  Kingman's House-of-Cards model is a simple and celebrated model to describe
the evolution of population under the competition of selection and mutation.
Letting mutation probabilities vary on generations makes the model more
realistic and meaningful. This paper considers the condensation phenomenon and
limit fitness distribution when Kingman's model is put into a random
environment consisting of i.i.d. random mutation probabilities. It turns out
that the random model is completely dominated by Kingman's model in terms of
condensation and fitness. Another random model where all mutation probabilities
are equal to the same random variable is also discussed. The relation between
the three models is subtle and shows how extra randomness perturbs Kingman's
model. The main tool is the matrix representation of the three models which is
discovered in this work and plays crucial roles in the comparison analysis.
