Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many more are currently being refined and developed. This article aims to deliver an up-to-date review of recent developments in sequential stopping rules, with a deliberate emphasis on Monte Carlo methods for estimating an unknown expectation, including binomial proportions, primarily under standard iid sampling and also under certain lightly generalized settings. These methodologies have long served and likely will continue to serve, as fundamental bases for both theoretical and practical developments in stopping rules for general statistical inference, advanced Monte Carlo techniques, and their modern applications. Building upon over a hundred references and empirical studies, we explore the essential aspects of these methods, such as core assumptions, numerical algorithms, convergence properties, and practical trade-offs to guide further developments, particularly at the intersection of sequential stopping rules and related areas of research.

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