  But the prospects are more promising for Humean views of chance (Lewis 1994; Loewer 2004), like the reductionist views discussed in supplements  A.1,  A.3,  and  D.  These are a species of product conception of chance, for a possible world will not feature chances unless the best (simplest, best fitting, and most informative) description of what events occur in that world involves a probability function. Two worlds couldn’t differ in their chances without differing also somewhere in the events which occur. Chance thus supervenes on the actual outcomes in a given world, but not necessarily in a direct way—in the service of simplicity, some deviation from the actual frequency values may yield a description that is better overall. There is considerable debate over whether a Humean best systems account can explain all of the things we know about chance. Lewis thought that chance was the ‘big bad bug’ for his broadly Humean world view (though he thought that the NP, discussed in supplement  A.1,  debugged Humean Supervenience: Lewis 1994), and there has been considerable debate over whether or not the PP or the BCP can be accounted for by the Humean, as the references in the  supplement A  attest. Moreover, there are problems about whether the notion of a probability distribution ‘fitting’ a set of outcomes makes sense (Elga 2004). But suppose a best systems account can be made to work.