  Prospects look rather better on a reductionist view of chance  (Supplement  A.3).  On such a view, we can say that worlds where an infinite sequence of heads does occur at some close possibility will look very different from ours; they differ in law or history to ours. In such worlds, the chance of heads is much closer to 1 (reflecting the fact that if a coin were tossed infinitely many times, it might well land heads on each toss)—the coin is not after all fair. The response, then, is that in any situation where the reductionist chance of heads really is 0.5, suitable outcome sequences in that situation or its nearest neighbours are in fact all unbiased with respect to outcome frequencies. That is to say, they at least satisfy the property of large numbers; and arguably they can be expected to meet other randomness properties also. So, on this view, there is no counterexample to RCT from the mere possibility of these kinds of extreme outcome sequences. This response depends on the success of the reductionist similarity metrics for chancy counterfactuals developed by Lewis (1979a) and Williams (2008); the latter construction, in particular, invokes a close connection between similarity and randomness. (Lewis’ original construction is criticised in Hawthorne 2005.)