The expected net increase in the number of word senses in L D during one step of the process is −t + (1 − t) = 1 − 2t, since the probability that a word sense is lost by obsolescence is t and the probability that a word sense is gained is 1 − t. If r denotes the expected net increase in the number of words in L D during one step of the process, then we must have 1−2t r = m, since m is a constant.
note that the number of words in L D would be constant if and only if t = 0.5.