Recent works have growingly shown that Cyber deception can effectively impede the reconnaissance efforts of intelligent cyber attackers. Recently proposed models to optimize a deceptive defense based on camouflaging network and system attributes, have shown effective numerical results on simulated data. However, these models possess a fundamental drawback due to the assumption that an attempted attack is always successful — as a direct consequence of the deceptive strategies being deployed, the attacker runs a significant risk that the attack fails. Further, this risk or uncertainty in the rewards magnifies the boundedly rational behavior in humans which the previous models do not handle. To that end, we present Risk-based Cyber Camouflage Games — a general-sum game model that captures the uncertainty in the attack's success. In case of the rational attackers, we show that optimal defender strategy computation is NP-hard even in the zero-sum case.We provide an MILP formulation for the general problem with constraints on cost and feasibility, along with a pseudo-polynomial time algorithm for the special unconstrained setting. Second, for risk-averse attackers, we present a solution based on Prospect theoretic modeling along with a robust variant that minimizes regret. Third, we propose a solution that does not rely on the attacker behavior model or past data, and effective for the broad setting of strictly competitive games where previous solutions against bounded rationality prove ineffective. Finally, we provide numerical results that our solutions effectively lower the defender loss.