  Differential privacy (DP) is a mathematical privacy notion increasingly
deployed across government and industry. With DP, privacy protections are
probabilistic: they are bounded by the privacy budget parameter, $\epsilon$.
Prior work in health and computational science finds that people struggle to
reason about probabilistic risks. Yet, communicating the implications of
$\epsilon$ to people contributing their data is vital to avoiding privacy
theater -- presenting meaningless privacy protection as meaningful -- and
empowering more informed data-sharing decisions. Drawing on best practices in
risk communication and usability, we develop three methods to convey
probabilistic DP guarantees to end users: two that communicate odds and one
offering concrete examples of DP outputs.
  We quantitatively evaluate these explanation methods in a vignette survey
study ($n=963$) via three metrics: objective risk comprehension, subjective
privacy understanding of DP guarantees, and self-efficacy. We find that
odds-based explanation methods are more effective than (1) output-based methods
and (2) state-of-the-art approaches that gloss over information about
$\epsilon$. Further, when offered information about $\epsilon$, respondents are
more willing to share their data than when presented with a state-of-the-art DP
explanation; this willingness to share is sensitive to $\epsilon$ values: as
privacy protections weaken, respondents are less likely to share data.
