It's the last (unofficial) holiday weekend of summer before the new year really gets down to business on Monday. So let's have some fun. Try yourself on this simple quiz.
Q1: Linda is 31 years old, single, outspoken and very bright. At uni, she majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Which of these two is more likely: that Linda is a bank teller or that Linda is a bank teller and is active in the feminist movement?
If you went for a feminist bank teller - sorry, wrong.
Q2: As an investor you're trying to decide between buying shares in three listed companies when you notice that one of them's been chosen as company of the year by a business magazine. Would that make it best bet of the three?
Q3: You're trying to decide which super fund to put your savings in, so you look up the figures to see which one had the highest returns last year. Would it be the best bet?
If you answered yes to those questions you're likely to be disappointed.
Q4: The instructors of fighter pilots found that pilots who were praised when they'd flown well always performed worse the next time, whereas those who were criticised for performing badly always performed better the next time.
The instructors concluded that criticism was more effective than praise. Were they right?
If you answered yes - sorry, wrong.
Q5: You flip an unbiased coin and it comes up five heads in a row. Which is more likely from the sixth throw: heads or tails?
Q6: Which is the more likely birth order in a family of six kids: B B B G G G or G B B G B G?
In the first case the sixth throw is just as likely to be another head as a tail. In the second, the two birth orders are equally likely.
Q7: Which would you prefer, an operation with a 90 per cent success rate, or a different one with a 10 per cent failure rate?
Answer: Have another think about the question.
Apart from the investment questions (which I threw in to please the business editor) all those questions come from best-selling business writer Michael Lewis' latest book, The Undoing Project.
It's the story of two Israeli-American academic psychologists, Daniel Kahneman and Amos Tversky, who demonstrated how wide of the mark is the assumption of conventional economics that we're all "rational" - coldly logical - in the decisions we make, thus giving a huge push to the new school of behavioural economics.
A lot of their experiments involved our understanding of maths. Don't feel bad if you failed many of them. Most of us do, even people good at maths.
The moral is, however much or little people know about maths, particularly the rules of probability, we have trouble applying this to our daily lives because we let our emotions distract us.
Q1 was about the rules of probability. Linda certainly sounded like a feminist, but a lot of bank tellers aren't feminists so, statistically, there was a higher probability that she was a bank teller than a bank teller and a feminist.
All that guff about her interests at uni engaged our emotions and distracted us from the simple probabilities.
The questions about investment choices and fighter pilots were about a key statistical regularity most of us haven't heard of, called "reversion to the mean".
The performance of companies, super funds or fighter pilots in any year is a combination of skill and luck. We're always tempted to attribute good luck to high skill.
The luck factor is random, so a performance that's way above average is likely to have been assisted by luck, just as a really bad performance is likely to have been worsened by bad luck.
If good luck and bad luck average out over time, an outstandingly good performance is more likely to be followed by a performance closer to the average than by another rip-snorter. Similarly, a really bad performance is more likely to be followed by one not so bad.
Note that we're only accounting for the luck factor in performance, so a policy of always predicting reversion to the mean gives you a slight advantage in the forecasting stakes, not a sure thing.
The pilot trainers were observing reversion to the mean, but falsely attributing it to their own efforts in awarding praise or criticism.
Sadly, this has left many of the world's bosses suffering the delusion that criticism works better than praise.
The questions on coin tosses and baby order were about the "law of large numbers", which says that if events have equal probability of occurring, eventually they'll occur an equal number of times.
We all know that if you toss a coin enough times you'll get a roughly equal number of heads and tails. And we all know the numbers of boys and girls being born are almost equal.
Trouble is, you need thousands of samples to be sure of getting that result. By expecting to see equal numbers in a sample as small as six, we've turned the statisticians' law of large numbers into our own imaginary "law of small numbers".
Remember, probability theory applies to independent events, where what's gone before has no effect on what happens next.
Humans are pattern-seeking animals, but sometimes we go too far and see patterns that aren't real. Five heads in a row, or three boys followed by three girls, may look unlikely but, because the law applies only to large numbers, are perfectly consistent with a random draw.
Whether it's heads or tails, boy or girl, the safest bet remains 50/50. In the case of the five heads in a row, no one told the coin its duty was to make its sixth toss a tail.
