Real-world contextual bandit problems with complex reward models are often tackled with iteratively trained models, such as boosting trees. However, it is difficult to directly apply simple and effective exploration strategies--such as Thompson Sampling or UCB--on top of those black-box estimators. Existing approaches rely on sophisticated assumptions or intractable procedures that are hard to verify and implement in practice. In this work, we explore the use of an exploration-free (pure-greedy) action selection strategy, that exploits the randomness inherent in model fitting process as an intrinsic source of exploration. More specifically, we note that the stochasticity in cross-validation based regularization process can naturally induce Thompson Sampling-like exploration. We show that this regularization-induced exploration is theoretically equivalent to Thompson Sampling in the two-armed bandit case and empirically leads to reliable exploration in large-scale business environments compared to benchmark methods such as epsilon-greedy and other state-of-the-art approaches. Overall, our work reveals how regularized estimator training itself can induce effective exploration, offering both theoretical insight and practical guidance for contextual bandit design.