Chutes and Ladders Dissertation Example

Ph. D.
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Chutes and Ladders Name Institution Affiliation Introduction One of the most common ancient board game that remains to be classic up to date is the chutes and ladders. The game originated from India, and it is played by one or more people. Ideally, the game involves connecting numbered squares on a ten by ten board using ladders and chutes. The number of squares a player navigates is determined by tossing a die thereby making the game an aspect of sheer luck and probability. The function of the ladders pictured on the board is to enhance the participant progress up the board while the chutes move the player down the board. All the players begin off the board and roll the dice once and move upper or down depending on the corresponding number of squares. If the toss of the die results in a number that lands at the foot of a ladder, the player instantly moves up. However, if the number lands the player at the top of a chute, the player slides down to an earlier square. Landing at the top of a ladder or the bottom of the chute does not affect the player’s movement. How Long Does the Game Take? Since the game is cyclic, it is not bound to a definite duration. However, the probability for a long game to end is infinite. While most of the games take less than a hundred moves to complete, the longest ever recorded ended after three hundred and ninety-four moves. Furthermore, the probability of winning or losing in either the short or the long game is independent of the past results. In this case, we use Markov chain analysis to determine the exact time a game is expected to take. The analysis implements stochastic processes as the game involves a series of possibilities defined using a probability distribution. When a single person is playing the game and starts a square xn at round n, the Markov chain in the future can be represented as xn +1 while the present can be represented as xn. The transition matrix P, of the chain, can be given by Pij = Pr (Xn+1...
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