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From Dust to Dust -- The Economy Thread


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#1 Hamlet

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Posted 22 August 2013 - 08:30 PM

I want to see if we can figure out the basic economics of expanding your collection. The big question is how many packs you can expect to take to finish out a collection. Given the non-trading nature of Hearthstone, that question can be answered more coherently than in most games. The big unknown is the card rarity distribution in packs, but pretty good progress can probably be made with even rudimentary estimates there.

Reviewing:
100 coins -> 1 pack
$1.50 to $1.30 -> 1 pack (price depending on bulk)
1 daily quest = 40 coins
1 game win = 1 coin
150 coins -> 1 arena
$2 -> 1 arena
1 arena -> 1 pack + coins and dust (seemingly averaging to around 50, but we don't have to get into the details of arena yet).

Disenchant values (golden):
common: 5 (50)
rare: 20 (100)
epic: 100 (400)
legendary: 400 (1600)

craft values (golden):
common: 40 (400)
rare: 100 (800)
epic: 400 (1600)
legendary: 1600 (3200)

Checking the card list (wowhead DB with "collectible" and "expert" filters set: Hearthstone Cards - World of Warcraft
We have something like:
94 common
81 rare
37 epic
33 legendary

A full playset (2 of each card (1 for legendaries)) would take:
106,120 dust (non-Golden)
428,800 dust (Golden)

The big question, as I said, is: what do you get in a pack on average. A quick glace at this thread:
Expert Pack Opening Rates and Arena Rates - Forums - Hearthstone
And for now I'll go with a quick ballpark of 1% legendary, 5% epic, 21% rare, 73% common, with 2.5% of all cards (uniformly distributed) being Golden. Refining this at some point will definitely be helpful. But for now, multiplying it all out would give each pack an average disenchant value of 93.8 Dust.

So if you disenchanted every card in a pack, you'd take something like 1131 packs to finish a non-foil set. This number is somewhat meaningless since most of the cards you'd open for a long time (especially non-common cards) will be cards you don't have 2 of yet, so the value of opening them is much better than their disenchant value. But it gives some perspective, as a number that we know is somewhat beyond what the real number might be.

To pull a number out of my hat, maybe it's an overestimate by a factor of around 2 (for example, imagine opening 500 packs and getting 25 legendaries--you'll have over half of your needed 33 covered before even having to craft anything). I'm going to think about a better way to do the computation for real, but a basic simulation might be easy for someone to set up. It's a bit hard to deal with the changing probability of getting duplicates as you've opened more and more packs. Maybe I'll do a simple version later that only considers legendaries and post that at least.

If you want all foils, things look much worse, for two reasons:
1) The commons are now expensive. The craft cost of the whole set has gone up by a factor of 4 or so.
2) The rate at what you open cards you need has slowed by a factor something like 40. Unlike the non-foil example, the approximation where you assume you have to craft everything from dust is not too far off the mark.
And crafting everything from dust is looking to take something on the order of 4570 packs.

Sticking just for a moment with that first-order guess of 800 packs, that would be $650 invested into the game (bearing in mind that you can earn off 52 cents for every daily quest you do). This is, interestingly, about the same order of magnitude as the cost of a full playset of any one Magic set.

Anyway, I'm not going to keep going until I back up and fill in more real math estimates, but I wanted to get this started so others can look into it and help start working it all out.
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#2 Moshne

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Posted 22 August 2013 - 08:39 PM

One crucial thing I was missing and I just discovered from your post: You can craft cards you don't already have. I didn't notice the "All Cards" tab in the collection book.

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#3 MysticalOS

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Posted 22 August 2013 - 08:44 PM

Yeah, I made a feral spirit card this way. Great way to grab some strong cards to fill some holes in deck. I'm saving up dust to produce some better epic cards too. At this point I may go on a "gold" destroying rampage to produce some better play cards since I'm not one for caring about pretty borders.

#4 Hamlet

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Posted 22 August 2013 - 08:52 PM

Yeah, stuff I should have mentioned about basic Dust management, assuming generally that you want to avoid being wasteful in the long run:
--Try not to disenchant cards until you have 3 of them. If you ever have to craft that card again, you've just deleted some dust.
--Don't disenchant Golds out of hand, even if you're not "collecting golds." They only give enough dust to rebuy the non-gold version of the same card, so if you ever have to do so, you've gained nothing. Once you have 3 of a card though, you get a bonus if one of them is gold so you can disenchant it.
--Try to keep crafting to a minimum (especially of non-rares) until your collection is more substantial. There's an obvious tension between immediate fun and efficiency here, and I don't want to get into people's preferences in too much detail. But just pointing out that it will hurt quite a bit if you've crafted a lot of cards that you later opened copies of.

e: To be clear, none of this matters at all if you're strictly thinking about the beta of course.

