Panini's World Cup sticker album will cost Â£774 to complete, says maths expert

Panini have attracted controversy with the release of their sticker album for this year's World Cup in Russia, due to a price rise and the very first digital edition. A mathematician at Cardiff University has crunched the numbers and has calculated that completing the sticker book will typically cost around £774. A pack of five stickers has increased 30p from the Euro 2016 edition to 80p. Collectors will have to fill 32 squads, plus managers, stadiums and World Cup legends, amounting to a grand total of 682 stickers. If a miracle occurred and a duplicate sticker was not encountered it would cost £109.60 to complete the entire album. However, anyone who has attempted to finish an album knows the frustrations of the duplicates and the illusive search for certain players. Therefore it is a much more trying task. Professor Paul Harper, from the School of Mathematics, explored what is realistic. “The first sticker you buy is absolutely guaranteed not to be a duplicate,” he said. “The second sticker you get has a 681/682 (99.85%) chance of being a new sticker. The third sticker you get has a 680/682 (99.7%) chance of being a new sticker, and so on.” Professor Harper added up all of the probabilities of getting a new sticker to obtain the following formula in terms of the total number of unique stickers required, n: n (ln (n) + γ) (where γ = Euler’s constant = 0.557) As the stickers come in packs of five an adjustment was made to the calculations using conditional probabilities. It showed that on average you would need to buy 4,832 stickers, or 967 packets, to complete the book, costing £773.60. “What is interesting is that to collect just the last 19 stickers for the book, you would still be required to buy 483 packets of stickers, or half the total number of expected packets. Put another way, you are only half way through when you have just 19 stickers left to collect,” Professor Harper said. One of the ways to keep the cost down is swapping with friends or other collectors. According to Professor Harper, two people collecting and swapping can reduce the number of packets by 30 per cent, five players by 57 per cent and 10 players by 68 per cent. Although, even with 10 friends swapping it could still cost up to £247 on average to complete the album. Professor Harper said: “I can still recall the joy of finally completing my first Panini album as a young boy for the 1982 World Cup in Spain. I must have used an awful lot of pocket money to do this, as well as having generous grandparents handing over bundles of packets of stickers, coupled with tense negotiations of swapping duplicates with friends in the school playground. “Filling an album has become progressively more expensive over the years since then, not just because there are typically more teams competing now, but because Panini have become more creative about allocating spaces."