Clarify the betting options and assumptions, then compute the expected value for each by summing the product of probability and payoff. Identify the option with EV > 0 and explain how you would prove it, including any necessary calculations or simulations.
Pro tip: Emphasize the importance of understanding the underlying probabilities and payoffs, and mention that in a real-world scenario, you'd also consider risk and variance, not just EV.
Ask questions to understand the betting options, probabilities, payoffs, and any constraints or assumptions. Ensure you know whether the probabilities are given or need to be derived.
State the formula for expected value: EV = Σ (probability of outcome × payoff for outcome). Explain that positive EV means the average outcome is profitable.
For each betting option, calculate the EV using the given probabilities and payoffs. Show your work step by step to demonstrate transparency.
Compare the EVs and identify which option(s) have EV > 0. If none, explain why and what would need to change.
Provide a mathematical proof or a clear calculation showing that the EV is positive. If applicable, mention simulation or empirical evidence as additional support.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.