Two-Coin Flip Game Expected Payout

This classic quant prep question is about turning a simple random experiment into a precise expected payout. It forces you to read a short game description, identify the underlying probabilistic structure, and translate words about winning or losing money into a clean mathematical expectation. Even though it uses coins, it mirrors the payoff logic of basic trading strategies and simple derivatives seen in quant interviews.

It trains discrete probability, expected value, and comfort with payoffs under uncertainty. You practice mapping every outcome to a profit or loss and combining them into a single number that summarizes the game's attractiveness. It also builds intuition for risk, reward, and how rare but large losses affect the overall expectation.

This matters for quant interviews because many firms use similar payoff questions to test clarity of thought, numerical instinct, and basic risk-reward reasoning before moving to more complex models.

What it tests

Expected value in discrete probability is fundamentally about weighting each possible outcome by its probability and summing these products. This approach works because, over many repetitions, the average result converges to this sum, reflecting the law of large numbers. The structure of such problems is always: enumerate all mutually exclusive outcomes, assign each a probability and a value, and sum the products. The key is that each outcome's contribution to the expectation is proportional to both its likelihood and its impact. This principle holds regardless of the surface story: coins, dice, or any random process with discrete outcomes.