  We consider the problem of communicating a message $m$ in the presence of a
malicious jamming adversary (Calvin), who can erase an arbitrary set of up to
$pn$ bits, out of $n$ transmitted bits $(x_1,\ldots,x_n)$. The capacity of such
a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or
not to erase bit $x_i$ depends on his observations $(x_1,\ldots,x_i)$ was
recently characterized to be $1-2p$. In this work we show two (perhaps)
surprising phenomena. Firstly, we demonstrate via a novel code construction
that if Calvin is delayed by even a single bit, i.e. Calvin's decision of
whether or not to erase bit $x_i$ depends only on $(x_1,\ldots,x_{i-1})$ (and
is independent of the "current bit" $x_i$) then the capacity increases to $1-p$
when the encoder is allowed to be stochastic. Secondly, we show via a novel
jamming strategy for Calvin that, in the single-bit-delay setting, if the
encoding is deterministic (i.e. the transmitted codeword is a deterministic
function of the message $m$) then no rate asymptotically larger than $1-2p$ is
possible with vanishing probability of error, hence stochastic encoding (using
private randomness at the encoder) is essential to achieve the capacity of
$1-p$ against a one-bit-delayed Calvin.
