How many packs of Pokémon cards do you have to buy to catch ’em all? Probably hundreds, and most will be quite boring

How many packs of Pokémon cards do you need to buy to collect them all? According to a mathematical analysis, the answer is likely to be several hundred, with most of the cards being duplicates along the way. As the Pokémon franchise celebrates its 30th anniversary, the trading card game continues to draw widespread interest, with collectors facing both excitement and frustration as they attempt to complete their collections. The study used data from six recent Pokémon Trading Card Game sets, including the base Mega Evolution set and five expansion sets: Phantasmal Flames, Ascended Heroes, Perfect Order, Chaos Rising, and Pitch Black. Each set consists of a range of cards, with the base set typically containing around 100 numbered cards, excluding rarer and more elusive special cards. The research aimed to determine how many booster packs a collector would need to open to complete the base set, using pull rates, estimates derived from thousands of actual booster packs opened by collectors. Using a computer simulation, researchers modeled the experience of 10,000 virtual collectors who each opened one pack at a time. Every pack contained ten cards, and the simulation tracked whether each card was new or a duplicate. For five of the six sets analyzed, the average number of packs required to complete the base set ranged from approximately 110 to 130. The Pitch Black set, the newest among the six, required a median of about 129 packs, while the Mega Evolution set needed about 130 packs. One notable outlier was the Ascended Heroes set, which required a median of about 771 packs. This was attributed to the inclusion of 39 “double rare” cards, significantly higher than the nine or ten found in other sets. This highlights a key challenge in random collection games: while obtaining the initial cards may be relatively straightforward, acquiring the last few missing cards can be exceptionally difficult and time-consuming. Beyond the mechanics of completing a set, the enjoyment factor of opening packs diminishes over time. Researchers introduced a “freshness” metric to quantify the novelty of newly opened cards. Initially, nearly every card in a pack is new, but as the collection grows, the proportion of unfamiliar cards decreases rapidly. For most sets, after opening about 15 packs, fewer than half the cards in subsequent packs are expected to be new. By the time a collector opens 30 packs, a typical booster pack is likely to contain only one or two new cards, with Ascended Heroes offering slightly more diversity but requiring significantly more effort to complete. The findings underscore the balance between variety and difficulty in collecting. While larger sets offer greater diversity, they also increase the number of packs needed to complete the collection. This dynamic reflects the broader appeal of the Pokémon Trading Card Game, where the thrill of discovery gradually gives way to the challenge of persistence. As the franchise marks its 30th anniversary, the demand for trading cards continues to rise, driven by nostalgia and the allure of collecting. However, the practical reality of completing a set remains daunting, with collectors needing to navigate the probabilities of randomness and the diminishing returns of repeated purchases. The results of this simulation provide a clearer understanding of the challenges faced by collectors, highlighting the blend of strategy, patience, and luck required in the pursuit of catching them all.