Meet-in-the-middle probability of success
In the sentence, the "probability of success" of «1 in $2^{2m - 2n}$» or «1 in $2^{3m - 2n}$» really is an approximation of the probability of concluding that the key was found, when in fact another key that happens to give the same result as the true key for 2 or 3 blocks was found.

It should be read "probability of wrongly concluding success" instead; or "probability of false positive".