PRACTICE GUIDE AKUNA CAPITAL
Akuna Capital Probability & Estimation Practice Test
Akuna Capital does not publish the shape of its probability & estimation screen, and candidates describe it as 10 to 20 questions in 15 to 45 minutes, roughly one to three minutes per question, answered by picking one of the options.
Those are ranges across firms running this format rather than Akuna Capital's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
Outcry is not affiliated with Akuna Capital and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Akuna Capital’s own.
What it screens
A Chicago options market maker with a strong C++ and derivatives-pricing focus.
- ✓Expected value computed fast and used to make a decision
- ✓Conditional probability and Bayes updates without formal notation
- ✓Ranking likelihoods rather than computing them exactly
- ✓Fermi estimation: decomposing an impossible question into three easy ones
Where it sits at Akuna Capital
A Chicago options market maker with a strong C++ and derivatives-pricing focus. What that means for the screen is that the questions tend to be drawn from the work rather than from a textbook, so the format below is the shape to train against rather than a syllabus.
Candidates also report 4 other screens at Akuna Capital, covered separately on this site. Where a firm runs several, they usually sit in one round rather than spread across the process, so the pacing of the whole set matters more than any single section.
The format
Akuna Capital does not publish this screen's shape, and it varies between firms, so these are the ranges candidates report rather than exact figures.
| Questions | 10 to 20 |
|---|---|
| Time | 15 to 45 minutes |
| Per question | one to three minutes |
| Negative marking | Varies by firm and year |
| Answer style | Multiple choice or a typed number |
| Where it sits | First round, or a second technical screen |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Akuna Capital’s.
Expected value and odds
Pricing a bet, converting between odds and probabilities, and deciding whether to take it.
Example
A fair 4-sided die is rolled once. Expected value?
- 4
- 3
- 2.5
- 2
Answer 2.5
(1 + 4) / 2 = 2.5.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example 1
How many distinct ways can 6 people line up single file?
Answer 720
6! = 720.
Example 2
A market is Calm or Volatile. Each day: Calm turns Volatile with probability 0.1, Volatile turns Calm with probability 0.3. Over the long run, what fraction of days are Calm?
- 1/4
- 3/4
- 1/2
- 9/10
Answer 3/4
Stationarity balances the flows: π(Calm)·0.1 = π(Vol)·0.3, so π(Calm) = 0.3/(0.1+0.3) = 3/4.
Example 3
Cards are dealt one at a time from a shuffled standard deck. Before each card you may call "red" - you win if that card is red, and the game ends. If you never call, the last card decides. What is your best possible probability of winning?
- It grows with patience
- 27/52
- 26/51
- 1/2
Answer 1/2
A martingale argument: whatever the strategy, the proportion of reds remaining is a martingale, so every stopping rule wins with exactly 1/2. No timing edge exists.
Distributions you should know cold
Binomial, geometric and uniform means and variances, applied rather than quoted.
Example
A fair 4-sided die is rolled until two 4s land back to back. How many rolls on average?
- 4
- 32
- 8
- 16
- 20
Answer 20
Let E be the answer from a fresh start. One roll hits with chance 1/4 and then needs one more hit. Solving gives 4² + 4 = 20.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
1. Fay finished ahead of Dee. 2. Exactly 2 runners finished between Bo and Dee. 3. Exactly 2 runners finished between Eli and Fay. 4. Fay did not finish 4th. 5. Bo did not finish 2nd. 6. Bo finished ahead of Eli.
Five runners finished a race with no ties. The notes above are all true. Who finished 1st?
- Dee
- Jo
- Fay
- Bo
Answer Bo
Five runners means 120 orders, and each note cuts the survivors down. The only order that satisfies every note is 1st Bo, 2nd Fay, 3rd Jo, 4th Dee, 5th Eli. So 1st is Bo. Fix the tightest note first, then propagate.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
How many observations are needed for a 95% confidence interval of half-width 2.5, when the standard deviation is 25?
Answer 385
n = (1.96σ/w)². Call it 2: (2 × 25/2.5)² = 400, which overshoots by 4%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
4 crates arrive at a receiving dock holding rivets, spacers, bushings and clips, one content each. Each crate carries a label naming one of those 4 contents, no two labels the same, and every label is on the wrong crate. Opening a crate shows what is in it. How many crates must be opened, in the worst case, to relabel all 4 correctly?
Answer 2
The label-to-contents map is a permutation with no fixed point, and there are 9 of those on 4 items. Opening a crate reveals its contents and splits the live set; picking the next crate after seeing the last result, a minimax search over every opening order gives 2 as the worst case. With 4 = 3 the two possible arrangements are the two rotations, and one look separates them. The general pattern: the last two crates settle themselves only when the two contents left both clash with their own labels.
What a good score looks like
Probability rounds are usually marked as part of a wider battery, so a standalone threshold is rarely reported. Where candidates do describe one it clusters around getting two thirds of the items right, with the caveat that these sections are short enough that two mistakes move you a long way.
How to train for it
- 01Work the standard results until they are recall, not derivation: complement, conditional, binomial mean and variance, geometric expectation.
- 02Do them timed. A probability question you can solve in four minutes and the paper gives you ninety seconds for is a question you cannot solve.
- 03Sanity-check the magnitude before committing. A probability above one or an expectation outside the range of outcomes is a caught error, and these papers plant both as options.
TRAIN IT HERE
The drills that match each section
Likelihood Ranking
Order events from most to least likely - the exact screen-question format.
Fermi Estimation
Piano tuners in Chicago, atoms in a body - scored on order of magnitude.
Quitters Never Lose
A casino stopping-strategy game that is secretly a martingale lesson.
Tail Risk
Rare events and fat tails, and what they do to a plain expected-value estimate.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Akuna Capital
Common questions
- Is the Akuna Capital probability & estimation test multiple choice?
- Reported as multiple choice or a typed number. Formats move, so treat this as the shape rather than a guarantee.
- How long is the Akuna Capital probability & estimation test?
- Candidates report 10 to 20 questions in 15 to 45 minutes, roughly one to three minutes per question.
- Is there negative marking on the Akuna Capital probability & estimation test?
- It varies by firm and by year. Where a paper does mark negatively, skipping beats guessing; where it does not, answer everything. Check the instruction screen before you start - it is always stated there.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts.
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