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ERIC Number: EJ959211
Record Type: Journal
Publication Date: 2011-Jan
Pages: 7
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0746-8342
EISSN: N/A
Available Date: N/A
Chutes and Ladders for the Impatient
Cheteyan, Leslie A.; Hengeveld, Stewart; Jones, Michael A.
College Mathematics Journal, v42 n1 p2-8 Jan 2011
In this paper, we review the rules and game board for "Chutes and Ladders", define a Markov chain to model the game regardless of the spinner range, and describe how properties of Markov chains are used to determine that an optimal spinner range of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov chain consists of 101 states, we demonstrate the analysis with a 10-state variation with a single chute and single ladder. The resulting 10 X 10 transition matrix is easier to display and the manipulations are comparable.We conclude with an unsolved problem about expected lengths for generalized "Chutes and Ladders" games.
Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A