Threshold Rules for the Classical Prophet Inequality

Jiechen Zhang

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arXiv · 2605.19871

Threshold Rules for the Classical Prophet Inequality

Jiechen Zhang

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Abstract

This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify several deterministic thresholds, including the median, half-mean, and balanced-surplus thresholds, and to give an averaged certificate for randomized thresholds distributed as the maximum.

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Jiechen Zhang. 2026-05-19. Threshold Rules for the Classical Prophet Inequality. https://arxiv.org/abs/2605.19871

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