You will be able to explain how people overweight small probabilities in lotteries, insurance and long-shot investments.
Darren is 29, healthy, and works in an office near a Singapore Pools outlet (all of his details are invented for this example). When the jackpot is large, the queue at the outlet runs out the door, and most weeks the prize is big Darren joins it and spends S$10 each time.
The same month, he turns down disability income cover at work. The premium seems like a waste: he is 29, he is healthy, and he thinks "nothing's going to happen". So he is paying for a tiny chance of a huge win while refusing to pay for protection against a much larger chance of a huge loss.
Lessons 2.1 and 2.2 introduced prospect theory, the work of Kahneman and Tversky. Its third part, probability weighting, describes how people do not weight probabilities the way arithmetic does. By arithmetic, a one-in-a-million chance should count for one millionth of the outcome. In practice, small chances that people notice get far more weight than they deserve, and outcomes that are close to certain get slightly less weight than they deserve.
Kahneman and Tversky also observed that very unlikely events are usually either overweighted or ignored completely. Which of the two happens seems to depend heavily on attention. Vivid outcomes that you are reminded of, such as a jackpot on a poster or a cracked phone screen, get overweighted. Dull outcomes nobody mentions, such as a long illness that stops you working, can be treated as if their probability were zero.
A lottery jackpot is the clearest case of overweighting. In a game where you pick six numbers from 49, there are 13,983,816 possible combinations, so one ticket has one chance in nearly fourteen million of matching all six. Singapore Pools publishes the odds for each prize tier of its games, and they are worth reading once. Most buyers know the odds are bad, but the feeling of "it could be me" is far bigger than the real odds. At S$10 a week over 52 weeks, Darren would spend S$520 a year.
Buying tickets for the fun of the draw is a fair thing to spend on. The problem starts when the same weighting carries over into investing. A penny stock that "could go up fifty times", a new crypto token, or a friend's start-up raising money in a chat group pulls money in the same way a jackpot does. The size of the possible payoff dominates the picture, while the chance of getting it, and the much likelier outcome of losing most of your stake, shrink in your mind.
The same pattern pushes insurance decisions wrong in both directions. At the small end, people pay to insure risks they could easily absorb, because a vivid loss feels likely and expensive. Darren pays S$12 a month for phone protection on a S$1,200 phone. Over a two-year contract that comes to S$288, nearly a quarter of the phone's price, to cover a loss he could have paid from savings.
At the large end, people leave big, less vivid risks uncovered. Losing your income for a year through illness or injury costs far more than any phone. For a young worker this is not a remote possibility; it simply has no vivid picture attached. Declining the disability cover took Darren less thought than buying the phone protection did.
Lesson 2.2 gave a test that sorts these cases: could you cover this loss from savings without real harm? Small, vivid risks usually pass the test, so insuring them is often poor value. Large risks usually fail it, and those are what insurance does best. Disability income cover is insurance that replaces a monthly pay cheque if illness or injury stops you working; Insurance Decoded, lesson 6.1, "Disability income insurance replaces a monthly pay cheque", explains how it works.
The fix is to get the probability onto the page as a number, so it can be weighed rather than felt. Before deciding, write the actual probability and the actual outcome in numbers, and put both side by side with the cost. If exact odds are not available, write a range. Note where each number came from; "the person selling it said" is a source worth noting. Then weigh the written numbers instead of the feeling.
For the decisions covered above, the written version looks like this:
Lottery ticket: S$10, nearly one in fourteen million for the jackpot, plus the smaller prize odds from the published table. Speculative investment: the amount you would put in, what happens if it goes to zero, and an honest guess at how likely that is. Phone protection: S$288 over two years against a repair you could pay for yourself. Income cover: the premium against a year or more without pay.
One Sunday Darren writes his own odds and costs down. He keeps the lottery, capped at S$10 on big draws, because he enjoys it and the cost is known. He drops the phone protection. He adds the disability cover to his list of things to ask HR about on Monday.
Look back over the past year for one long-shot bet and one small insurance purchase of your own, and find the real odds and the real cost of each.
List one long-shot bet and one small insurance purchase you have made and write the real odds and cost of each.
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