14 June 2018

Why maths shows you probably won't win £100 million predicting World Cup winners

Ahead of the FIFA World Cup in Russia, a betting company has launched a promotion offering a £100 million prize if entrants correctly predict the outcome of all 64 matches in the FIFA World Cup in Russia.

Why maths shows you probably won't win £100 million predicting World Cup winners

However, to guarantee success in predicting the correct outcome of all the matches, betting at a rate of one bet a second you'd have to have started placing bets more than a billion years before the universe existed, according to an academic from the University of Sheffield.

Dr Fionntan Roukema, a University Teacher in Mathematics at the University of Sheffield, suggests that guessing randomly, you'd need to make more than a million times the number of grains of sand on the planet worth of guesses to take home the cash.

As Dr Roukema explained: “I was a huge football fan during the golden era when Hristo Stoichkov won a golden boot, Ray Houghton lobbed Gianluca Pagliuca, and Gazza performed an outlandish chip over Colin Hendry! But that was the nineties and I hadn't found mathematics. Now I know some mathematics, but I've become 100 per cent ignorant of contemporary football. However, even though I have a complete lack of footballing knowledge, I'd like to explain to you how we can win the £100 million prize by only multiplying some numbers together, using a little imagination, and applying a modest amount of elbow grease.


To guarantee success in predicting the correct outcome of all the matches, betting at a rate of one bet a second you'd have to have started placing bets more than a billion years before the universe existed."

Dr Fionntan Roukema

University Teacher in Mathematics at the University of Sheffield


“In order to guarantee a win, you need to bet on all possible outcomes. There more than five octillion different possible outcomes in the World Cup, where one octilion is a billion billion, billions - which is a lot of billions. To put the number five billion billion billion in context, this is about the same as the area of 10,000 planet earths put together and measured in millimeters squared!”

Dr Roukema suggests that:

  • Betting at a rate of one bet a second you'd have to have started placing bets more than a billion years before the universe existed to guarantee a win.
  • Instead of going back to before the Big Bang to place bets, an alternative strategy would be to ask your friends to place bets for you. However, even if you take all humans who have ever lived on this planet back to the birth of the universe and persuaded them all to bet once a second until the beginning of the World Cup 2018, you still wouldn't have enough time to guarantee a bet with the correct outcome!
  • Even if you did somehow manage to make all possible bets, and had to record all your bets on individual bits of paper, then you'd have more a billion piles of paper, with each pile stacked up to the surface of the Sun, so some at the top of the pile might burn and you might not be able to claim your prize.
  • Even if you're the greatest master of football knowhow on the planet and you're able to predict the outcome of any football game with 90 per cent success, then your odds aren't much better than 1 in a 1000 when you place a single bet.

Dr Roukema added: “The mathematics of why there are so many choices boils down to there being a total of 64 games in the World Cup, which is large, and the incredibly fast growth of exponentiation means the number of possible options is outrageous. Almost as outrageous as the 1986 Argentinian handball or England’s record with penalties!”

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