Multimodal Large Language Models (MLLMs) have become widely deployed, yet their safety alignment remains fragile under adversarial inputs. Previous work has shown that increasing inference steps can disrupt safety mechanisms and lead MLLMs to generate attacker-desired harmful content. However, most existing attacks focus on increasing the complexity of the modified visual task itself and do not explicitly leverage the model's own reasoning incentives. This leads to them underperforming on reasoning models (Models with Chain-of-Thoughts) compared to non-reasoning ones (Models without Chain-of-Thoughts). If a model can think like a human, can we influence its cognitive-stage decisions so that it proactively completes a jailbreak? To validate this idea, we propose GAMBI} (Gamified Adversarial Multimodal Breakout via Instructional Traps), a novel multimodal jailbreak framework that decomposes and reassembles harmful visual semantics, then constructs a gamified scene that drives the model to explore, reconstruct intent, and answer as part of winning the game. The resulting structured reasoning chain increases task complexity in both vision and text, positioning the model as a participant whose goal pursuit reduces safety attention and induces it to answer the reconstructed malicious query. Extensive experiments on popular reasoning and non-reasoning MLLMs demonstrate that GAMBIT achieves high Attack Success Rates (ASR), reaching 92.13% on Gemini 2.5 Flash, 91.20% on QvQ-MAX, and 85.87% on GPT-4o, significantly outperforming baselines.