Airin Ahmad: Slumpvandring och slantsingling

Abstract

This thesis aimed to observe the random walk of a game of coin toss, where two people got the chance of betting if the random walk would reach the state of -9 before reaching +10, given that they start at state 0. With the use of Markov chains and simulations in the programme RStudios, I could see that reaching the state of -9 at the end of a random walk, which would mean to lose in the game, is more likely to happen. The simulations showed more exactly that the random walk would reach the absorbent state of -9 with 53 %.

The difference between the probability of winning and losing was not enough to guarantee an outcome. An alternative way was to have an unfair distribution of the coin. With a distribution of 0.55 and 0.45, making the coin toss more likely to result in tails, we could guarantee an outcome, that the probability of losing would be with 90 %.

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