10 Heads in a Row Flip Count
Average flips for 10 heads in row is a medium quant interview question on Expected Value, reported to have been seen at Citadel, Goldman Sachs, IMC, Jane Street, Squarepoint Capital, Two Sigma and WorldQuant.
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This quant interview question is about understanding how long you typically have to wait, in a random process, before a particular pattern shows up. It turns a simple setting into a subtle probability puzzle, forcing you to think in terms of states and how they evolve. It often surprises candidates whose intuition about "rare streaks" is not well calibrated, making it a favorite in top-tier quant prep materials.
It trains your grasp of expected value in sequential settings, especially when outcomes depend on a running streak. You practice modeling memory through a compact state description, working with stochastic dynamics and recursive structure. It also develops comfort with translating a seemingly simple story into a precise probabilistic framework.
This matters for quant interviews because many trading and risk problems involve waiting times, path-dependent behavior, and regime shifts. Interviewers use it to see whether you can abstract a messy narrative into a clean model, reason rigorously under uncertainty, and stay organized through multi-step quantitative arguments. These are core skills for quant roles in research, trading, and systematic strategy design.
What it tests
Problems that ask for the expected waiting time until a specific sequence appears in a sequence of random trials (like coin tosses) are governed by the structure of Markov chains and recurrence relations. The key is to recognize that the system's memory is fully captured by the current 'state'—here, the length of the current streak—so the future is independent of the past beyond this state. This allows us to set up recursive equations for the expected time to reach the target, with each equation expressing the expectation in terms of possible next states and their probabilities. The pattern holds because, at every step, the process either progresses toward the goal or resets, and the expected value must account for both possibilities weighted by their likelihood. The exponential growth in expected waiting time for longer sequences arises because each failure resets progress, compounding the difficulty multiplicatively.
Practise this question with written feedback, or hear it in a spoken mock interview.
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