Understanding and measuring the underlying probability of sporting events is the challenge for all bettors. The same mathematics equally apply - though are less considered - for all kinds of recreational situations from Monopoly to Game Shows as well as life-and-death situations like criminal trials or health diagnoses. Recognising this human blind-spot for the role of probability John Haigh in his book ‘Taking Chances’ provides a fascinating analysis of chance in everyday life and how to make it work in your favour.
The birth of probability
It is hard to believe but up until the 17th century, mankind was ignorant of the concept of probability. Ironically, the story can be traced to one of the most famous and fundamental bets of all time - Pascal’s wager. In grappling with the question of God’s existence the mathematician, Blaise Pascal, theorised as follows:
“Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing.”
He arrived at the position that believing in God provided superior expected value (the eternal after-life) than not believing (infinite oblivion). In simple terms - it was better to hedge his bet.
Four hundred years on, and though our lives constantly demand decision-making under uncertainty, the average person’s grasp of probability remains poor; if that rings true for you, then ‘Taking Chances’ provides an excellent primer on the mechanics of chance, and how to turn them in your favour.
Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Blaise Pascal
Author, John Haigh - Emeritus Reader (Mathematics, Probability and Statistics Research Group) at the University of Sussex - isn’t focused on the role of probability in such meaty questions as the existence of deities, but instead shines a light on the role it plays in much more practical, but no less important, decisions and circumstances.
Avoiding the pitfalls of probability
The book’s Preface sets a perfect tone:
“Anyone who buys Lottery tickets, plays games with cards or dice or bets on the Grand National, is aware of the operation of random chance. Even if we do not sit down to make the calculations, we have some intuition and experience that tells us what is possible, what is likely, and what is typical. These assessments are usually good enough for practical purposes, but without a sound approach to combining and interpreting probabilities, it is easy to blunder’
That passage hints at our hard-wired inability to make sound probabilistic judgements - something we elaborate on widely in Betting Resources - but the focused of ‘Taking Chances’ is grounded in the maths rather than the psychology.
The whole gamut of chance based events
Across 14 chapters Haigh introduces probability theory then explains how it operates for example in Lotteries and board games. Those subjects might be light but the analysis is thorough yet entertaining.
If you are in middle age, and good health, your chance of death within the next year might be one in a thousand: that means the chance in the next week is about one in 52,000, in the next day is about one in 365,000. Even your chance of death in the next hour is about one in nine million, still higher you chance of winning the jackpot [for a 49 ball lottery]. If the winning numbers are drawn at 8.05pm, and you buy your ticket before 7.20pm, you are more likely to expire before the draw is made, than win a share of the Jackpot.
John Haigh, Taking Chances
On that basis, a middle-aged reader has a roughly one in 54 million chance of dying while reading this, but that probability and Haigh’s approach is not to frighten - either literally or through numbers - but to inform. Board games, Dice, Coin Flipping and popular sports are all examined.
Haigh is aware that too much maths can intimidate - ‘every mathematical expression in a popular book halves the readership’ - but rather than dumb it down presents the basis of the basic maths within each chapter but provides an Appendix for those that want the full enchilada.
As Reader at Sussex University (UK) he is a mathematician - not a tipster - so don’t expect fool-proof systems. There is, however, solid advice, ranging from the value and necessity of being truly random in your choice of Lottery numbers to helping HR Managers make an optimal decision when they faced with an impossibly large number of candidates to consider.
Understanding probability in all contexts
Some of ‘Taking Chances’ relates to recreation - such as board or dice games - some to sports and an entire chapter is devoted to both sports betting and casinos, but it isn’t a frivolous dissection of the best way to win at Monopoly. The book covers game theory - which applies to military tactics provides advice - and ends on a very serious note, with the final chapter considering the role of probability (or lack of it) in law and how a measure of Guilt ‘beyond reasonable doubt’ often comes down to a degree of certainty that can mean more murders than shoplifters go free.
Haigh argues persuasively for the place of Bayesian or Conditional probability in assessing the chance that a defendant is guilty. He also touches on the lack of understanding of probability with the legal profession itself, which in truth is worthy of a book of its own (such as ‘Bad Science’ by Ben Goldacre a debunking of medical misuse of data).
‘Taking Chances’ really has a lot to offer anyone who wants to improve decision making under uncertainty. You may feel happy to leave the chances of winning a game of Monopoly to pure luck, but understanding the role of probability in things we do for amusement can also enable us to also to make much more accurate assessments when we have real skin in the game, whether that be money or something even more important.
Taking Chances is available from Amazon and other well known online bookstores.