  Consider the following experiment: a deck with $m$ copies of $n$ different
card types is randomly shuffled, and a guesser attempts to guess the cards
sequentially as they are drawn. Each time a guess is made, some amount of
"feedback" is given. For example, one could tell the guesser the true identity
of the card they just guessed (the complete feedback model) or they could be
told nothing at all (the no feedback model).
  In this paper we explore a partial feedback model, where upon guessing a
card, the guesser is only told whether or not their guess was correct. We show
in this setting that, uniformly in $n$, at most $m+O(m^{3/4}\log m)$ cards can
be guessed correctly in expectation. This resolves a question of Diaconis and
Graham from 1981, where even the $m=2$ case was open.
