We introduce CUBE, Contrastive Understanding by Balanced Experiments, to estimate main effects and pairwise Banzhaf interactions over a fixed two-state probe space using shared balanced queries. Each design cancels constant and odd-order contamination from pairwise estimates, while randomization ensures unbiasedness and explicit alias probabilities yield exact mean squared errors without sparsity assumptions or order truncation. Matching risk bounds establish asymptotic minimax optimality within a specified class of nonadaptive, equal-weight, reversal-symmetric balanced contrast estimators, as admissible budgets grow while remaining small relative to the full probe space. Experiments reveal different interaction-specific risks despite identical output distributions and low-order effects, and different sign risks despite equal mean squared errors. Across evaluated tabular models, CUBE generally outperforms several sampling-based estimators, while Faith-Banzhaf-2 achieves the lowest mean error at the largest tested budgets.

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