Paul the octopus. (AP)

New Delhi, July 12: Paul the octopus may have captivated football watchers nearly as much as the 2010 World Cup matches in South Africa, but math and marine biology may explain its game-forecasting antics.

The Netherlands versus Spain game was also a forecasting contest between Paul, a two-year old octopus in an aquarium in Oberhausen, Germany, and Mani, a 13-year-old parrot living with a fortune-teller in Malaysia.

The octopus appeared to have successfully predicted the match-winning country eight out of eight times in the 2010 World Cup, diving into one of two boxes marked with the flags of the competing countries lowered into its tank with mussel — food — inside.

In Malaysia, the parrot picked cards hiding the flags of winning countries six out of seven times ahead of their matches — but then wrongly predicted that the Netherlands would win the World Cup.

A mathematician who specialises in the theory of probability said Paul’s 8/8 score may be explained as a chance event —similar to a person receiving any triplet or a triplet of aces when a deck of 52 cards is distributed to players.

“Eight out of eight predictions is enough to cause a sensation, but a gambler may have a great night —some chance events are rare, but they do occur,” said Rajeeva Karandikar, a professor at the Chennai Mathematical Institute.

He said the chance of an octopus predicting a winning nation eight out of eight matches would be smaller than a card player receiving a triplet. Given that the first three matches could have ended in a draw, the chance of an 8/8 score is 1/864, which is smaller than the 1/425 chance that a card player gets a triplet from well-shuffled cards. Yet the chance of a player receiving a triplet of aces is even smaller — 1/5500.

“It may be rare, but card players do get three aces,” Karandikar told The Telegraph.

Scientists say it is only the short snapshots that the world gets to see of the octopus and the parrot that create an illusion of psychic powers.

They say the illusion will fade and evidence of chance — that Mani picking the right cards and Paul opting to dine in the right boxes are only chance events — will emerge only when the numbers of tests grow very large.

“When you toss an unbiased coin three times, you may get a head-head-head, or a tail-tail-tail,” said Gadadhar Misra, a senior mathematician at the Indian Institute of Science, Bangalore. “When you toss it 1000 times, the number of heads and tails are closer to the 50:50 distribution you expect.”

But some marine biologists say it is possible that the octopus may be guided by its response to stimuli that it encounters inside its tank.

“The octopus is among the most intelligent of the invertebrates,” said Annaian Shanmugam, a professor at the Centre for Advanced Studies in Marine Biology at Parangipettai in Tamil Nadu. “They can be trained for repetitive tasks and have been shown to have spatial memory.”

Some scientists have speculated that the octopus might be picking boxes on the basis of the flags marked on them. “There is no evidence that octopuses can tell the difference between colours, but experiments suggest they can distinguish between shapes and objects,” Shanmugam said.

And Mani the parrot, mathematicians say, may be just another fortune-telling bird whose owners’ fortunes hinge on a game of chance and on the gullible who appear convinced that the future will be told by the beaks of a parrot.