In a bag, there are two dice, each with sides weighted differently. I know the weighting of the two dice. I reach into the bag and pick one out with equal probability. I want to know how many rolls it will take for me to know, with high probability, which die I am rolling.
Put differently, I believe I am trying to find the sample complexity of an algorithm that distinguishes between two different discrete distributions. I believe I have a way to do this for two weighted coins (using a tail bound on the binomial distribution) and I'm pretty sure there should be a simple reduction, but I can't find a good explanation online, perhaps because I lack the proper vocabulary (I come from a CS background and don't know stats/probability super well).
Ultimately what I want is that if someone tells me the distribution of the two dice, I plug those distributions into a function that tells me how many rolls it will take for me to make a guess that will be correct (say) 90% of the time.