We sought to identify key determinants of the likelihood of provider-patient discussions about smoking and to understand the effects of these determinants. We used data on 3666 self-reported current smokers who talked to a health professional within a year of the time the survey was conducted using the 2017 National Health Interview Survey. We included wide-ranging information on 43 potential covariates across four domains, demographic and socio-economic status, behavior, health status and healthcare utilization. We exploited a principled nonparametric permutation based approach using Bayesian machine learning to identify and rank important determinants of discussions about smoking between health providers and patients. In the order of importance, frequency of doctor office visits, intensity of cigarette use, length of smoking history, chronic obstructive pulmonary disease, emphysema, marital status were major determinants of disparities in provider-patient discussions about smoking. There was a distinct interaction between intensity of cigarette use and length of smoking history. Our analysis may provide some insights into strategies for promoting discussions on smoking and facilitating smoking cessation. Health care resource usage, smoking intensity and duration and smoking-related conditions were key drivers. The "usual suspects", age, gender, race and ethnicity were less important, and gender, in particular, had little effect.