Abstract

The FIFA World Cup 2026 will be accompanied by the largest official sticker album released so far. Due to the expansion of the tournament from 32 to 48 national teams, the album size has increased to 980 stickers, while the number of stickers per pack has increased from 5 to 7. Such an expansion is expected to increase the total completion cost. However, this increase is not linear, because the collection process becomes dominated by duplicate accumulation in its final stage. The aim of this paper is to estimate, a priori, the expected number of packs, total number of stickers, and financial cost required to complete the album under a uniform random-acquisition baseline. The process is modeled using an exact finite-state recursive formulation for multi-item sampling, while Monte Carlo simulations based on 10,000 independent trials are used to characterize the distribution and variability of completion outcomes. Under the uniform random-acquisition baseline, the exact recursive expectation is about 1042 packs, while the Monte Carlo mean is about 1044 packs. This corresponds to approximately 7311 purchased stickers in the Monte Carlo estimate, of which only about 13% contribute directly to completion, while 87% are duplicates. The engineering relevance of the acquisition structure is examined through a real LoRaWAN dataset case study, where address-level first coverage, repeated device observations, and packet de-duplication show analogous long-tail acquisition behavior in an IoT data-acquisition system.

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