Random logic at work

CHANCE
The science and secrets of luck, randomness and probability
Edited by Michael Brooks
Profile Books
266 pages; Rs 399

This book is part of the popular New Scientist series, compiling extracts from articles written by many people, who have contemplated the workings of chance in different fields. That means a fair amount of variation in terms of style and quality. It also ensures the content is broad spectrum.

In our personal lives, we deal with chance everyday when we make choices, big or small. But few of us realise the big role chance played in shaping the universe. If the distribution of matter in the early universe had been a little different, it would have been a very different place. Random accidents such as meteorite strikes also played a major role in extinctions and evolution.

It is a useful evolutionary trait to look for patterns in random phenomena and humans are hard-wired to do so. This incessant search for patterns causes selection bias. We notice the unusual data-points and ignore the ordinary. For example, we may meet an old friend we have not seen for a long time when taking a flight and we remember this. But we fail to note the number of times we took flights and did not meet anybody we knew.

Chance, luck, risk, probability and randomness overlap as concepts. But they are not quite the same things. Some random things are amenable to calculation. For example, given a random group of 22 persons, as in a cricket match, we know there's roughly an even chance that two will share a birthday.

Other random things are not calculable. We cannot predict the weather with much accuracy, even though we understand the physical laws. Nor can we model the price of crude oil. These are dynamically non-linear or chaotic systems, with in-built unpredictability. In some fields such as fluid dynamics, things can be unpredictable (movements at molecular level) and predictable (macroscopically when calculating the effects of air resistance), at the same time.

Attempts to use and decode chance started with dice games 4,500 years ago. The maths of probability theory developed in the 17th century and it helps in the understanding and utilisation of the workings of chance. It is the basis for smart strategies in many games. In casino games like roulette and blackjack, and in backgammon, poker and bridge, smart strategies take probability into account.

When different bookies are offering different odds, gamblers can sometimes arbitrage to lock in sure returns on sporting events. In a cricket match for example, if Team A is available at odds of three to one on one site, and Team B is available as one to two favourites on a second site, calibrated bets will win a little money for sure. Bet Rs 40 on Team A (winning Rs 120, and getting Rs 40 back, if A wins) and bet Rs 100 on Team B (getting Rs 50 plus Rs 100 back if B wins). More complex arbitrages are often possible in games with more contenders.

Some interesting strategies based on understanding probability are involved in solving the so-called "matrimonial game". Say, an anxious parent wishes to arrange the marriage of an eligible son. There are 20 potential brides. Each woman may be interviewed, in random order. Each interview will culminate in a matrimonial offer, which must be accepted or rejected immediately.

What is the best way to select the "best" bride? One option is to meet 10 women and reject them, while using the "best" candidate as a benchmark. Starting at #11, take the next offer that beats the benchmark. This strategy offers roughly 25 per cent chances of selecting the "best".

A better strategy was derived by John Gilbert and Frederick Mosteller of Harvard University. They suggested dividing the number of potential brides by 2.718 (the infinite series "e"). This equates to 7.35 women. Round off and interview the first seven women to set the benchmark. Then adopt the strategy of accepting the next offer that beats the benchmark. This raises the odds of selecting the "best" to roughly 37 per cent (100 divided by e). Confirmed bachelors may use similar strategies to sell used cars (divide potential buyers by e), or to hire employees (divide applicants by e).

Conditional probability, based on applying Bayes' Theorem, is hard to understand and counter-intuitive. It is also very important in many legal and medical contexts, such as criminal cases involving DNA matches, or in calculating the efficacy of drug trials. This lack of understanding creates higher probability of miscarriages of justice, or of poor medical treatment.

One of the more intriguing assertions is that it is possible to train somebody to be "lucky". Optimists who are open to the vagaries of chance, are apparently more likely to seize opportunities, as and when those come by. If this is true, life coaches serve a useful purpose even if indulge in major psycho-babble and woo.

There are similar interesting ideas scattered across the book. There's something here for everyone. There is no need for specialised knowledge to enjoy this entertaining lucky dip of a read.