This paper investigates two types of conditional strong law of large numbers (SLLN) under G-expectations, focusing on conditionally independent random variables related to the symmetry G-function. The study establishes that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with G-capacity one. For conditionally independent random variables with identical conditional distributions, the paper shows the existence of two cluster points corresponding to the essential minimum and maximum expectations with G-capacity one. The paper introduces the concept of conditional G-capacity and its properties, extending the classical SLLN to the framework of G-expectations. It proves two types of conditional SLLN under G-expectations: one for conditionally independent random variables and another for conditionally identically distributed random variables with respect to a fixed filtration. These results are derived under the condition of finite conditional (1 + α)-th moments for upper expectations. The paper also demonstrates that the empirical averages converge to the essential minimum and maximum expectations with G-capacity one, providing a foundation for future applications in machine learning, reinforcement learning, and stochastic filtering simulations within the G-expectation framework. The results are supported by various lemmas and theorems, including the conditional Borel–Cantelli lemma and properties of G-capacities. The study contributes to the understanding of the behavior of empirical averages under non-additive expectations and extends the classical SLLN to the context of G-expectations.This paper investigates two types of conditional strong law of large numbers (SLLN) under G-expectations, focusing on conditionally independent random variables related to the symmetry G-function. The study establishes that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with G-capacity one. For conditionally independent random variables with identical conditional distributions, the paper shows the existence of two cluster points corresponding to the essential minimum and maximum expectations with G-capacity one. The paper introduces the concept of conditional G-capacity and its properties, extending the classical SLLN to the framework of G-expectations. It proves two types of conditional SLLN under G-expectations: one for conditionally independent random variables and another for conditionally identically distributed random variables with respect to a fixed filtration. These results are derived under the condition of finite conditional (1 + α)-th moments for upper expectations. The paper also demonstrates that the empirical averages converge to the essential minimum and maximum expectations with G-capacity one, providing a foundation for future applications in machine learning, reinforcement learning, and stochastic filtering simulations within the G-expectation framework. The results are supported by various lemmas and theorems, including the conditional Borel–Cantelli lemma and properties of G-capacities. The study contributes to the understanding of the behavior of empirical averages under non-additive expectations and extends the classical SLLN to the context of G-expectations.