Passing the Buck and Firing Fibonacci: Adventures with the Stochastic Abacus. Issue 5 (28th May 2019)

• Record Type: Journal Article
• Authors: Torrence, Bruce
• Is Part Of: American Mathematical Monthly. Volume 126:Issue 5(2019)
• Page Start: 387
• Page End: 399
• Publication Date: 2019-05-28
• Subjects: MSC: Primary 60J22 -- Secondary 65C40 -- 82C20; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2019.1577089
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: A "pass-the-buck" game begins with n players arranged as the vertices in a graph. One player has a dollar bill. The game is played in turns where, at random, the current bill-holder either wins outright or else passes the bill to a player on an adjacent vertex. If the vertex of the bill-holder has degree d, then each of the d + 1 outcomes is equally likely. We analyze this class of game using Arthur Engel's stochastic abacus—a chip firing algorithm—revealing a natural relationship with the Fibonacci numbers.