 and thus preference for a conditional bet on \(\r{T}\) (given the various levels of \(B\)) does not imply preference for the unconditional bet on \(\r{T}\) (see  Section 2).  However, Savage certainly did not intend the sure-thing principle to be a theorem of probability. To evaluate it as a principle that guides proper decision-making, we must consider cases where the predictor variable (here: treatment/control) stands for a proper act that affects the outcome via multiple paths.