Large language models (LLMs) have recently demonstrated strong capability in understanding and simulating humans’ decisions, suggesting a new way to use LLMs as tools to study social systems. We study two-sided-matching markets, such as dating and job matching. Classical matching models assume deterministic, strict preferences, which violate real-world setting. We focus on stable matching under stochastic decision behavior and use LLMs to simulate human-like preferences and probabilistic choice patterns. Based on this, we introduce Expected Blocking Pairs (EBP), a continuous measure to quantify stability that generalizes the classic blocking pair notion. We further propose a Hybrid GS–LLM matching method that integrates the celebrated Gale–Shapley (GS) algorithm with probabilistic acceptance decisions. Experiments show that the proposed hybrid method outperforms classical baselines in terms of stability, suggesting that LLMs provide a principled tool for modeling human decisions and for improving robustness of matching under uncertainty.