# What are the chances Paul the octopus is right?

• 9 July 2010

Germany's oracle octopus, Paul, has become a worldwide celebrity for his apparent ability to accurately predict the outcome of football matches.

Paul has correctly forecast the result of six of Germany's World Cup games, and has now plumped for Spain to take the title.

So just how extraordinary is this cephalopod?

Paul is a common octopus, which is considered the most intelligent of all invertebrates.

In experiments it has seemingly distinguished the brightness, size and shape of different objects.

But mathematicians point out that his run of predictions is not that extraordinary.

As Paul was predicting two possible outcomes (win or lose, and not a draw), he had a 1/64 chance of predicting six correct outcomes - a 1/2 chance of predicting the first game correctly, then a 1/4 chance of predicting the first two games, a 1/8 chance of predicting all the first three games, and so on.

The chances of him correctly predicting seven games, up to the final, is 1/128.

## 'Spooky'

Chris Budd, professor of applied mathematics at the University of Bath, says that even highly experienced people find it difficult to predict the outcome of a football game, and compares Paul's feat of "prophecy" to the tossing of a coin.

"If you toss a coin and it comes down heads six times, that is unlikely," he says. "However it is not as unlikely as predicting which numbers will win the [UK] lottery, which is 1/14 million."

"Mathematics can be spooky in the way it can appear to predict things," he says.

"You can use mathematics to predict things in the future. When I get on an aeroplane, for example, I know I am not going to fall out of the sky because mathematics has predicted the plane will not do that. But that doesn't mean I'm psychic."

David Spiegelharter, the Winton Professor of the Public Understanding of Risk at Cambridge University is not convinced either that Paul's predictions are that remarkable.

The octopus's run of correct predictions is all down to luck, he says.

Using the coin analogy, he says that if someone flips a coin and gets the same result nine or 10 times, it is not remarkable in itself, but it will seem remarkable to the person flipping the coin.

## Hole-in-one

It is all down to our skewed perception of chance.

"Our perception about how chance happens is not very good, it is not part of our human characteristics," Prof Spiegelharter says.

"The mathematics of chance have only really developed in the past 300 years or so," he points out.

He says it is important to think about all the other animals that have attempted but failed to predict the outcome of football matches.

"It's like seeing footage of a golfer getting a hole-in-one," he says. "We're not seeing the millions of times the golfer made the shot and it didn't go in."

"What would be different would be if the golfer said it would happen in advance."

So the publicity surrounding Paul's latest prediction is an opportunity for greater scrutiny of his powers.

Nick Weinberg, a spokesman for Ladbrokes in the UK, said that there was evidence of people betting small sums based on the octopus's predictions.

"People are coming in and saying they are waiting for his predictions, and betting £5 or £10 (\$7-\$15)," he says.

However, it remains to be seen whether Paul's selection will influence the odds on who will ultimately take home the World Cup.

As the world digested Paul's prediction Spain were indeed the bookmakers' favourites - exactly as they have been throughout the tournament.