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The most central considerations for us have to do with facts about the chances of various conditionals and the levels of confidence we should have in them.  Since confidence-theoretic arguments have been the subject of intense scrutiny in the literature on indicative conditionals, we will try to keep things fresh by starting with the case of counterfactuals.  Consider one of the coins that stayed in your pocket all day yesterday.  How likely was it, yesterday morning, that that coin would have landed Heads if you had tossed it exactly once during the day?  We submit that unless you are in the habit of carrying around trick coins, the correct answer to this question is *about 50%*.  To bolster this judgment, suppose that you also own a double-Headed coin and a double-Tailed coin.  Surely the chance that that the normal coin would have landed Heads if it had been tossed was much higher than the chance that the double-Tailed coin would have landed Heads if it had been tossed, and lower, by about the same margin, than the chance that the double-Headed coin would have landed Heads if it had been tossed.  For the same reasons, it seems that the chance that the coin would have *failed* to land Heads if you had tossed it exactly once during the day was also about 50%.  But chances obey the axioms of the probability calculus, and one basic principle of this calculus that the sum of the probabilities of two propositions equals the sum of the probabilities of their disjunction and their conjunction.  And in this case, the conjunction---namely that if the coin had been tossed it would have landed Heads, and if the coin had been tossed it would have failed to land Heads---is absurd, and had no chance of being true.  So the chance of the disjunction---which is an instance of CEM---must have been roughly one.  In fact, there is reason to think that it was exactly one, insofar as any considerations which would support the view that the chance of one disjunct was less than 50% would to the same degree support the view that the chance of the other disjunct was greater than 50% by the same amount.  This is not yet a watertight case that the disjunction in question is true---after all, we had better not rule out the possibility that a false proposition had chance 1 at some point, given that there seem to be some truths---for example truths about the exact position of a dart on a dartboard---that arguably had chance 0 just because of their sheer specificity.  Nevertheless, finding that a specific proposition had chance 1 at some time surely constitutes an extremely strong reason for believing that it is true, one which we could contemplate overruling only in the most surprising circumstances.  

What general principle underlies the judgment that the chance that the coin would have landed Heads if it had been tossed was 50%?  The judgment clearly does not turn on any particular view about the chance that the coin would in fact be tossed---the case for it remains just as strong whether we think the coin was almost certain to be tossed, or almost certain not to be tossed, or anywhere in between.  But it does seem intimately related to the judgment that the chance that the coin would be tossed---whatever it was---was twice the chance that the coin would be tossed and land Heads.  A tempting thought here is to connect the chance of the conditional proposition *if P had been true Q would have been true* to the so-called "conditional chance" of Q given P---the chance of P and Q, divided by the chance of P.

The Chance Equation
: At any time $t$, the chance that $Q$ would be true if $P$ were true equals the conditional chance of $Q$ given $P$.