How do people navigate the exploration-exploitation (EE) trade-off when making repeated choices with unknown rewards? We study this question through the lens of multi-armed bandit problems and introduce a novel behavioral model, Quantal Choice with Adaptive Reduction of Exploration (QCARE). It generalizes Thompson Sampling, allowing for a principled way to quantify the EE trade-off and reflect human decisionmaking patterns. The model adaptively reduces exploration as information accumulates, with the reduction rate serving as a parameter to quantify the EE trade-off dynamics. We theoretically analyze how varying reduction rates influence decision quality, shedding light on the effects of "over-exploration" and "under-exploration." Empirically, we validate QCARE through experiments collecting behavioral data from human participants. QCARE not only captures critical behavioral patterns in the EE trade-off but also outperforms alternative models in predictive power. Our analysis reveals a behavioral tendency toward over-exploration.