hard · Quantitative Finance

In a sequential-choice game with N possible items, if the player's goal is to maximize the *expected value* of the chosen item (rather than the probability of picking the best), how does the threshold change as N increases?

1. The threshold increases and approaches the maximum possible value of the distribution.
2. The threshold decreases to 1/e of the maximum value.
3. The threshold remains constant at the mean of the distribution.
4. The threshold becomes zero as N goes to infinity because all items are equally likely.

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