Card guessing with partial feedback

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