Chutes and Ladders for the Impatient

Autor/inn/en	Cheteyan, Leslie A.; Hengeveld, Stewart; Jones, Michael A.
Titel	Chutes and Ladders for the Impatient
Quelle	In: College Mathematics Journal, 42 (2011) 1, S.2-8 (7 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0746-8342
DOI	10.4169/college.math.j.42.1.002
Schlagwörter	Markov Processes; Mathematics Instruction; Games; Teaching Methods; Mathematical Concepts; Matrices; Problem Solving; College Mathematics + Suchen Sie Ihr Suchwort? Markowscher Prozess; Mathematics lessons; Mathematikunterricht; Game; Spiel; Spiele; Teaching method; Lehrmethode; Unterrichtsmethode; Matrizenrechnung; Problemlösen
Abstract	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. (As Provided).
Anmerkungen	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
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10