 The point of the two Convergence Theorems explored in this section is to assure us, in advance of the consideration of any specific pair of hypotheses, that if the possible evidence streams that test them have certain characteristics which reflect their evidential distinguishability, it is highly likely that outcomes yielding small likelihood ratios will result. These theorems provide finite lower bounds on how quickly convergence is likely to occur. Thus, there is no need to wait through some infinitely long run for convergence to occur. Indeed, for any evidence sequence on which the probability distributions are at all well behaved, the actual likelihood of obtaining outcomes that yield small likelihood ratio values will inevitably be much higher than the lower bounds given by Theorems 1 and 2.