The sticker fever is back, with the arrival of the World Cup album. The biggest sporting event in the world starts on June 11th, but part of the excitement is off the field: collecting. However, completing is not an easy task and mathematics helps explain why.
For Milton Jara, physicist and mathematician at Impa (National Institute of Pure and Applied Mathematics), in an interview with CNN Brasil, It’s easier to win at Mega da Virada than without taking any retakes. “The chance is an astronomical number, it is infinitely easier to win Mega da Virada. If you write the zero numbers on a sheet of paper, it would give the distance from Earth to the next star in the galaxy”, jokes the expert.
The illustrated book will have space for , 68 of which are special, with all 48 teams that will participate in the tournament. The price per envelope is R$7.00 and comes with seven stickers.
“The average number of stickers you would have to buy is 6,750 stickers (964 packets). If they are printed in a balanced way and there are none” says Milton Jara.
The calculation made by the mathematician considers that the printing is equivalent, with the same quantity for all stickers. In this simulation exercise, the collector would not exchange, just buy. A probability phenomenon is that if you share the act of collecting with someone, the chances increase.
“Between two people, they would need to buy 8,700 stickers (1,242 packs), they can complete two albums, that would be 4,350 (621 packs) per person. If there are three albums, the number is 2,600, if there were four albums, the number goes to 12,500 and so on…”, adds Jara.
Markov Chain
At IMPA, during probability classes, researchers use sticker collecting to illustrate the theory of ‘Markov Chains’. A process where the chance of obtaining an unprecedented sticker depends only on how many stickers the collector already has. As the album approaches its end, the feeling of finding a new piece becomes increasingly rare due to the geometric probability distribution.
For the 2018 World Cup album, for example, it is estimated that a collector who does not trade would need to buy around 6,018 stickers to have a 90% chance of completing the collection, according to the article by researchers Leandro Batista Morgado and Leonardo Silveira Borges, both from UFSC (Federal University of Santa Catarina);
Andrei Andreyevich Markov was a Russian mathematician who obtained fundamental results about a specific type of stochastic phenomenon, random processes that deal with the probability of uncertain outcomes.
Images of envelope separation;
sticker album
The official release of the album is scheduled for May 1st. The book will have some options for the collector, the simplest is the paperback (R$24.90), as well as hardcover models (R$74.90) and even a “Premium” (R$359.90). The latter is sold exclusively on the Panini website.
Panini behind-the-scenes video;
FIFA World Cup 2026
The 2026 World Cup will be the first edition with an increased number of teams. Since France 1998, the World Cup had 32 participants, but now there will be 48 in total. . Groups tend to be, theoretically, less deadly, as less expressive teams will have more chances and can “invade” a possible group with traditional teams.
Furthermore, the number of those classified for the next phase increases. Now there will be 32 teams advancing to the knockout stage, with the two best in each group, in addition to the eight best placed, reducing the chance of a powerhouse falling in the group stage.
The big difference in the change of path is at the beginning of the qualifierss. Now, the knockout stage has one more game, the 16th round.
*With information from Leonardo Martins
