You will be able to spot choices where a bad outcome is too costly to accept, whatever the expected value.
A friend of Siti's has a proposition. He has found a business opportunity he is sure about and wants her to put in her entire savings of S$40,000. If it works, he says, she will double her money within a year. He thinks there is a 90 percent chance it works. Siti has just learned expected value in lesson 7.2, so she does the sum: 90 percent of S$80,000 is S$72,000, far more than the S$40,000 she has now. On average, it is a great bet.
She still feels it is a terrible idea. Her instinct is right, and this lesson explains why. Expected value is a powerful tool, but it tells you only about the average, and some decisions turn on what happens if things go badly. The figures in this lesson are examples, and the calculations have been checked.
Start with a choice most people make without thinking of it as a bet. Suppose, as a made-up example, you pay S$300 a year to insure against an event that has a 1 in 1,000 chance of costing you S$100,000. The expected loss from the event is S$100,000 divided by 1,000, or S$100 a year. You pay S$300 to cover an expected loss of S$100, which gives the insurance an expected value of minus S$200 a year.
Insurance has to work this way on average. Premiums have to cover the insurer's payouts, its costs and its profit, so across all customers, people pay in more than they get back. If you judged insurance only on expected value, you would never buy any.
People buy it anyway, and often they are right to, because the S$100,000 loss is not just a bigger number than S$300. For many people it is a loss they could not recover from: years of savings gone, debt, a home at risk. Insurance swaps a small certain loss for protection against a large one that would take years to repair. The expected value is negative, and the decision can still be sound.
Which risks are worth insuring, and how, is a topic for a finance course and a qualified adviser. The point for this lesson is the reasoning. When an outcome would be ruinous, avoiding it can be worth more to you than the average suggests.
Now go back to the friend's proposal. The expected value is positive, but there is a 10 percent chance Siti loses everything she has saved. One time in ten is not rare. And losing all her savings would not just be a bad year. It could mean no emergency fund, delayed plans for a home, perhaps debt if anything else went wrong at the same time.
The rule that follows is simple: avoid any bet where the worst case would ruin you, however good the average looks. Ruin is different from an ordinary loss because you cannot recover from it and try again. Expected value assumes you get to play many times so the average can work out. If one bad outcome takes you out of the game, you never reach the average.
What counts as ruin depends on you. For one person, losing S$40,000 is painful but survivable. For another, it is everything. The same bet can be reasonable for one and reckless for the other.
Here is a made-up illustration of why the number of bets matters. Imagine a bet where you win S$100 with a 60 percent chance and lose S$100 with a 40 percent chance. The expected value is S$20 per bet, which is a good bet.
Make it once, and you have a 40 percent chance of losing. Make it a hundred times, at S$100 each, and the expected total is S$2,000. The chance of ending up behind after a hundred bets is under 2 percent. The more times you can repeat a positive bet at a size you can afford, the more reliably your results move towards the average.
That is why small, repeated decisions with positive expected value tend to pay off over time. Think of running many small experiments at work, or sending many job applications, or pitching to many clients: any single one can fail, and across dozens of them the average shows through. One large, all-or-nothing bet does not get that protection. You get one draw.
This also suggests a way out of a risky big bet: break it into smaller ones. If Siti believed in her friend's business, she could put in an amount she could afford to lose, and add more later only if it proved itself.
The practical habit is one extra question after every expected value calculation: what happens if I am wrong? Not on average, but in the bad case. Could I recover from it? How long would it take? Who else would it affect?
At work, this changes some decisions. A project with a high expected return but a small chance of losing your biggest client might not be worth it. A career move with a better average outcome but a real chance of leaving you without income for a year needs a savings buffer first. Lesson 6.1, One-way doors and two-way doors, gives you the same instinct from a different angle: ruinous outcomes are usually one-way doors.
Siti tells her friend she will not put in her savings. If he gets the business running, she says, she might put in a small amount she could afford to lose.
Choose one financial or career choice you are weighing up now. The activity below asks you to set its expected value next to its worst case and judge whether you could recover.
For one financial or career choice, write the expected value, the worst case and whether you could recover from it.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).