In the era of digital communication, understanding the dynamics of opinion formation and polarization on social media platforms is crucial for both scientific inquiry and societal well-being. This work develops a probabilistic framework to model and simulate opinion dynamics on X (formerly Twitter) using retweet interactions between users and influential accounts (“leaders”). The model introduces a two-stage process—content exposure followed by engagement—parametrized by interpretable variables representing algorithmic influence and user behavior. Empirical data from Italian Twitter (2018–2022) inform model calibration, enabling accurate monthly predictions of user-leader retweet matrices. Analytical insights are drawn through connections to population genetics models, revealing how algorithmic biases and levels of user engagement jointly drive polarization dynamics.