clarify the betting terminology: fair decimal odds of 1/p mean that a successful $1 stake returns 1/p (including the original stake), so net profit is (1/p) - 1. To achieve a net profit of $1000, set stake * ((1/p) - 1) = 1000, giving stake = 1000 * p / (1 - p). Then handle edge cases: if p <= 0 or p >= 1, the odds are invalid; if p = 0.5, stake = $1000; if p > 0.5, stake < $1000; if p < 0.5, stake > $1000.

Pro tip: Explicitly state your assumptions about the odds convention (decimal odds include stake) and validate p before computing; this shows attention to detail and prevents off-by-one errors in a trading context.

1. Clarify the odds convention

Confirm that 'fair decimal odds' of 1/p means a winning $1 stake returns 1/p, so net profit per dollar is (1/p) - 1.

2. Derive the stake formula

Set up the equation: stake * ((1/p) - 1) = 1000, then solve for stake = 1000 * p / (1 - p).

3. Validate p and handle edge cases

Check that 0 < p < 1; if p <= 0 or p >= 1, the odds are invalid (division by zero or negative odds). Also consider p = 0.5 as a sanity check.

4. Compute and verify

Plug in p to compute the stake, then verify that a win yields exactly $1000 net profit by checking stake * ((1/p) - 1) = 1000.

Key Points to Mention

  • Definition of fair decimal odds: 1/p includes the original stake, so net profit per unit stake is (1/p) - 1.
  • Derivation of the stake formula: stake = 1000 * p / (1 - p).
  • Edge cases: p <= 0 or p >= 1 are invalid; p = 0.5 gives stake = $1000; p > 0.5 gives stake < $1000; p < 0.5 gives stake > $1000.
  • Validation of p before computation to avoid division by zero or negative stakes.
  • Verification step: ensure the computed stake indeed yields $1000 net profit.
  • Potential floating-point precision issues when p is very close to 0 or 1.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.