  Theory and observations agree that the accreted stellar halos (ASHs) of Milky
Way-like galaxies display significant scatter. I take advantage of this
stochasticity to invert the link between halo assembly history (HAH) and ASH,
using mock ASHs corresponding to 750 $\Lambda$CDM HAHs, sharing a final virial
mass of $M_{h}(z=0)=10^{12.25}M_\odot$. Hosts with poor/rich ASHs assemble
following orthogonal growth-patterns. Hosts with rich ASHs experience accretion
events (AEs) with high virial mass ratios (HVMRs, $M_s/M_h\gtrsim 0.1$) at
$0.5\lesssim z_{infall}\lesssim1.5$, in a phase of fast growth. This maximizes
the accreted stellar mass under the condition these satellites are disrupted by
$z=0$. At similar times, hosts with poor ASHs grow slowly through minor
mergers, with only very recent HVMR AEs: this results in a globally more
abundant satellite population and in distinctive surviving massive satellites
(stellar mass $\log M_{s,*}/M_\odot\gtrsim 9$). Several properties of the Milky
Way are in agreement with the predictions of this framework for hosts with
poor, concentrated ASHs, including: i) the recent infall of Sagittarius and
Magellanic Clouds, ii) the likely higher-than-average concentration of its dark
halo, iii) the signatures of fast chemical enrichment of a sizable fraction of
its halo stellar populations.
