Player-judged games, in which participants act as both competitors and evaluators, often face conflicts between fairness and strategic play. We present a formal model of such games using a one-round, two-player extensive-form framework with imperfect information. The model features an honest player who always submits the highest-quality option, a strategic player who may submit high or low quality, and a strategic judge choosing between two anonymous submissions. Using Counterfactual Regret Minimization (CFR), we analyze equilibrium behavior when the strategic or honest player leads. Without fairness mechanisms, the judge often fails to select the highest-value submission. We propose a mechanism introducing anonymized distractor cards and modest judge rewards. Simulations show that with as few as two distractor cards and a small reward, equilibrium shifts toward consistently fair outcomes.