Heads I Win, Tails You Lose

Randolph Nelson
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Chapter Chapter 6 in A Brief Journey in Discrete Mathematics, 2020, pp 79-92 from Springer

Abstract: Abstract Consider a game where two players toss a coin. If the coin lands heads up, player 1 wins a dollar. Otherwise player 2 wins a dollar. If the coin is fair, then each player has the same chance of winning. A few things about the game are obvious from the outset. Since neither player has an edge over the other, there is little chance that one of them will win a lot of money. Thus, the game should hover around break even most of the time. Additionally, each player should be ahead of the other about half of the time. Another feature of the game concerns its duration if there is an agreed stopping event. For example, suppose the game stops the first time heads is ahead of tails. Then, clearly, the game should end fairly quickly. These observations are all straightforward which suggests that coin tossing does not have much to offer in terms of mathematical results. To show this, and move on to a more interesting topic, let us quickly dispense with the mathematical analysis that establishes these obvious, intuitive, observations.

Date: 2020
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DOI: 10.1007/978-3-030-37861-5_6

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