Theories of decision-making are routinely based on the notion that decision-makers choose alternatives which align with their underlying preferences—and hence that their preferences can be inferred from their choices. In some situations, however, a decision-maker may wish to hide his or her preferences from an onlooker. This paper argues that such obfuscation-based choice behavior is likely to be relevant in various situations, such as political decision-making. This paper puts forward a simple and tractable discrete choice model of obfuscation-based choice behavior, by combining the well-known concepts of Bayesian inference and information entropy. After deriving the model and illustrating some key properties, the paper presents the results of an obfuscation game that was designed to explore whether decision-makers, when properly incentivized, would be able to obfuscate effectively, and which heuristics they employ to do so. Together, the analyses presented in this paper provide stepping stones towards a more profound understanding of obfuscation-based decision-making.