Turing Test game theory: The machine chooses to deceive (D) or reveal (R); the interrogator chooses to probe deeply (P) or accept superficially (A). Payoffs depend on deception skill d, detection ability q, human cooperation h, and effort cost c. Nash equilibrium: neither player benefits from unilateral deviation. When d > q (machine is more capable than interrogator), the equilibrium involves probabilistic mixed strategies and the test loses validity. Arms race: increasing d forces increasing q, which forces increasing d — an indefinite escalation. The test "breaks" when optimal play makes the outcome arbitrary.