A note on the closed-form solution for the longest head run problem of Abraham de Moivre
Links to Fileshttps://arxiv.org/abs/2009.07765
MetadataShow full item record
Type of Work6 pages
journal articles preprints
Citation of Original PublicationMalinovsky, Yaakov; A note on the closed-form solution for the longest head run problem of Abraham de Moivre; History and Overview (2020); https://arxiv.org/abs/2009.07765
RightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
The problem of the longest head run was introduced and solved by Abraham de Moivre in the second edition of his book Doctrine of Chances (de Moivre, 1738). The closed-form solution as a finite sum involving binomial coefficients was provided in Uspensky (1937). Since then, the problem and its variations and extensions have found broad interest and diverse applications. Surprisingly, a very simple closed form can be obtained, which we present in this note.