UBC Probability Seminar: Andrea Ottolini

The Zener cards are a deck of nm cards where each of n symbols is depicted on exactly m cards. The following experiment \((n=mu=5)\)has been used since the early ‘30s to test for extrasensory perceptions: the alleged telepath tries to guess cards one at a time, receiving some feedback after each attempt, until there are no cards left. The total number of correct guesses can be thus interpreted as a measure of their psychic powers. A very first step in the analysis of such experiments is to determine the optimal (non-psychic) expected score \(S_{n},_{m}\). After an overview of the problem, I will focus on joint work with Steinerberger on the complete feedback case, where we determine the leading and next-to-leading order for \(S_{n},_{m}\) in a wide range of regimes. In particular, this includes the case \(n=mu\), answering a conjecture of Diaconis.