Large language models (LLMs) are increasingly deployed as autonomous agents in uncertain, sequential decision-making contexts. Yet it remains poorly understood whether the behaviors they exhibit in such environments reflect principled cognitive patterns or simply surface-level prompt mimicry. This paper presents a controlled experiment in which GPT-4.1 was assigned one of three socioeconomic personas (Rich, Middle-income, and Poor) and placed in a structured slot-machine environment with three distinct machine configurations: Fair (50%), Biased Low (35%), and Streak (dynamic probability increasing after consecutive losses). Across 50 independent iterations per condition and 6,950 recorded decisions, we find that the model reproduces key behavioral signatures predicted by Kahneman and Tversky's Prospect Theory without being instructed to do so. The Poor persona played a mean of 37.4 rounds per session (SD=15.5) compared to 1.1 rounds for the Rich persona (SD=0.31), a difference that is highly significant (Kruskal-Wallis H=393.5, p<2.2e-16). Risk scores by persona show large effect sizes (Cohen's d=4.15 for Poor vs Rich). Emotional labels appear to function as post-hoc annotations rather than decision drivers (chi-square=3205.4, Cramer's V=0.39), and belief-updating across rounds is negligible (Spearman rho=0.032 for Poor persona, p=0.016). These findings carry implications for LLM agent design, interpretability research, and the broader question of whether classical cognitive economic biases are implicitly encoded in large-scale pretrained language models.