In this paper we propose the use of machine learning methods to estimate inequality of opportunity. We illustrate how our proposed methods - conditional inference regression trees and forests - represent a substantial improvement over existing estimation approaches. First, they reduce the risk of ad-hoc model selection. Second, they establish estimation models by trading off upward and downward bias in inequality of opportunity estimates. The advantages of regression trees and forests are illustrated by an empirical application for a cross-section of 31 European countries. We show that arbitrary model selection may lead to significant biases in inequality of opportunity estimates relative to our preferred method. These biases are reflected in both point estimates and country rankings. Our results illustrate the practical importance of leveraging machine learning algorithms to avoid giving misleading information about the level of inequality of opportunity in different societies to policymakers and the general public.