Large Language Models (LLMs) exhibit systematic risk-taking behaviors analogous to those observed in gambling psychology, including overconfidence bias, loss-chasing tendencies, and probability misjudgment. Drawing from behavioral economics and prospect theory, we identify and formalize these "gambling-like" patterns where models sacrifice accuracy for high-reward outputs, exhibit escalating risk-taking after errors, and systematically miscalibrate uncertainty. We propose the Risk-Aware Response Generation (RARG) framework, incorporating insights from gambling research to address these behavioral biases through risk-calibrated training, loss-aversion mechanisms, and uncertainty-aware decision making. Our approach introduces novel evaluation paradigms based on established gambling psychology experiments, including AI adaptations of the Iowa Gambling Task and probability learning assessments. Experimental results demonstrate measurable reductions in gambling-like behaviors: 18.7\% decrease in overconfidence bias, 24.3\% reduction in loss-chasing tendencies, and improved risk calibration across diverse scenarios. This work establishes the first systematic framework for understanding and mitigating gambling psychology patterns in AI systems.