Even though observational data contain an enormous number of covariates, the existence of unobserved confounders still cannot be excluded and remains a major barrier to drawing causal inference from observational data. A large-scale propensity score (LSPS) approach may adjust for unobserved confounders by including tens of thousands of available covariates that may be correlated with them. In this paper, we present conditions under which LSPS can remove bias due to unobserved confounders. In addition, we show that LSPS may avoid bias that can be induced when adjusting for various unwanted variables (e.g., M-structure colliders). We demonstrate the performance of LSPS on bias reduction using both simulations and real medical data.