In recent years, many Machine Learning (ML) explanation techniques have been designed using ideas from cooperative game theory. These game-theoretic explainers suffer from high complexity, hindering their exact computation in practical settings. In our work, we focus on a wide class of linear game values, as well as coalitional values, for the marginal game based on a given ML model and predictor vector. By viewing these explainers as expectations over appropriate sample spaces, we design a novel Monte Carlo sampling algorithm that estimates them at a reduced complexity that depends linearly on the size of the background dataset. We set up a rigorous framework for the statistical analysis and obtain error bounds for our sampling methods. The advantage of this approach is that it is fast, easily implementable, and model-agnostic. Furthermore, it has similar statistical accuracy as other known estimation techniques that are more complex and model-specific. We provide rigorous proofs of statistical convergence, as well as numerical experiments whose results agree with our theoretical findings.