WorldQuant Quantatitive Researcher Interview Question
In the quantitative research community, interview questions often challenge candidates to display both mathematical insight and algorithmic thinking. One classic problem—frequently seen in interviews at leading quantitative firms such as WorldQuant—is: How can you simulate a fair die using a biased one? Understanding and implementing this solution not only tests your grasp of probability theory, but also your ability to design algorithms under constraints. In this article, we’ll explore this problem in depth, covering the necessary probability background, presenting step-by-step solutions, analyzing their efficiency, and discussing extensions relevant to quantitative research.
Before jumping into solutions, let's clarify the challenge. Suppose you only have access to a biased die—that is, a six-sided die where each face may have a different probability of occurring. However, your task is to simulate the behavior of a fair six-sided die, where each face appears with probability \( \frac{1}{6} \). You can roll the biased die as many times as needed, but you cannot physically alter it.
This problem is a variation of a fundamental theme in probability and computer science: how to generate fair random outcomes from biased sources. It appears in areas from cryptography to randomized algorithms and is highly relevant to quantitative finance, where simulation and random sampling are core techniques.
