<p>We propose a framework for quantizing randomized quantum games in which entanglement is examined as a tunable fairness resource without relying on fine-tuned strategy parameters. As a case study of the Monty Hall problem, we show that initial entanglement between host and player registers neutralizes classical asymmetry at the distribution level, driving win-probability distributions under different strategic conditions to converge. Implemented on IBM’s Eagle processors via four-qubit encodings, our experiments span a continuum of entanglement strengths and employ extensive randomized trials over broad strategy ensembles. Although the mean no-switch probability remains fixed at its classical value, stronger entanglement progressively suppresses distributional signatures of asymmetric play, yielding increasingly uniform outcome statistics across adversarial conditions. Within the pure-state setting studied here, these findings provide evidence for an experimentally accessible route to quantify entanglement-enabled fairness in quantum games and suggest relevance to quantum information settings involving strategic decision-making under asymmetry.</p>