Fair Coin Betting Game Interview Questions
Fair coin betting game interview questions covering expected value, variance, repetition, and bankroll constraints in toy coin bets.
Candidates practicing simple betting games before moving to bankroll or utility variants.
Model the coin bet
Start by naming the event, probability, win payoff, loss payoff, and cost. For a fair coin, heads and tails each have probability 1/2 unless the prompt changes the setup.
Fair does not mean attractive
A fair coin with symmetric net payoffs has expected value zero. That means it is fair in the risk-neutral arithmetic, not that it is worth taking under every constraint.
Concrete example
If heads wins 1 and tails loses 1, the expected value is 0.5 x 1 + 0.5 x -1 = 0. If the entry cost is 0.10, the expected value becomes -0.10.
Repetition changes the discussion
Repeated fair bets still have zero expected value when each round is independent and payoffs are unchanged. But the distribution of outcomes widens as the number of rounds grows.
Bankroll constraints matter
A zero-EV or positive-EV coin bet can still be unacceptable if the stake is large enough to violate a bankroll, drawdown, or ruin constraint.
Common mistakes
Candidates sometimes stop after saying the coin is fair. Interviewers often want the full payoff model, the net expected value, and the caveat that utility and constraints can change the decision.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.