Say I have two dice which have different probability distributions but I don't know which probability distribution belongs to what dice. I now throw one of them exactly one time and the result is x. I know that die A has probability pA(x) for rolling x and die B has probability pB(x). I want to find out if the die I rolled was die A or B. Obviously my best strategy is to guess the die for which the probability for rolling x is the bigger. But what is my probability for being correct? I have been trying to figure out this problem for days. Obviously if pB(x)=0 while pA(x)>0 I have 100% chance of being correct. Moreover if pB(x)=pA(x) then I have 50% chance of being correct. But is there an expression for arbitrary probabilities and how do I find it?