We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence (``freedom-of-choice'') loophole are reformulated as structural constraints in a sequential hidden-variable game between Scientists and Nature. We construct a loopholes-closed game with capital processes that test (i) convergence of empirical conditional frequencies to the CHSH correlations and (ii) the absence of systematic correlations between measurement settings and Nature's hidden-variable assignments, and prove that Nature cannot satisfy both simultaneously: at least one capital process must diverge. This yields an operational winning strategy for Scientists and a game-theoretic probabilistic interpretation of experimentally observed CHSH violations.

翻译：本研究从信息论与时间敏感性的视角，运用无需预设概率空间的博弈论概率方法，对CHSH不等式进行探究。我们将定域性漏洞与测量依赖性（"选择自由度"）漏洞重新表述为科学家与自然之间序贯隐变量博弈的结构性约束。通过构建资本过程，我们设计了一个闭合漏洞的博弈框架，该框架可检验：（i）经验条件频率向CHSH关联值的收敛性；（ii）测量设置与自然隐变量赋值之间系统性关联的缺失。我们证明自然无法同时满足这两个条件：至少有一个资本过程必然发散。这为科学家提供了可操作的获胜策略，并为实验观测到的CHSH违背现象提供了博弈论概率解释。