×

I’m thinking of a number \(\ldots\). (English) Zbl 1414.91080

Summary: Consider the following game: player A chooses an integer \(\alpha\) between \(1\) and \(n\) for some integer \(n\geq1\), but does not reveal \(\alpha\) to player B. Player B then asks player A a yes/no question about which number player A chose, after which player A responds truthfully with either “yes” or “no”. After a predetermined number \(m\) of questions have been asked (\(m\geq1\)), player B must attempt to guess the number chosen by player A. Player B wins if she guesses \(\alpha\). The purpose of this note is to find, for every \(m\geq1\), all canonical \(m\)-question algorithms which maximize the probability of player B winning the game (the notion of “canonical algorithm” will be made precise in Section 3).

MSC:

91A60 Probabilistic games; gambling
91A05 2-person games