#5 Moshne

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Posted 22 August 2013 - 08:55 PM

I think the "wait till later to craft" is certainly valid later. Right now, all of our cards are getting destroyed at some point. There is likely some merit in actually getting to test things while we have the chance to press a reset button on our bad decisions.

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#6 Hamlet

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Posted 22 August 2013 - 09:37 PM

Oh you can only have one of any legendary in a deck, can't you. I'll edit through the OP.

#7 kasik047

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Posted 22 August 2013 - 09:39 PM

Oh you can only have one of any legendary in a deck, can't you. I'll edit through the OP.


I beleive it is one legendary of a single card per deck, though that may need to be checked.

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#8 Moshne

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Posted 22 August 2013 - 09:56 PM

You can certainly have more than one legendary, just one of a given name.

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#9 Hamlet

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Posted 22 August 2013 - 10:02 PM

Right, that's all I meant--a complete collection only needs 1 of each legendary (this would actually be true either way).

#10 Hamlet

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Posted 22 August 2013 - 10:26 PM

Slightly more concrete math on amassing legendaries (just easy to work out by hand when you're considering one card type). The expected number of legendary loots in order to have collected N out of 33 is:

33 * (Sigma 1/(34-k) for k=1 to k=N) (I think latex isn't working around here at the moment).

For example, for N=33 (all the legendaries) it's 135:
sum(33/(34-n)) from n=1 to 33 - Wolfram|Alpha

At N=26, it's 49 loots. That means that after pulling 49 legendaries from packs, you expect to have 26 of the 33 covered, and therefore have 23 duplicates. The duplicates can be disenchanted down to 6 more unique legendaries, getting you most of the way there. So I think that at around 50-52 legendary pulls on average, you'd have all of them.

If 1% for legendaries is right, then that's around 1000 packs, far more than we expect to actually need. So in reality, dust contribution from lower->higher rarities is going to be important for bringing that number down (furthering the conclusion that you should try not to craft low rarities). A more complex calculation will be needed.

#11 Arxkanite

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Posted 23 August 2013 - 07:39 PM

I wrote a simulator to figure this out using your numbers. It will open packs and disenchant duplicates. The simulation runs until the dust collected is more than or equal to the amount of dust required to craft the rest.

Here are the results based on 100 simulations.
https://docs.google....Znc&usp=sharing

Complete Gold & Standard Collections
[TABLE]Packs Opened|Dust Collected |Dust Spent|Dust Remaining|Cards Collected|Cards Crafted|% Collected|% Crafted
|||||||
Medians|||||||
3,316|256,408|256,000|120|726|188|79.43%|20.57%
|||||||
Averages|||||||
3,317|255,856|255,596|260|726|188|79.44%|20.56%
[/TABLE]

Complete Gold Collections (No Standard Cards)
[TABLE]Packs Opened|Dust Collected |Dust Spent|Dust Remaining|Cards Collected|Cards Crafted|% Collected|% Crafted
|||||||
Medians|||||||
3,120|262,603|262,400|63|260 |197|56.89%|43.11%
|||||||
Averages|||||||
3,109|262,702|262,516|186|260|197|56.99%|43.01%
[/TABLE]

Complete Standard Collection (No Gold Cards)
[TABLE]Packs Opened|Dust Collected |Dust Spent|Dust Remaining|Cards Collected|Cards Crafted|% Collected|% Crafted
|||||||
Medians|||||||
491|28,150|27,900|108|432|25|94.53%|5.47%
|||||||
Averages|||||||
492|28,511|28,171|340|433|24|94.64%|5.36%
[/TABLE]

This is to collection 2 of both the normal and gold versions of every card (1 for legendaries). I'll make more simulations to narrow down just class cards or gold or just standard versions.

So we're looking at an average cost of $4,312.10 if you buy packs with the bulk discount.

If we collect data on what prizes are obtained based on records in the Arena we could also determine how many average wins per $1.99 / 150 Gold you will need to make the Arena more economical.

#12 Hamlet

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Posted 23 August 2013 - 08:15 PM

Yeah, could you do non-gold and gold separately? (ideally, non-gold should actually be neutral to gold status, just getting 2 of each card, but depends on how the sim works).

A key helpful result is what % of cards are opened vs. crafted. You very consistently have 80% opened, which is definitely curious if you're making a full gold set and open them rarely. Want to see what it looks like for non-gold and gold individually.

#13 Arxkanite

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Posted 23 August 2013 - 08:42 PM

Pastebin is being a butt, I'll paste my code in a minute. I'm sure there is something I'm overlooking. It doesn't make sense that 80% are being opened.

