BY Tim - Aug 9, 2013

## I have an idea…

And, even better than that, it’s an actuarial idea. Now I know what you’re thinking. Actuaries have the most amazing spreadsheets, the funniest jokes, and the best estimates (that’s a funny joke right there, trust me), but they tend not to have that many new ideas.

Ah, but we do.

For example, did you know that it was an actuary that invented the telephone? That’s right, Herbert J Smigglepants invented it over lunch one day in 1822, because he was sick of talking to people face to face. History gives all the credit to Alexander Graham Bell, of course, but history is full of lies, isn’t it. Like the moon landing.

These days actuaries are still having ideas. Although actuarial techniques were developed primarily in the field of insurance, today those techniques are applied to a whole range of industries and issues. From managing the distribution of electricity, to climate change and weather forecasting, it often helps to think about things actuarially.

And that’s what I’m going to do.

Before we get to the actual idea, however, I have to explain a few concepts. So prepare yourself – you’re about to attend your first actuarial lecture. If it’s anything like my first actuarial lecture, you’ll trip on the way in, ask a stupid question, and then fall asleep. Yours won’t be quite that fun, but pretty close.

All actuarial science is built on three distinct but related concepts. The first two are chance and consequence. That is, “What is the probability that a particular event will occur?” and “What are the consequences if it does occur?”. Throw in an allowance for the time-value of money, and boom, that’s the essence of anything actuarial. Normally the goal is to estimate these probabilities and consequences, and use them to work out the expected cost of a particular set of events, over a given period of time. This cost is called the “expected value”, and is essentially the distillation of a wide range of possible scenarios into a single, average outcome.

As with most new concepts, it helps to look at an example. Suppose you find yourself in the world’s most boring casino, a not-for-profit Mormon church hall with beige corduroy couches that only serves *light beer*. In this casino, there is only one game you can play, called Satan’s Evil Coin Toss Game. A man in a Satan suit flips a coin, and if you guess right, you win a dollar, which you can then use to buy some magic underpants in the gift shop. The question is, how much should the casino charge people to play, if they want to break even in the long run?

As it turns out, we can work this out by calculating the average outcome, or expected value. In this example, it’s calculated as:

Expected Value = 50% x $1 + 50% x $0 = $0.50

That is, if the casino charges everyone 50 cents to play Satan’s Evil Coin Toss Game, they can expect to break even in the long run.

Easy, right?

Where expected values really come in handy is comparing two different sets of events, with two ranges of possible outcomes. Once again, it helps to look at an example. Suppose you go to the slightly more exciting casino up the road. This one has full strength beer, leather couches, and *two* games to choose from. In the first game, you have to pick a number between 1 and 1,000, and if you guess correctly, you win $1,000,000. In the second game, they just give you $1,000. If both games are free to play, which game should you choose if you’re being completely rational?

At this point, you’re probably thinking one of three things:

- Oh man, a 1 in a 1,000 chance at a million, sign me up!
- A guaranteed $1,000? Lock it in, Eddie.
- Why the fuck am I still reading this? The Bachelorette is on.

The answer, however, is “either”. That is, a rational person should be completely indifferent between the two games. That may sound odd, but don’t be alarmed, it just means you’re reckless. Or boring. Or irrational.

The answer lies in the expected values, which, as you’ve now probably guessed, are the same for each game:

**Game 1**

Expected Value = 0.1% x $1,000,000 + 99.9% x $0 = $1,000

**Game 2**

Expected Value = 100% x $1,000 = $1,000

As I said, all of this is just groundwork for my grand, actuarial idea. I still need to explain a few more things, which I will do over the next few posts, but the main thing to remember from this post is that:

- An expected value is essentially an average outcome for a wide range of probabilities and consequences; and
- We should be indifferent between two sets of events that have the same expected value.

OK, I think I’ve bored you enough for now. Who wants to play Satan’s Evil Coin Toss Game? $1 a throw.