  We present an extensive peakbagging effort on Kepler data of $\sim$50 red
giant stars in the open star cluster NGC 6819. By employing sophisticated
pre-processing of the time series and Markov Chain Monte Carlo techniques we
extracted individual frequencies, heights and linewidths for hundreds of
oscillation modes.
  We show that the "average" asteroseismic parameter $\delta\nu_{02}$, derived
from these, can be used to distinguish the stellar evolutionary state between
the red giant branch (RGB) stars and red clump (RC) stars.
  Masses and radii are estimated using asteroseismic scaling relations, both
empirically corrected to obtain self-consistency as well as agreement with
independent measures of distance, and using updated theoretical corrections.
Remarkable agreement is found, allowing the evolutionary state of the giants to
be determined exclusively from the empirical correction to the scaling
relations. We find a mean mass of the RGB stars and RC stars in NGC 6819 to be
$1.61\pm0.02\,\textrm{M}_\odot$ and $1.64{\pm}0.02\,\textrm{M}_\odot$,
respectively. The difference $\Delta M=-0.03\pm0.01\,\textrm{M}_\odot$ is
almost insensitive to systematics, suggesting very little RGB mass loss, if
any.
  Stars that are outliers relative to the ensemble reveal overmassive members
that likely evolved via mass-transfer in a blue straggler phase. We suggest
that KIC 4937011, a low-mass Li-rich giant, is a cluster member in the RC phase
that experienced very high mass-loss during its evolution. Such over- and
undermassive stars need to be considered when studying field giants, since the
true age of such stars cannot be known and there is currently no way to
distinguish them from normal stars.
