Calculating effect of duplicate protection

hearthstone 4 - Calculating effect of duplicate protection

Hey all, I have calculated how many packs one needs to open in order to have the whole collection for a
Whispers of the Old Gods - Calculating effect of duplicate protection

typical set. I have taken the frequency of finding different rarity of cards from the hearthstone pack statistics. For simplicity, I have ignored golden cards altogether. The frequency of golden cards is ~2% and they yield 4x rewards, so I would roughly estimate the number of packs to be 6% less if disenchanting golden cards was also considered.

Given 1000 simulations each, how many simulations opened exactly that many packs

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
hearthstone packs full collection - Calculating effect of duplicate protection

github page

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 , Ashes of Outland has , namely 135 cards. However, this set is a bit heavy on legendaries because they have just released the new hero. I have also extrapolated WOTOG to 10 heroes, I get , namely 143 cards. Plugging that data into model I get somewhat less optimistic results


Still 1000 simulations, comparing only the duplicate-protected method for AOA vs extrapolated WOTOG

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

WOTOG9, before protection, 338 packs opened. Missing many legendaries and few rares

WOTOG9, after protection, 285 packs opened. Only missing some legendaries (although sometimes you may also be missing rares)

WOTOG10, after protection, 291 packs opened. Only missing some legendaries (although sometimes you may also be missing rares)

AOA, after protection, 328 packs opened. Only missing some legendaries (I think you are almost never missing rares given so many legendaries)

Hope this helps.

Source: Original link

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