Hey all, I have calculated how many packs one needs to open in order to have the whole collection for a
So, according to the above graph the expected number of packs you need to open to get the whole collection went from 340 to 280, which is approximately 17.5% decrease in the cost of the game, when measured in terms of value per pack. Note, that this percentage is only applicable directly to those who wish to assemble the whole collection. If you only care to have like 2-3 playable decks, the effect is significantly lower. If you only open like 100 packs, you do not saturate epics and legendaries, so the probability of getting doubles there is not that high. So for most people the only real effect of this is that they will likely need to craft rares and commons much less frequently.
The code can now be found on my
EDIT 2: Some of you rightfully made a note that 10 heroes is not the same as 9. So here are two more models. Using the format
The means end up to be 303 for AOA and 293 for WOTOG. Apparently those extra legendaries really count. Take a note that AOA has much more variance because of the extra legendaries, so making predictions about how many packs you will spend is harder.
The second point was about distribution of cards into ranks, after all the necessary packs have been opened. In the below plots, I show how many of each card you will have for a typical pack opening, To make plots look nicer, I sort each plot to have most frequently opened cards come first
Hope this helps.
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