  What fraction of the single item $n$ buyers setting's expected optimal
revenue MyeRev can the second price auction with reserves achieve? In the
special case where the buyers' valuation distributions are all drawn i.i.d. and
the distributions satisfy the regularity condition, the second price auction
with an anonymous reserve (ASP) is the optimal auction itself. As the setting
gets more complex, there are established upper bounds on the fraction of MyeRev
that ASP can achieve. On the contrary, no such upper bounds are known for the
fraction of MyeRev achievable by the second price auction with eager
personalized reserves (ESP). In particular, no separation was earlier known
between ESP's revenue and MyeRev even in the most general setting of
non-identical product distributions that don't satisfy the regularity
condition. In this paper we establish the first separation results for ESP: we
show that even in the case of distributions drawn i.i.d., but not necessarily
satisfying the regularity condition, the ESP cannot achieve more than a $0.778$
fraction of MyeRev in general. Combined with Correa et al.'s result (EC 2017)
that ESP can achieve at least a $0.745$ fraction of MyeRev, this nearly bridges
the gap between upper and lower bounds on ESP's approximation factor.
