Shapley values are a popular model-agnostic explanation framework for explaining predictions made by complex machine learning models. The framework provides feature contribution scores that sum to the predicted response and represent each feature's importance. The computation of exact Shapley values is computationally expensive due to estimating an exponential amount of non-trivial conditional expectations. The KernelSHAP framework enables us to approximate the Shapley values using a sampled subset of weighted conditional expectations. We propose three main novel contributions: a stabilizing technique to reduce the variance of the weights in the current state-of-the-art strategy, a novel weighing scheme that corrects the Shapley kernel weights based on sampled subsets, and a straightforward strategy that includes the important subsets and integrates them with the corrected Shapley kernel weights. We compare these new approximation strategies against existing ones by evaluating their Shapley value accuracy as a function of the number of subsets. The results demonstrate that our sampling strategies significantly enhance the accuracy of the approximated Shapley value explanations, making them more reliable in practical applications. This work provides valuable insights and practical recommendations for researchers and practitioners seeking to implement Shapley value-based explainability of their models.