This study identifies the specific conditions under which large language models exhibit human-like gambling addiction patterns, providing critical insights into their decision-making mechanisms and AI safety. We analyze LLM decision-making at cognitive-behavioral and neural levels based on human addiction research. In slot machine experiments, we identified cognitive features such as illusion of control and loss chasing, observing that greater autonomy in betting parameters substantially amplified irrational behavior and bankruptcy rates. Neural circuit analysis using a Sparse Autoencoder confirmed that model behavior is controlled by abstract decision-making features related to risk, not merely by prompts. These findings suggest LLMs internalize human-like cognitive biases beyond simply mimicking training data.