  A string is sent over a noisy channel that erases some of its characters.
Knowing the statistical properties of the string's source and which characters
were erased, a listener that is equipped with an ability to test the veracity
of a string, one string at a time, wishes to fill in the missing pieces. Here
we characterize the influence of the stochastic properties of both the string's
source and the noise on the channel on the distribution of the number of
attempts required to identify the string, its guesswork. In particular, we
establish that the average noise on the channel is not a determining factor for
the average guesswork and illustrate simple settings where one recipient with,
on average, a better channel than another recipient, has higher average
guesswork. These results stand in contrast to those for the capacity of wiretap
channels and suggest the use of techniques such as friendly jamming with
pseudo-random sequences to exploit this guesswork behavior.
