Randomized controlled trials (RCTs) are pivotal for evaluating the efficacy of medical treatments and interventions, serving as a cornerstone in clinical research. In addition to randomization, achieving balances among multiple targets, such as statistical validity, efficiency, and ethical considerations, is also a central issue in RCTs. The doubly-adaptive biased coin design (DBCD) is notable for its high flexibility and efficiency in achieving any predetermined optimal allocation ratio and reducing variance for a given target allocation. However, DBCD does not account for abundant covariates that may be correlated with responses, which could further enhance trial efficiency. To address this limitation, this article explores the use of covariates in the analysis stage and evaluates the benefits of nonlinear covariate adjustment for estimating treatment effects. We propose a general framework to capture the intricate relationship between subjects' covariates and responses, supported by rigorous theoretical derivation and empirical validation via simulation study. Additionally, we introduce the use of sample splitting techniques for machine learning methods under DBCD, demonstrating the effectiveness of the corresponding estimators in high-dimensional cases. This paper aims to advance both the theoretical research and practical application of DBCD, thereby achieving more accurate and ethical clinical trials.