PRACTICE GUIDE OPTIVER
Optiver Likelihood List Practice Test
Likelihood List practice trains ordering outcomes from the information supplied: dice, cards, conditional events and visual distributions. Work out what event is being ranked before doing arithmetic.
The linked Outcry drill uses eight questions with a clock for each question. It is independent practice; use your assessment invitation for the actual test length and marking.
Outcry is not affiliated with Optiver 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 Optiver’s own.
What it screens
A global market maker headquartered in Amsterdam, trading options, ETFs and futures on major exchanges.
- ✓Complement probabilities and repeated independent trials
- ✓Conditional probability with a changed sample space
- ✓Reading probability from density and frequency charts
- ✓Ranking outcomes without confusing expected value with probability
Where it sits at Optiver
This page focuses on likelihood list skills for Optiver preparation. The linked exercise is built by Outcry and is not the firm’s assessment.
Check the role-specific invitation for required modules, timings and marking. These can differ by office and recruitment year.
The format
These are Outcry's practice-game settings, not verified figures for the firm's assessment.
| Questions | 8 |
|---|---|
| Time | Varies by question |
| Per question | Each question has its own clock |
| Negative marking | No |
| Answer style | Arrange outcomes from most to least likely |
| Where it sits | Outcry skill practice; follow your invitation for the firm's format |
What it tests, with a worked example
These worked examples are written by Outcry to explain the skills practised here. They are not the firm's questions.
Use the complement
At least one is often easier to calculate as one minus none.
Example
Rank most likely first: A = at least one head in 3 fair flips; B = exactly 1 head in 3 fair flips; C = 3 heads.
Answer A > B > C
A = 1 - (1/2)^3 = 7/8. B = 3/8. C = 1/8.
Count equally likely outcomes
Compare favourable cases over the full sample space.
Example
Rank: A = sum 7 on two fair dice; B = doubles; C = sum 12.
Answer A = B > C
There are 36 ordered outcomes. Sum 7 has 6, doubles has 6 and sum 12 has 1. A and B tie; do not invent a strict order.
Update the sample space
Given information changes the denominator.
Example
A fair die is known to show an even number. Rank: A = result above 3; B = result 2; C = result 5.
Answer A > B > C
The possible results are 2, 4 and 6. A has probability 2/3, B has 1/3 and C has 0.
Read area under a density
A continuous density height is not itself a point probability.
Example
X is uniform on [0, 10]. Rank: A = 2 < X < 7; B = X > 8; C = X = 5.
Answer A > B > C
The interval lengths give A = 5/10 and B = 2/10. An exact point has probability zero for this continuous distribution.
Weight frequencies
The tallest bar need not represent the most observations when bin widths differ.
Example
Histogram density: interval [0,2] has height 0.2; [2,5] has height 0.1; [5,6] has height 0.3. Rank their probabilities.
Answer [0,2] > [2,5] = [5,6]
Multiply width by height. The three areas are 0.4, 0.3 and 0.3, summing to 1.
Separate payout from chance
A large expected payout does not mean a large chance of winning.
Example
Rank the chance of a positive payout: A pays $100 on a fair die showing 6; B pays $1 on a fair coin showing heads; C pays $20 on drawing an ace from 52 cards.
Answer B > A > C
The probabilities are 1/2, 1/6 and 4/52 = 1/13. Prize amounts do not change these chances.
What a good score looks like
Use accuracy and the reasoning behind each answer to judge progress. No verified firm pass mark is asserted here.
How to train for it
- 01Compute or bound each probability before arranging the outcomes. Use a common denominator when it helps.
- 02For charts, check axes, bin widths and conditioning before comparing regions.
- 03Review the explanation after every round and redo the ranking from the underlying probabilities.
TRAIN IT HERE
The drills that match each section
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 Optiver
Common questions
- What do I practise here?
- Rank possible outcomes using probabilities, counts and charts. Compare events on the same scale before committing to an order.
- How long is the practice?
- The linked Outcry drill uses eight questions with a clock for each question. It is independent practice; use your assessment invitation for the actual test length and marking.
- How should I improve?
- Review the explanation after every round and redo the ranking from the underlying probabilities.
- Where do I start?
- Use the Likelihood Ranking game linked under Train it here after working through the examples.