Paul The Octopus is famous for picking the winner in 8 out of 8 games at the FIFA World Cup in 2010. How did he achieve this amazing feat? Was he skilled or was he lucky?
To get 8 out of 8 games right where each game is a 50-50 guess the probability is 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.0039 (or one chance in 256). This seems too incredible. An octopus can't be that good.
Where is the flaw in this probabilistic reasoning?
The answer is that the probability that Paul got a game right was not 0.5 but more. Much more. In fact the probability was much closer to one. Here is the explanation:
Paul, a German octopus, was only used to pick German games, usually picked the German team, and the German team usually won. So the chance that Paul picked the winner was more than 0.5 for each game. That accounts for 5 of the 8 games.
What about the games that Germany lost and the game where Germany didn't play? Let's take a guess.
This tournament was was not Paul's first time at playing the game. He had learned previously that there was always food under the German flag. Paul - with some ability to distinguish the flags of different countries - usually went for the German black, red, and yellow. He might have had monochrome eyesight which is why he picked Serbia as a winner in the game against Germany because in monochrome the Serbian and German flags look similar.
For the final Germany wasn't playing so Paul went for the most German looking flag - that of Spain (red, yellow, red) . He seems to have a preference for that flag since he also predicted the win of Spain over Germany in the semi-finals. All flags picked by Paul had horizontal stripes.
So Paul was lucky but not as lucky as the 1 in 256 chance suggests. His main luck was that his team was one of the best teams in the tournament and that some of the other good teams had similar flags.
Will Richie McCow be successful at picking the winner of the All Black games in the Rubgy World Cup? Possibly - as long as he keeps picking the All Blacks and the All Blacks keep winning. Will the All Blacks keep winning? Check out the probabilities here.