Optiver Online Assessment Practice: Math & Probability

Train accuracy first, then speed. For an Optiver trading assessment, being able to recognize a simple calculation quickly is more useful than memorizing a complicated trick you cannot apply under pressure. Start with arithmetic, move to probability and expected value, and finish with mixed timed practice.

This guide gives you original exercises, complete solutions, and a seven-day schedule. For the exact modules, timing, calculator rules, and navigation in your assessment, use your invitation. Optiver publishes separate recruiting guidance for the US, Europe, and Sydney.

Choose your first practice session from the invitation

For trading, use arithmetic and probability to establish a baseline; for research or engineering, adjust the mix to the role. Read the invitation before paying for a simulated test. Record the modules, deadline, navigation rules, calculator policy and device requirements in one place.

Optiver's Europe recruitment FAQ says eligibility depends on the job description, asks candidates to use a suitable device and stable connection, and provides a route for reasonable adjustments. As checked October 13, 2026, it also describes an eight-month assessment reset/retake restriction once an attempt has started. That is regional guidance: check your own office and invitation before starting an attempt just to inspect the format.

Read your score as a diagnosis

Imagine you answer eight of ten unfamiliar questions correctly untimed, then only five correctly with a timer. Separate the three additional errors into copying mistakes, rushed arithmetic, and models you never finished. Spend the next session on the recurring cause. If you are inaccurate untimed too, shortening the timer is unlikely to help.

Worked speed check: estimate before calculating

Which is larger: 49 × 51 or 50²? The first is 2,499, because (50 − 1)(50 + 1) = 2,500 − 1. The difference-of-squares method also explains why the answer is slightly below 2,500. A reasonableness check makes a fast answer safer than an unexplained shortcut.

For a variation, compare 98 × 102 with 100²: the difference is four. Then generate your own pair around a round number. You are practicing a transferable relationship rather than memorizing an answer.

Build the arithmetic foundation

Start with this six-question set. Solve it untimed, check your work, then repeat with fresh numbers and a three-minute practice budget. The budget is a training choice, not the employer's official test format.

After every session, record accuracy, completion time, and the error type. Keep a list of conversions that slow you down: halves, quarters, eighths, thirds, and common percentage changes.

For a longer firm-neutral practice set, use mental math for quant trading. When arithmetic is no longer the bottleneck, try the market-making interview exercises to practice quotes, position limits and decisions with changing information.

A percentage trap worth fixing

A quantity rises 20% and then falls 20%. What is the overall change?

Start at 100. It becomes 120, then 96. The overall change is −4%, because the two percentages have different bases. Multiplying the factors, 1.2 × 0.8 = 0.96, is the general method.

Follow-up: after a 20% loss, a 25% gain is needed to recover: 0.8 × 1.25 = 1. This comes up whenever a problem mixes relative changes.

Practice probability with explicit assumptions

Question 1: at least one success

Two fair dice are rolled independently. What is the probability at least one shows six?

Solution: use the complement. The probability neither is six is (5/6)² = 25/36. Subtract from one: 11/36.

Do not add 1/6 + 1/6 without correcting for the case where both dice show six. That double-counts one outcome.

Question 2: a conditional draw

A deck has 52 cards, including four aces. You draw two cards without replacement. Given that the first was an ace, what is the probability the second is an ace?

Solution: three aces remain among 51 cards, so 3/51 = 1/17. The condition has already happened; do not multiply by the probability of the first ace again.

Follow-up: before either draw, the probability of two aces is 4/52 × 3/51 = 1/221.

Question 3: a fair entry price

A ticket pays $12 if the sum of two fair dice is seven, and zero otherwise. What is its expected payout?

Solution: six of the 36 ordered outcomes sum to seven. Expected payout is $12 × 6/36 = $2. An entry price of $2 gives zero expected net profit for a risk-neutral player.

Follow-up: at an entry price of $1.50, expected net profit is $0.50. The positive average does not mean every ticket wins.

Practice changing your decision

Roll a fair die. You can keep the result or reroll once, accepting the second result. What should you do?

The reroll is worth 3.5 in expectation. Reroll 1, 2, or 3; keep 4, 5, or 6. The expected score of this policy is (3 × 3.5 + 4 + 5 + 6) / 6 = 4.25.

Now introduce a one-point reroll cost. The expected value of rerolling becomes 2.5, so reroll only 1 or 2. Good preparation includes these changes of assumption: explain what changed and update the decision.

Use sequences as reasoning practice

Find a simple continuation of 3, 7, 16, 35, 74.

One rule is to double the previous term and add an incrementing integer: +1, +2, +3, +4. That gives 153 next, since 2 × 74 + 5 = 153. Check the rule against every given term before committing.

A finite sequence can have multiple continuations. The task is to recognize a simple consistent pattern. First try differences, then ratios, then alternating subsequences. Set a practice time limit so one puzzle does not consume the whole session.

A seven-day preparation schedule

If probability is your main weakness, use the SIG practice guide for another set of worked problems. If your preparation needs longer, follow the four-week study plan.

Questions candidates ask

Should I focus only on mental math?

No. Use it as one part of your preparation. Arithmetic speed helps you execute, but probability and expected value determine whether your approach is right. Build both, then combine them in mixed practice.

What accuracy should I aim for?

Use 90% as a practice target before reducing the time budget. This is a training benchmark. Review the reason for every miss; a high score on memorized questions says less than consistent reasoning on unfamiliar variations.

Should software applicants follow this plan?

Use the arithmetic and probability sections if they appear in your assessment, but put coding, algorithms, and relevant systems first for software roles. Optiver's regional recruiting guidance separates role-specific preparation; match your work to the position.

Get feedback on your reasoning

Our interview preparation program combines lessons, practice, and mock interviews so you can work on both the calculation and the explanation. Book a free quant consultation to discuss your interview goals and preparation, or explore the Optiver career guide and question collection.

Further reading: Optiver's regional recruiting pages linked above, checked October 13, 2026. The exercises here are original practice material from Quant Blueprint.