The use of anti-forensic techniques is a very common practice that stealthy adversaries may deploy to minimise their traces and make the investigation of an incident harder by evading detection and attribution. In this paper, we study the interaction between a cyber forensic Investigator and a strategic Attacker using a game-theoretic framework. This is based on a Bayesian game of incomplete information played on a multi-host cyber forensics investigation graph of actions traversed by both players. The edges of the graph represent players’ actions across different hosts in a network. In alignment with the concept of Bayesian games, we define 8 two Attacker types to represent their ability of deploying anti-forensic techniques to conceal their activities. In this way, our model allows the Investigator to identify her optimal investigating 10 policy taking into consideration the cost and impact of the available actions, while coping with the uncertainty of the Attacker’s type and strategic decisions. To evaluate our model, we construct a realistic case study based on threat reports and data extracted from the MITRE ATT&CK STIX repository, Common Vulnerability Scoring System (CVSS), and interviews with cyber-security practitioners. We use the case study to compare the performance of the proposed method against 15 two other investigative methods and three different types of Attackers.