  A number of the constraints discussed above require the legitimacy of single-case chance. The objection to frequentist accounts of chance that the frequency might misrepresent the chance if the number of actual outcomes is too low apparently requires that there be non-trivial chances even for events resulting from a type of trial that occurs only very few times, and perhaps even can only occur very few times (Hájek 2009: 227–8). The strong connections between possibility and chance mooted by the BCP and variants thereof also require that there are single-case chances. For the BCP requires that, for every event with some chance, it is possible that the event has that same chance and occurs. As noted in Supplement  A.2,  this renders the chances relatively independent of the occurrent frequencies, which in turn requires single-case chance. For some single outcomes—for example, the next toss of a coin that is biased ⅔ towards heads—only very few assignments of credence are reasonable; in that case, we should, if we are rational, have credence of ⅔ in the coin landing heads. The rationality of this unequal assignment cannot be explained by anything like symmetry or indifference. Its rationality can be explained by the PP only if the single-case chance of heads on the next toss is ⅔. Moreover, the existence of this constraint on rational credence should have an explanation. Therefore the PP, if it is to play this necessary explanatory role, requires single-case chance.