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See our Youtube video Estimating the Probability of Heads for a Coin Toss.

Summary of coin toss probability formulas (pdf, 8 pages) in this book.

Need to decide something? Use our coin tosser.

Try our Coin Toss Runs Calculator.

Try our Coin Toss (Binomial) Distribution Calculator.

The Coin Toss: Probabilities and Patterns

Stefan Hollos and J. Richard Hollos

This title is no longer available.
The new edition is:
Coin Tossing: The Hydrogen Atom of Probability

Format and pricing:
Kindle/pdf (123 pages) $5.99
ISBN: 9781887187084
Publication date: Sep 2012,
updated Nov 2012

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Table of Contents

The coin toss is really just a metaphor for a random event that has only two possible outcomes. The actual tossing of a real coin is just one way to realize such an event. There are many examples of questions that are equivalent to a coin toss:

Because a coin toss is equivalent to such a wide variety of questions, the results in this book are widely applicable.

With this book, you can answer questions like:

Because the coin toss is the simplest random event you can imagine, many questions about coin tossing can be asked and answered in great depth. The simplicity of the coin toss also opens the road to more advanced probability theories dealing with events with an infinite number of possible outcomes.

This book is very mathematical. Some knowledge of calculus, discrete math, and generating functions is helpful to get the most out of it. A review of discrete math is provided in the index, and a free copy of Herbert Wilf's book generatingfunctionology can get you up to speed on generating functions.

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About the authors: Stefan Hollos and J. Richard Hollos are physicists by training, and enjoy finding patterns and information in data, and anything related to the calculation of probabilities. They are the authors of Probability Problems and Solutions, Combinatorics Problems and Solutions, Bet Smart: The Kelly System for Gambling and Investing, as well as Simple Trading Strategies That Work and Pairs Trading: A Bayesian Example, and are brothers and business partners at Exstrom Laboratories LLC in Longmont, Colorado. The websites for their work are Exstrom.com and QuantWolf.com.

Table of Contents

Send comments to: Richard Hollos (richard[AT]exstrom DOT com)
Copyright 2012-2014 by Exstrom Laboratories LLC