Roulette Wheel Probability Puzzle

This puzzle describes a simple gambling game based on a stylized roulette wheel with a few possible payouts and a fixed entry fee per spin. The candidate is asked to decide whether it is a good idea to play, first when the game can be repeated indefinitely and then when it can only be played once. The contrast between these two scenarios highlights the difference between long-run average performance and the experience of a single, risky outcome, a distinction that often appears in interviews for trading and risk-related roles.

To answer convincingly, the candidate must compute the expected payoff of a single spin and compare it with the cost of playing. The question leans on basic probability, linearity of expectation, and an intuitive understanding of the law of large numbers. An interviewer is looking for comfort with translating a word description into a probability model, clarity on how expected value guides decisions over repeated trials, and an ability to discuss how risk, variance, and personal preferences enter when the decision is about a one-off play.

What it tests

The core structure in problems like this is the comparison of expected value to cost, which is foundational to decision-making under uncertainty. The expected value aggregates all possible outcomes, weighted by their probabilities, to give a single number representing the average result over many trials. If the expected value of a game or investment exceeds its cost, then, on average, participating is profitable in the long run. This principle holds because, as the number of repetitions increases, the actual average outcome converges to the expected value by the law of large numbers. The key is that randomness smooths out over many trials, so the expected value becomes a reliable guide for repeated decisions, but for single plays, variance and risk preferences also matter.