Risk and Uncertainty

What’s it all about?

Understanding how the chance that something won’t go the way you want it to can be taken into account in business decisions.

Some things probably aren’t predictable at all though…


Further Reading

The Lottery.

What are your chances of winning?

Big rollovers are a function of a reduced chance of winning.



Which numbers should you be choosing?

You can’t really predict what’s going to come up by counting how many times numbers ahve come up. there have been far too many draws for this to be relevant. You can perhaps make sure you are less likley to share the prize though.


Misunderstanding probability.

Another Lottery example where Camelot said the chance of winning a 1/17 million prize twice was 1/283 billion. Actually, it is still 1/17 million.


Gender bias in financial risk taking.

Even when we know the right approaches to take, we don’t always act rationally.

Us men eh?

“When researchers give experimental subjects real opportunities for risk taking, men tend to be less cautious. When they ask hypothetical questions about gambling decisions, men tend to take more risks. When they look at people’s pension-plan allocation decisions, they find that men tend to put more of their money into risky assets. Although there is the occasional study finding specific situations where the difference goes away, the vast weight of evidence says that the gender difference – on average – is real.”


Changes to your chances of winning in the lottery.


Note how this is sold to us as having more numbers to choose from like that is a good thing!

1. What does this mean for my chance of winning the jackpot?

The odds of winning a Lotto jackpot will be around 1 in 45 million on the new game. The new Millionaire Raffle will mean you have more chances than ever before to become a millionaire. In fact, the odds of becoming a millionaire on Lotto from October will be 1 in 10 million, which is better than the odds of winning the jackpot on the current game.

For the full set of odds, please see the above prize structure table.

2. How has my chance of winning changed now there are more numbers?

Your overall odds of winning a Lotto prize will improve – so rather than a 1 in 54 chance of winning any prize on the current game, from October onwards, you will have a 1 in 9.3 chance of winning a prize. This means that while the overall odds of winning the jackpot will become longer, you’ll have more chances to become a millionaire than ever before, plus there will be nearly two million additional lucky winners per week. In fact, in an average week, the odds of becoming a millionaire on Lotto from October will be better than winning the jackpot on the current Lotto game.

The chances of winning a £1 million have reduced, but they are still astronomic. The chance of you winning £ squillions are now even worse. And the chances of you winning a prize though have reduced.

You used to have a 1/49 chance for each of your numbers coming out first, a 1/48 for one coming out second, 1/47 for one coming out third and so on.

The extra choice you have now got means that the chance of one of your numbers coming out is now 1/59 – how is that better?

The Expected Value of a prize has gone up, the chance of you winning a prize has gone down.

So why bother? It’s one of those ‘Black Swan’* things – if it happens the change to your life is huge, even at just £1 million. Gives me something to fantasise about for a cost of £4 per week.

*What’s a ‘Black Swan’? It comes from a book, ‘The Black Swan: The Impact of the Highly Improbable’by Nassim Nicholas Taleb. It refers to completely unexpected events and comes from the observation that all the swans in the world were believed to be white until someone went to Australia where the swans are black. So, an event that completely changes things – winning a few billion on the lottery would certainly change things for you and it is totally unexpected, even if wished for.


We human beings have a strange perception of risk, and a bias against losses.

A good example is given by Richard Thaler, a Professor of Behavioural Science & Economics.

He was giving a class to 23 heads of Division of a major publishing company, so these are all business people at a very high level.

He offered them a theoretical project with a 50% chance of a $2,000,000 profit and a 50% chance of a $1,000,000 loss.

So what would you have said?

Of the 23 present, 3 said they would take the business opportunity.

The Chief Executive officer was also present and was asked would he take the project. Yes, 23 times.

Richard Thaler’s comment to the CEO was that he had an institutional problem where the senior managers were afraid to take risks.

What should the Heads done?

50% of $2m = $1m profit
50% of $1m = $0.5m loss.

The Expected Value is therefore a $.5m profit.

Agreed as we have said before, if you only do it once, then there is a chance of either a $2m profit or $1m loss, you won’t get $.5m. But if done 23 times? The managers should have been prepared to take the risk

Read more about how people’s behaviour doesn’t take the real ‘maths of the world’ in to account in Prof Thaler’s book – Misbehaving.


Interesting short piece on our perception of risk in a business situation.

“We don’t assess risk based on probability, but on plausibility. What matters to our assessment is not any objective calculation of probability, but how easy the risk is to imagine. The risks of doing something different are easy to imagine vividly, while the risks of not doing are abstract, hard to visualise, counterintuitive and so implausible, unreal.”


Possible Written Questions.

(No indication of marks – the more marks a question gets, the more you are expected to write – detail that is, not just words!) If you can’t answer these, you need to do some more reading. I do ‘find’ questions elsewhere, so these aren’t all questions I have used myself.

Explain the term Probability.