I thank Leighton Vaughan Williams and Mike Smith for helpful information on horse racing odds, Les Miller for the results of his simulation of roulette spins, Ian McHale for his detailed explanation of how to estimate the winning chances of the 32 teams in the finals of soccer’s World Cup, and Derek Robinson for his help with the diagrams. I am particularly grateful to an anonymous referee, whose acute and constructive comments have helped me remove ambiguities, order the material more coherently, and seek to draw out the central ideas of the subject.

I beg forgiveness from those others who recognize themselves as the unacknowledged origin of the information, opinions, or anecdotes in this book, but I have relied on too many sources to give individual credit every time. This is not an academic treatise, with every assertion traceable to its roots, but an attempt to sharpen the reader’s appreciation of what the subject of probability is about, how it has developed, and to where it might be applied.

All errors and imperfections that remain are mine alone.

John Haigh

August 2011