Expected return of a three dice matching game

What this expected-value probability question tests

This is a medium-difficulty probability question common in quant interview loops, designed to test your ability to partition an outcome space into mutually exclusive events, assign probabilities to each partition, and compute expected value cleanly. The three payoff regimes force you to think carefully about how to classify dice outcomes.

Successful candidates enumerate the relevant cases (matching all three, matching exactly two, all different), compute the probability of each case from first principles, and then apply the linearity of expectation to sum the weighted payoffs. The question rewards systematic reasoning and accurate counting over pattern-matching or guessing.

• Partitioning sample spaces into disjoint events
• Counting outcomes under constraints (e.g., "exactly two match")
• Weighting payoffs by their probabilities
• Interpreting expected value as a long-run average