Meet-in-the-middle probability of success In page 358 of Bruce Schneier's Apllied Crypto, when explaining the meet-in-the-middle attack, he states that the success probability is «1 in $2^{2m - 2n}$» with two plaintext/ciphertext pairs, and «1 in $2^{3m - 2n}$» if one uses one additional pt/ct pair. $n$ is the key length, and $m$ the block length.

My question is: shouldn't $m$ and $n$ be reversed? I.e. «1 in $2^{2n - 2m}$» and «1 in $2^{2n - 3m}$»? As stated in the book, we would get a lower success probability when using 3 pairs, as «1 in $2^{2m - 2n}$» is a bigger probability than «1 in $2^{3m - 2n}$» (because $2^{3m - 2n}$ > $2^{2m - 2n}$).

Or is there something obvious that I am not seeing?
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".