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Quantumness refers to the peculiar and counterintuitive characteristicsexhibited by quantum systems. Tsirelson inequalities have emerged as a powerfultool in quantum theory to detect quantumness and entanglement of harmonicoscillators, spins undergoing uniform precession, and anharmonic systems. Inthis paper, we harness the versatility of Tsirelson inequalities to address twodistinct problems: detecting cheating in classic shell games and probingquantumness in harmonic oscillators. By adopting a black-box approach and ageometric characterization of the space of conditional probabilities, wedemonstrate that Tsirelson inequalities can be used in both scenarios, enablingus to uncover quantum signatures and identify cheaters in a single unifiedframework. This connection provides an intuitive new perspective on quantumnessof mechanical systems.

Tsirelson Inequalities: Detecting Cheating and Quantumness in One Fell Swoop