 Most people appear to (strictly) prefer \(f_1\) to \(f_2\) and (strictly) prefer \(f_4\) to \(f_3.\) They would rather bet on the known or objective probability than the unknown or subjective one—in the first pair, red has an objective probability of \(\lfrac{1}{3}\), whereas black has a possible objective probability ranging from 0 to \(\lfrac{2}{3}\); in the second pair, black or yellow has an objective probability of \(\lfrac{2}{3}\) whereas red or yellow has a possible objective probability ranging from \(\lfrac{1}{3}\) to 1. These preferences violate the Sure-thing Principle. (To see this, notice that the only difference between the two pairs of acts is that the first pair yields $0 on yellow and the second pair yields $100 on yellow.)