HackTheRounds Interview Experiences

Optiver OA Interview Experience (2026) - Correlation Range, Ball-Drawing EV & Magic Coin Game Theory, Passed

Optiver 2026 SWE OA walkthrough: three math heavy problems in 100 minutes covering correlation matrix PSD bounds, optimal stopping DP on ball draws, and sequent

By Anonymous ยท 2026-03-21

Background

Going into Optiver's 2026 OA I had already burned through the Jane Street and Citadel OA pools, so I expected the "three math problems in 100 minutes" format to feel familiar. It did not. Optiver's OA is less about recognizing LeetCode patterns and more about setting up the right probabilistic or algebraic model and then writing the code as an afterthought. I am a masters student in quantitative finance with a CS undergrad and two summers of trading-tech internships. Applied through the Optiver 2026 Software Engineer posting in early March, got the OA invite five days later. This writeup covers the three problems I saw and the mental model I wish I had before I sat down.

Timeline

Online Assessment (100 min, proprietary platform)

Three problems, 100 minutes total, and the in-browser editor supports Python and C++ only. There is no stdlib probability helper and no scipy, so any numerical work has to be written by hand. The problems are framed as "here is a trading or gambling setup, compute the expected value under optimal play." You are not expected to write production code. You are expected to identify the closed-form or short recurrence and implement it cleanly.

Problem 1: Correlation Matrix Range

Problem: You have a 3 x 3 correlation matrix with the entries at positions [1,2] and [2,3] given as a and b respectively. Compute the valid range of the remaining correlation entry at [1,3] , which I will call x . Return the range as a two-element list of floats.

The underlying math is that any correlation matrix must be positive semi-definite. For the 3 x 3 case with diagonal entries all 1 , the determinant inequality simplifies to a quadratic constraint in x : 1 - a^2 - b^2 - x^2 + 2 a b x = 0 . Solving that quadratic for x gives the closed-form range a b - sqrt((1 - a^2) (1 - b^2)) on the lower end and a b + sqrt((1 - a^2) (1 - b^2)) on the upper end.

The code is four lines once you have the derivation. The only traps are numerical: when a or b is close to +/- 1 , the term under the square root approaches zero and round-off makes the bounds collapse. Clamp to [-1, 1] at the end. Also double-check orientation of the output, some variants of the problem want [low, high] and others want [high, low] .

Practice it: no exact match in the current Optiver set, so I did not link this one.

This question is coming soon to HackTheRounds.

Problem 2: Ball-Drawing Game Value

Problem: A bag contains N balls, half red and half green where N is even. Each draw pulls uniformly at random without replacement. A red draw pays +$1 and a green draw pays -$1 . You may stop at any time after any draw. Under optimal play, return the expected value of the game.

This is a classic optimal-stopping problem that collapses to a two-dimensional DP on the current bag composition. State: (red, green) counts remaining. At each state the optimal action is max(0, expected value of continuing) , because stopping is always an option worth zero additional dollars. The continuation value is (red / total) (1 + V(red - 1, green)) + (green / total) (-1 + V(red, green - 1)) .

Build the table bottom-up from V(0, 0) = 0 and roll outward. The state space is O(N^2) which is trivially within the 100-minute budget for N up to a few thousand. The sanity checks from the prompt are N = 2 yielding 0.5 and N = 8 yielding 1.0 . Both fall out if you get the recurrence right.

The trap is the temptation to derive a closed-form using the ballot problem or Catalan identities. There is a beautiful closed form, but it is easy to get wrong under time pressure. DP is safer.

Practice it: no exact match in the current Optiver set, so I did not link this one.

This question is coming soon to HackTheRounds.

Problem 3: Magic Coin Game Theory

Problem: You and an opponent each pick a probability of "heads" for a magic coin, any real number in [0, 1] . You declare your probability first, then your opponent picks theirs knowing yours. Both coins flip once, and your payoff depends on the joint outcome: heads-heads pays a , heads-tails pays c , tails-heads pays b , tails-tails pays d . Under optimal play by both sides, return the expected value of the game for you.

This is a sequential game where you are the leader and your opponent is the follower. Given your choice p , the opponent picks q in [0, 1] to minimize your expected payoff. Your expected payoff as a function of (p, q) is linear in q after fixing p , specifically it is a linear function of q with slope depending on p . That means the opponent's optimal q is either 0 or 1 (corner solution), and you know which by the sign of the slope.

So your problem reduces to maximizing over p of the min between the payoff when opponent picks q = 0 and the payoff when opponent picks q = 1 . Both of those are linear in p , so the maximum of the minimum of two linear functions is either at the intersection point or at p = 0 or p = 1 . Solve for the intersection explicitly, then take the max over the three candidate points.

The two example cases from the prompt verify the formula. For a = 10, b = -8, c = -10, d = 7 , the answer is approximately -2.857 . For the symmetric a = d = 1, b = c = 0 , the answer is 0.5 . Both check out if the algebra is clean.

Practice it: no exact match in the current Optiver set, so I did not link this one.

This question is coming soon to HackTheRounds.

Result

Passed all three problems with the correct numerical answers on the hidden tests. The grader notifies you per problem on submission, which is useful for time management: once you see a pass, move on instead of polishing. I got the trader tech round invite four business days later and the loop is still in progress at the time of writing.

Tips

  1. Derive the math before you touch the editor. Optiver OA problems are not algorithmic. They are mathematical modeling problems with code as the delivery mechanism. Spend the first five minutes per problem with pen and paper.
  2. Two-dimensional DP on bag composition is the pattern for any ball-drawing or card-drawing optimal-stopping question. Expected value in state `(a, b)` equals the max of zero and the recursion over single-draw outcomes. Internalize the template.
  3. Game-theoretic prompts with a "declare first, then opponent responds" structure reduce to minimax over a small domain. When the payoff is linear in each player's mixed strategy, the opponent always plays a corner, and your problem collapses to maximizing over a piecewise-linear function with two pieces.
  4. Watch numerical stability. The correlation matrix problem has a square root of a product of near-zero terms at the extremes. Clamp inputs to `[-1, 1]` and clamp outputs too. Numerical precision failures on hidden tests are an Optiver OA classic.
  5. The proprietary editor has no external libraries. Do not plan on scipy, numpy, or even Python's statistics module. Write your probability from scratch, and test your closed-forms against the prompt's worked examples before submitting.
  6. If you finish early, do not leave. Re-verify. All three problems have hidden numerical tests, and a sign error in one line of DP can pass the given examples while failing 3 of 5 hidden tests. Use every remaining minute to re-run your answers against edge cases like `N = 2`, symmetric payoff matrices, and `a = b = 0.5`.

This question is coming soon to HackTheRounds.