  We study halo assembly bias for cluster-sized halos. Previous work has found
little evidence for correlations between large-scale bias and halo mass
assembly history for simulated cluster-sized halos, in contrast to the
significant correlation found between bias and concentration for halos of this
mass. This difference in behavior is surprising, given that both concentration
and assembly history are closely related to the same properties of the
linear-density peaks that collapse to form halos. Using publicly available
simulations, we show that significant assembly bias is indeed found in the most
massive halos with $M\sim 10^{15}M_\odot$, using essentially any definition of
halo age. For lower halo masses $M\sim 10^{14}M_\odot$, no correlation is found
between bias and the commonly used age indicator $a_{0.5}$, the half-mass time.
We show that this is a mere accident, and that significant assembly bias exists
for other definitions of halo age, including those based on the time when the
halo progenitor acquires some fraction $f$ of the ultimate mass at $z=0$. For
halos with $M_{\rm vir}\sim 10^{14}M_\odot$, the sense of assembly bias changes
sign at $f=0.5$. We explore the origin of this behavior, and argue that it
arises because standard definitions of halo mass in halo finders do not
correspond to the collapsed, virialized mass that appears in the spherical
collapse model used to predict large-scale clustering. Because bias depends
strongly on halo mass, these errors in mass definition can masquerade as or
even obscure the assembly bias that is physically present. More physically
motivated halo definitions using splashback should be free of this particular
defect of standard halo finders.
