This study explores how the physical presence of an AI system influences user trust, fairness perceptions, and engagement in AI-driven decision-making. We designed a human-AI Rock-Paper-Scissors game and compared user interactions with Pepper, an embodied robot, and Amazon Alexa, a disembodied voice assistant. 71 participants provided quantitative and qualitative data on their experiences, allowing us to examine factors like trust, perceived cheating, and enjoyment. Our results show that participants placed significantly greater trust in Pepper, underscoring the importance of embodiment in fostering trust. Pepper's transparency, achieved through its physical actions and cues, contributed to a stronger sense of fairness, while winning or losing the game did not significantly impact trust levels. These findings support established theories like the Technology Acceptance Model (TAM) and the Computers Are Social Actors (CASA) paradigm, highlighting the crucial role of embodiment and transparency in facilitating positive human-AI interactions. This research offers valuable guidance for designing AI systems that leverage physical embodiment and transparency-enhancing features to promote trust and engagement, with potential applications across diverse fields such as education, healthcare, and customer service.