The study of coin-tossing protocols lies at the intersection of cryptography and game theory, where parties with potentially conflicting interests aim to jointly generate an unbiased random bit. Classical cryptographic results establish that strong fairness is achievable with an honest majority in the statistical setting, but impossible with a dishonest majority. In parallel, game-theoretic approaches [TCC 2018, Eurocrypt 2022 & CRYPTO 2024] have demonstrated that weaker equilibrium-based fairness guarantees can sometimes circumvent cryptographic lower bounds, raising the question of whether such techniques can overcome impossibility in the statistical regime. In this work, we answer this question negatively. To establish these results, we refine existing frameworks for game-theoretic fairness to capture both broadcast and point-to-point communication models. Together, our results establish the boundaries of game-theoretic fairness in multi-party coin tossing: while it extends feasibility in the computational setting, it offers no advantage in the statistical setting once an honest majority is lost.