# A Brief Journey in Discrete MathematicsHeads I Win, Tails You Lose

A Brief Journey in Discrete Mathematics: Heads I Win, Tails You Lose [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Brief Journey in Discrete MathematicsHeads I Win, Tails You Lose

13 pages

Publisher
Springer International Publishing
© Springer Nature Switzerland AG 2020
ISBN
978-3-030-37860-8
Pages
79 –92
DOI
10.1007/978-3-030-37861-5_6
Publisher site
See Chapter on Publisher Site

### 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.]

Published: Feb 12, 2020