IJPAM: Volume 59, No. 3 (2010)

PATTERN MATCHING PROBABILITIES AND PARADOXES
AS A NEW VARIATION ON PENNEY'S COIN GAME

Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa, Osaka, 533-8533, JAPAN
e-mail: [email protected]


Abstract.This paper gives an outline of an interesting probability game related to coin arrangements discovered by Walter Penney in 1969, and explains John Conway's concept of leading numbers and his algorithm for using them to automatically calculate mutual odds of winning. I will show that Conway's elegant algorithm is correct by using average waiting times as proposed by Stanley Collings, and discuss the effect of applying the rules of this coin game to a card game instead.

Received: February 11, 2010

AMS Subject Classification: 60C05, 91A60, 97A20

Key Words and Phrases: Penney Ante, pattern matching, odds, non-transitive relation, Conway's algorithm, average waiting time

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 3