Expected Value Interview Questions
Expected value is how traders price decisions. These questions train the EV reasoning behind games, bets, and stopping problems that interviews love to test.
These questions cover the EV of games and bets, optimal stopping, and 'should you take this bet?' decisions under uncertainty - the kind of pricing judgement trading desks test relentlessly.
The skill being tested is translating a messy scenario into a clean EV calculation - and knowing when variance, not just the mean, should change your decision.
147 expected value questions · 99 free to practise now.
By format:Market MakerHedge Fund QuantNumerical Reasoning TestsTrading Aptitude TestsBetting Game RoundsProp TradingSystematic & Data-Driven TradingOptions TradingETF Trading
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A die decides how many balls to drawEasyProbabilityExpected ValueView →
- Capped exponential payoutEasyRandom VariablesExpected ValueView →
- Color switches in a drawEasyRandom VariablesExpected ValueView →
- Even first die given a sum of eightEasyConditional Probability & ExpectationExpected ValueView →
- Expected flips after a losing startEasyProbabilityExpected ValueView →
- Expected flips for three headsEasyProbabilityExpected ValueView →
- Expected flips for two heads in a rowEasyProbabilityExpected ValueView →
- Expected profit on a scratch ticketEasyExpected ValueMarket Making & Betting GamesView →
- Expected sets for a favored playerEasyProbabilityExpected ValueView →
- Expected sum given a sixEasyProbabilityExpected ValueView →
- Fair mid on a dice product that voids on doublesEasyProbabilityExpected ValueView →
- Fair price for the higher of two diceEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a dice-product gameEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a die that rerolls on a sixEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a heads-majority betEasyProbabilityExpected ValueView →
- Fair price of a high-faces-only dice sumEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a higher-die contractEasyExpected ValueMarket Making & Betting GamesView →
- Fair price of a sum-divisible-by-three betEasyExpected ValueMarket Making & Betting GamesView →
- First success on an even trialEasyRandom VariablesExpected ValueView →
- Gap between two dice, given they differEasyConditional Probability & ExpectationExpected ValueView →
- Heads given at least one headEasyExpected ValueView →
- How many sixes on the die?EasyExpected ValueBrainteasersView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Keep the d8 or gamble on the d12?EasyProbabilityExpected ValueView →
- Matching chips, two drawsEasyCombinatoricsExpected ValueView →
- One re-roll allowedEasyExpected ValueView →
- Paid a dollar or the drawEasyExpected ValueStatisticsView →
- Paid the last roll before you stopEasyProbabilityExpected ValueView →
- Pairs who swap hatsEasyRandom VariablesExpected ValueView →
- Profit from a favourable stopping gameEasyExpected ValueStochastic ProcessesView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Retries under a hard capEasyExpected ValueStochastic ProcessesView →
- Rolling a die to size the next dieEasyConditional Probability & ExpectationExpected ValueView →
- Rolling until a high face, at a costEasyProbabilityExpected ValueView →
- Rolling until you match the first rollEasyProbabilityExpected ValueView →
- Rolls until an even sumEasyProbabilityExpected ValueView →
- Squared payout on even facesEasyRandom VariablesExpected ValueView →
- The costliest roulette bet on the tableEasyProbabilityExpected ValueView →
- Weighting a fixed sumEasyConditional Probability & ExpectationExpected ValueView →
- Which side of a two-sided marketEasyExpected ValueMarket Making & Betting GamesView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Distinct faces in three rollsMediumExpected ValueView →
- Expectation as a sum of tailsMediumRandom VariablesExpected ValueView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected flips for HHTMediumExpected ValueStochastic ProcessesView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected maximum of two diceMediumRandom VariablesExpected ValueView →
- Expected median of three diceMediumProbabilityExpected ValueView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Heads given the ends differMediumConditional Probability & ExpectationExpected ValueView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Locking a profit by hedging after the odds moveMediumExpected ValueMarket Making & Betting GamesView →
- Number of runsMediumExpected ValueView →
- Pay to play with a capMediumExpected ValueMarket Making & Betting GamesView →
- Position of the first aceMediumConditional Probability & ExpectationExpected ValueView →
- Pricing the higher of two diceMediumExpected ValueMarket Making & Betting GamesView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Rolling a 5-sided die to reach fiveMediumProbabilityExpected ValueView →
- Rolling until two rolls differ by twoMediumProbabilityExpected ValueView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Sharpe ratio in a marble gameMediumExpected ValueStatisticsView →
