Hearthstone's latest expansion, Journey to Un'Goro, introduced a total of 135 new cards, and at launch many players expressed frustration about seemingly opening too many duplicates and not enough legendaries. Blizzard has said there's nothing wrong with Un'Goro's distribution rates, but how much does it actually cost to complete the set? Redditor Seaserpent02 ran the numbers, and it turns it's a lot.
Using data from more than 1000 Un'Goro pack openings to determine the assumed probability of Un'Goro's 49 commons, 36 rares, 27 epics, and 23 legendaries, Seaserpent wrote a Python script to do a Monte Carlo simulation of opening Un'Goro packs.
"Five cards were randomly generated in accordance with their rates, and the number of cards collected were tallied" Seaserpent said. "Repeats and all goldens are dusted, and two of each common, rare, and epic card are collected. Once the simulation had a sizable collection and enough dust to craft the missing cards, the number of packs opened was recorded. This process was repeated for 10,000 trials."
Seaserpent found that it took an average of 316 packs (with a standard deviation of 32 packs) in order to collect every card in the set. At best, it took only 214 packs, while the worst trial took a total of 437.
Using the bundle price of 40 packs for $49.99, this calculates out to just shy of $400 in order to complete a full Journey to Un'Goro collection. There are other, slightly cheaper, ways to purchase Hearthstone packs, such as the $70 60-pack bundle or using Amazon Coins, but 40 for $50 is a standard rate most people use.
In the Reddit thread's comments, one user pointed out that this equates to roughly $3 per card. Once you factor in relative rarity, you could say that commons cost $0.20 to $0.50, rares are around a dollar, epics $5-ish, and legendaries $20 or more. That's roughly in line with prices of physical card games like Magic: The Gathering, but in those cases prices are driven up due to being able to buy, sell, or trade individual cards—meaning better cards tend to fetch higher prices.
Of course, most Hearthstone players don't go for set completion—it doesn't take all 23 Un'Goro legendary cards to build a viable competitive deck—but $400 is still a bitter pill to swallow for those who do, and gathering more than 300 packs is no small task for free-to-play players. For those interested in poking around the Python simulation, Seaserpent put the script up on Pastebin.