Dice Expected Value Interview Questions
Dice expected value interview prep for direct EV, sums, rerolls, thresholds, fair prices, and simple stopping games.
Candidates practicing dice EV and stopping variants for quant interviews.
Direct dice expectation
A fair six-sided die has expected value 3.5. For sums, linearity means the expected sum of n fair dice is 3.5n. You do not need to list every combined outcome.
Expected payoff
If a game pays based on the die roll, multiply payoff by probability and sum. Keep track of whether the question asks for gross payoff, profit after cost, or fair price.
Concrete example
If a die pays its face value in dollars and costs 4 dollars to play, the expected payoff is 3.5 dollars and expected profit is -0.5 dollars. The cost changes the decision, not the die expectation.
Rerolls and thresholds
Reroll games require comparing the observed roll to continuation value. With one optional reroll of a fair die, rerolling is worth 3.5, so keep 4, 5, and 6.
Fair price framing
A fair price is the expected payoff under the model. If variance, bankroll, or limited repetition matters, discuss those after computing expected value.
Common mistakes
Candidates often confuse expected value with the most likely roll, or forget to subtract the cost of playing. State the payoff clearly before calculating.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.