To maximize expected value, one should:

To maximize expected value, one should:

• A. Choose actions with the highest probability of success
• B. Choose actions that lead to the highest weighted average of outcome values
• C. Choose actions that minimize risk at any cost
• D. Choose actions randomly to diversify risk

Answer: (B)

The main idea is maximizing expected value, which means choosing the action that gives the largest probability-weighted payoff. The expected value is the average outcome you would get if you could repeat the action many times, calculated by summing each possible payoff times its probability. This is why the best choice is the one with the highest expected payoff. For example, one option might pay $100 with a 1% chance (EV = $1), while another pays $3 with a 50% chance (EV = $1.50). Even though the first option has a big payoff, its low probability makes its EV smaller than the second option, so the latter is the better choice for maximizing EV. The other options miss the point. Focusing only on the probability of success ignores how large the payoff can be when it occurs. Trying to minimize risk at any cost can destroy positive expected value, since you would avoid profitable opportunities with high variance. Finally, choosing randomly doesn’t aim at maximizing the average payoff and thus won’t reliably maximize expected value. So, pick the action with the largest expected payoff—the highest probability-weighted average of possible outcomes.

The main idea is maximizing expected value, which means choosing the action that gives the largest probability-weighted payoff. The expected value is the average outcome you would get if you could repeat the action many times, calculated by summing each possible payoff times its probability.

This is why the best choice is the one with the highest expected payoff. For example, one option might pay $100 with a 1% chance (EV = $1), while another pays $3 with a 50% chance (EV = $1.50). Even though the first option has a big payoff, its low probability makes its EV smaller than the second option, so the latter is the better choice for maximizing EV.

The other options miss the point. Focusing only on the probability of success ignores how large the payoff can be when it occurs. Trying to minimize risk at any cost can destroy positive expected value, since you would avoid profitable opportunities with high variance. Finally, choosing randomly doesn’t aim at maximizing the average payoff and thus won’t reliably maximize expected value.

So, pick the action with the largest expected payoff—the highest probability-weighted average of possible outcomes.