Although, maybe it does because I'm opening until there is enough dust to simply buy the rest.

So lets say I open 3300 packs. I'll have opened 16,500 cards. There are only 914 Cards to obtain. 15,586 cards would be disenchanted. I think it's safe to say at that level (And looking at Gold Only and Standard Only simulations) that every STANDARD card would be purchased by that point.

457 Cards are Standard and would have been opened. (50%). another 274 Gold cards would need to have also been opened to get to 80%. At 2.5% Chance of obtaining a gold card, we would have opened 413 from the 16,500 cards. The number of packs you're going to have to open will depend on the number of duplicates within those 413 cards as well as their rarity.

So it does sound possible to open 80% of the cards you need. You need TONS and TONS of dust to buy out the gold cards you need.

#14 Astrylian

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Posted 24 August 2013 - 02:00 AM

I think a better way of looking at it for the % opened vs crafted would be to weight the cards by their crafting cost. Sure, if you open 500 packs, you're going to have opened 95% of the cards... but those 5% you have to craft are probably almost all legendaries and epics, and probably cost as much to craft as all of the common/rare combined.
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#15 fr0d0b0ls0n

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Posted 24 August 2013 - 03:31 PM

You could use a more realistic model, and not global %.

As we know there is 2 different slots with different chances in the packs, pretty similar to how Diablo 3 rolls work:

Slot #1:
1% Legendary
5% Epic
100% Rare

Slot #2-5:
1% Legendary
5% Epic
~10% Rare (pretty hard to tell until we have better data, as can be confused with Slot #1)
100% Common

Also it seems that the Golden chance is independent for each card after the rarity is chosen, and also it doesn't seem to be the same for all rarities. With the data we have, I'll say is 2% for Commons, and 5% for Rare/Epic/Legendary.
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#16 Arxkanite

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Posted 24 August 2013 - 10:51 PM

Here is the code I used:

[ActionScript 3] Hearthstone Collection Simulation Code - Pastebin.com

Another class just runs that over and over and saves the results to CSV. Should be able to easily modify it into any language.

#17 Hamlet

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Posted 26 August 2013 - 09:01 PM

I think a better way of looking at it for the % opened vs crafted would be to weight the cards by their crafting cost. Sure, if you open 500 packs, you're going to have opened 95% of the cards... but those 5% you have to craft are probably almost all legendaries and epics, and probably cost as much to craft as all of the common/rare combined.


Yeah, I think this does explain the 80% opened ratio. Breaking it out by rarity would be interesting, although it's really only important as a sanity check that the simulation's working right.

You could use a more realistic model, and not global %.

As we know there is 2 different slots with different chances in the packs, pretty similar to how Diablo 3 rolls work:

Slot #1:
1% Legendary
5% Epic
100% Rare

Slot #2-5:
1% Legendary
5% Epic
~10% Rare (pretty hard to tell until we have better data, as can be confused with Slot #1)
100% Common

Also it seems that the Golden chance is independent for each card after the rarity is chosen, and also it doesn't seem to be the same for all rarities. With the data we have, I'll say is 2% for Commons, and 5% for Rare/Epic/Legendary.


I don't think the distinction between the guaranteed rares and the other cards affects anything for this purpose, since you get them in a fixed ratio. The average number of rares in a pack is the piece of information that's needed. Technically the info about the guaranteed rare affects the variance slightly, but that difference is probably negligible over hundreds of packs. Could tweak the sim slightly if anyone ever worked out the details.

Golden being dependent on rarity would be a big deal--do you know anyone who's tried to look into this in detail?

Here is the code I used:

[ActionScript 3] Hearthstone Collection Simulation Code - Pastebin.com

Another class just runs that over and over and saves the results to CSV. Should be able to easily modify it into any language.


Is there something I can download to run this code in so I can play with it and make a few tweaks?

#18 Arxkanite

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Posted 27 August 2013 - 06:59 AM

You can run it inside Flash Develop. Let me put a project package together for you.

#19 Hamlet

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Posted 27 August 2013 - 06:06 PM

Tried linking here and asking the question: What's the best known info on card rarity breakdown in packs? : hearthstone

#20 fr0d0b0ls0n

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Posted 27 August 2013 - 09:06 PM

Golden being dependent on rarity would be a big deal--do you know anyone who's tried to look into this in detail?


All the big pools I have seen are closer to the golden ratio I said, and not an average 2.5%.

For example the one linked in the OP:

Commons = 489
Rares = 156

Golden Common = 8
Golden Rare = 8

Doesn't seem probable with a 2.5% for every card.

I also did a simulator btw, I got 515 packs on average for a non-golden collection with these chances. The golden collection was around ~2663, smaller, but it's logical with almost double number of golden legendary/epic/rare.
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