IJPAM: Volume 66, No. 1 (2011)

INTERESTING PROBABILITY CALCULATIONS USING
CARDS TO WIN THE RED OR BLACK 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 article introduces an interesting probability game that uses playing cards. The game places 52 cards, 26 red and 26 black, face down. The object is to predict the color of a card before turning it over. It would seem that a player should average 26 correct answers per game, but this article describes a strategy that results in an average of 30 correct answers. The course of the game is formulated as a probability problem, and a mathematical proof is given using advanced mathematics such as convolutions of generating functions and the use of Taylor expansions.

Received: October 27, 2010

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

Key Words and Phrases: Bernoulli trial, probability, generating function, convolution, Catalan number

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 1