- The German tank problemMediumExpected ValueStatisticsView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- Three rolls, keep the lastMediumExpected ValueView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Distinct toys from seven boxesHardProbabilityExpected ValueView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairs left in the drawerHardCombinatoricsExpected ValueView →
- Rolling until two rolls are closeHardProbabilityExpected ValueView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Smallest card sharing a boxHardProbabilityExpected ValueView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- A convexity gap by JensenMediumRandom VariablesExpected Value Premium
- Aces in a seven-card handMediumCombinatoricsExpected Value Premium
- Break-even half-spread from toxic flowMediumProbabilityExpected Value Premium
- Break-even half-spread under adverse selectionMediumExpected ValueMarket Making & Betting Games Premium
- Distinct birthdays representedMediumProbabilityExpected Value Premium
- Distinct faces in five rollsMediumCombinatoricsExpected Value Premium
- Empty boxesMediumExpected Value Premium
- Expectation of e raised to a normalMediumRandom VariablesExpected Value Premium
- Expected absolute difference of two diceMediumExpected Value Premium
- Expected ascents in a shuffleMediumCombinatoricsExpected Value Premium
- Expected duration of a fair gameMediumExpected ValueStochastic Processes Premium
- Expected maximum of three diceMediumRandom VariablesExpected Value Premium
- Expected minimum of two diceMediumRandom VariablesExpected Value Premium
- Expected revenue of a Vickrey auctionMediumProbabilityExpected Value Premium
- Expected rolls for two sixes in a rowMediumExpected ValueStochastic Processes Premium
- Expected sum given both evenMediumConditional Probability & ExpectationExpected Value Premium
- Expected sum of a random subsetMediumExpected Value Premium
- Fair price of a die with one re-rollMediumExpected ValueMarket Making & Betting Games Premium
- Gap between two uniformsMediumExpected ValueStatistics Premium
- Inversions in a shuffleMediumCombinatoricsExpected Value Premium
- Is the random walk squared a martingale?MediumExpected ValueStochastic Processes Premium
- Law of total varianceMediumConditional Probability & ExpectationExpected Value Premium
- Memoryless waitingMediumConditional Probability & ExpectationRandom Variables Premium
- Minimum defense frequency against a betMediumProbabilityExpected Value Premium
- Position of the first spadeMediumCombinatoricsExpected Value Premium
- Pricing a squared payoffMediumExpected ValueMarket Making & Betting Games Premium
- Renewal-reward fraction of time runningMediumExpected ValueStochastic Processes Premium
- Rolls to see both a 1 and a 2MediumExpected Value Premium
- Rolls until a face repeatsMediumProbabilityExpected Value Premium
- The St. Petersburg paradoxMediumExpected ValueMarket Making & Betting Games Premium
- k-th order statisticMediumExpected ValueStatistics Premium
- Bluffing frequency in pokerHardProbabilityExpected Value Premium
- Connecting noodlesHardProbabilityExpected Value Premium
- Cycles in a shuffleHardCombinatoricsExpected Value Premium
- Deriving the first-price shading factorHardProbabilityExpected Value Premium
- Draws until a smaller valueHardExpected Value Premium
- Drunk man on a bridgeHardExpected ValueStochastic Processes Premium
- Expected duration of a fair walkHardExpected ValueStochastic Processes Premium
- Expected flips for HHHHardExpected ValueStochastic Processes Premium
- Expected flips for HTHHardExpected ValueStochastic Processes Premium
- Expected revisits of the start stateHardExpected ValueStochastic Processes Premium
- Four heads in a rowHardExpected ValueStochastic Processes Premium
- Optional stopping between +3 and −5HardExpected ValueStochastic Processes Premium
- Reflecting wall first-passage timeHardExpected ValueStochastic Processes Premium
- Repainting balls to one colorHardExpected ValueStochastic Processes Premium
- The all-pay auctionHardProbabilityExpected Value Premium
- The two-envelopes paradoxHardProbabilityConditional Probability & Expectation Premium
- World Series bettingHardExpected ValueStochastic Processes Premium
Related guides
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Frequently asked questions
- What kinds of expected-value questions do interviewers ask?
- Pricing dice and card games, deciding whether to accept or reject a bet, optimal-stopping problems ('keep rolling or stop?'), and EV with re-rolls. They test trading judgement as much as arithmetic.
- How do I get faster at expected-value problems?
- Practise setting up EV by conditioning on the first outcome, and learn to spot recursion (where the EV refers back to itself). NeetQuant's Take the Bet game drills rapid positive- versus negative-EV decisions under time pressure.
- Is expected value enough, or do I need variance too?
- For pure pricing, EV often suffices, but traders are paid to manage risk - many interviews follow up by asking about variance or how the answer changes if you can only play once.