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Title: EXPLICATING MARKOV CHAINS AND TRANSITION PROBABILITY MATRICES VIA SIMPLE BOARD GAMES
Authors: Kkhushi Verma
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Kkhushi Verma Student , Department Of Statistics, Ram Lal Anand College, Delhi UniversityBenito Juarez Marg, South Campus, South Moti Bagh, New Delhi, Delhi 110021
MLA 8 Verma, Kkhushi. "EXPLICATING MARKOV CHAINS AND TRANSITION PROBABILITY MATRICES VIA SIMPLE BOARD GAMES." Int. j. of Social Science and Economic Research, vol. 6, no. 12, Dec. 2021, pp. 4865-4877, doi.org/10.46609/IJSSER.2021.v06i11.027. Accessed Dec. 2021. APA 6 Verma, K. (2021, December). EXPLICATING MARKOV CHAINS AND TRANSITION PROBABILITY MATRICES VIA SIMPLE BOARD GAMES. Int. j. of Social Science and Economic Research, 6(12), 4865-4877. Retrieved from doi.org/10.46609/IJSSER.2021.v06i11.027 Chicago Verma, Kkhushi. "EXPLICATING MARKOV CHAINS AND TRANSITION PROBABILITY MATRICES VIA SIMPLE BOARD GAMES." Int. j. of Social Science and Economic Research 6, no. 12 (December 2021), 4865-4877. Accessed December, 2021. doi.org/10.46609/IJSSER.2021.v06i11.027.
References [1]. Baris Tan, Markov Chains and the RISK Board Game, this Magazine 70 (1997), 349– 357. [2]. Bilisoly, Roger. (2014). Using Board Games and Mathematica to Teach the Fundamentals of Finite Stationary Markov Chains. [3]. Robert Ash and Richard Bishop, Monopoly as a Markov Process, this Magazine 45 (1972), 26-29. [4]. https://study.com/academy/lesson/markov-chain-definition-applications- examples.html [5]. https://en.wikipedia.org/wiki/Markov_chain#Definition [6]. https://en.wikipedia.org/wiki/Memorylessness [7]. Zin Mar Tun(2021). Markov Process of Snake And Ladders Board International Journal of Mathematics Trends and Technology, 44-52. [8]. L.A. Cheteyan, S. Hengeveld, M,A,Jones, and “Chutes and Ladders for the impatient”, vol.42, No1, the mathematical association of America, The College Mathematics Journal, January (2011). [9]. Norris, J. R. (James R.) Markov chains / J. R. Norris. p. cm. – (Cambridge series on statistical and probabilistic mathematics ; no. 2)
Abstract: A fairly common, and simple, way to statistically model random and stochastic processes is Markov chains. They have been applied to a wide variety of fields, like text generation, financial modelling, production, linguistics, marketing, computer science, and Signal Processing[1]. Simple board games can be used to illustrate its fundamental concepts, as in many popular board games, probabilistic reasoning plays a crucial role. For example, in Monopoly, which is a looping board game that consists of all recurrent states, for imperative purposes, the primary quantity of interest is the probability of being on any of the 40 positions in a specific turn. Ash and Bishop [3], determined the steady state probability of a player landing on any Monopoly square under the assumption that if a player goes to jail, he or she stays there until the Monopoly player rolls doubles or has spent three turns in jail. This model leads to an extremely practical observation for people who play the game often. [1]. In another chance based board game like Snakes & Ladders, games where players win by reaching a final square which consists of all transient states excluding the recurring ending state, players are interested in the probability of finishing the game in certain moves. Thus, understanding of mathematical model behind these games becomes quite crucial and significant in terms of game design, since any modification in rules and parameters could change the whole occurrence. This paper explores a method to analyse the prototype of chance based simple board games, depicting the application of Markov chain and using these as a basis to further indicate how complex games can be tackled.

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