Demystifying Crown Crate Drop Chances with 80,000 Simulations

Dominoid
Dominoid
Community Ambassador
This experiment uses many assumptions that will be proven correct or not over the next few weeks and months. Hopefully an enterprising add-on maker will make a "Crate Opening" add-on that will automatically record all the cards awarded so we can better extrapolate the odds. If there is interest, I will fine-tune the parameters and features of the program and maybe get it to work as a Google Sheet for others to enjoy.

This uses information gathered by people who have purchased and opened crates, but is mainly based upon the community document started by Enodoc on the official forums:
https://docs.google.com/spreadsheets/d/1Zt5oj7PWNFFaTykgXhWQOOkVl1ekHAJgcJpueRN3C40/htmlview

This places the following odds of a reward PER CARD - not per crate.
WbO79th.png

Additional Assumptions and Actions
  • You appear to be guaranteed at least one superior or higher reward per four cards. We did not force this in our simulations as the Card Odds reported by players take this into account. This results in some four card draws resulting in all consumables but this should statistically works itself out in the end of 10,000 simulations.
  • The fifth extra card also appears to be a guaranteed superior or higher reward. We did force this reward in our simulations with the odds of 72, 16, 9, and 3 percent for Superior, Epic, Legendary and Apex. These odds are based upon the reported drop rates overall for the card types.
  • We used a 20% chance to receive a bonus card
  • For gem count, we sold Grand and Major XP Scrolls from the Legendary and Epic reward trees.
  • For gem count, we sold all Fine and Common rewards
  • Our simulations assumed a player started with zero rewards in their account inventory - worse case scenario
  • When a duplicate reward was awarded in our simulations, the reward was converted to gems at the trade-in value.

We then ran 10,000 simulations for each of the following scenarios:
fsupXDA.png

Some Rough Conclusions
  • The chance of landing an Apex mount from a single crate comes in at about 4.44% per crate. This takes into account the 1% chance of an apex reward per four guaranteed cards and having a 20% chance of landing a bonus card with a roughly 3% chance of being an Apex.
  • Opening a 15 crate bundle gives you a roughly 50/50 chance at an Apex Mount
  • If you want a particular Apex mount, you will need to open 39 crates on average to get the exact mount you want or 400 gems to outright purchase said mount - whichever comes first.

You can find the data on all 80,000 simulations below:
https://docs.google.com/spreadsheets/d/1cQGgZPcQC3cYa5EVhOAONuPRJbBR7Ov_VkBap1Tmx5M/edit?usp=sharing


Edited by Dominoid on December 6, 2016 1:02AM
  • Waffennacht
    Waffennacht
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    Thanks! :)
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  • Abeille
    Abeille
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    Thank you, @Dominoid !

    And also @Enodoc for the spreadsheet!
    Just so that everyone knows, my Altmer still can't have black hair. About a dozen of Altmer NPCs in the game have black hair. Just saying.

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  • Lukums1
    Lukums1
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    This seems very accurate, looking at this and my friends who purchased 15 crates total we all got an apex mount.

    Non the less the gem count also from your calculations seems to be spot on aswell avg 82 gems per 15 crates.

    Nice job really. I'd suggest everyone to look into this more when buying crates.

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  • Stargazer126
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    Interesting stuff. Thanks for taking the time to put this together!
  • Prof_Bawbag
    Prof_Bawbag
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    Dominoid wrote: »
    Valethar wrote: »
    Translation: Crown crates are a blatant ripoff, and they should have stuck to populating the store at reasonable prices instead.

    They're actually a pretty good deal if you don't care what you get - if you just want a variety of virtual goodies. If you want something in particular, it would certainly be better to be able to buy it outright.

    I agree. I swapped over from xbox to PS4 and had 3 mounts (the imperial mount, dlc guar and the skyrim mount) and nothing else. No costumes, no pets nothing. Other than that crab you get obviously. Upon buying 13000cr worth of crates, I have all the mounts, 3 apex mounts, all the costumes and a lot of tat obviously. People continuously state that to win big, you need to have filled in all the blanks below. Not true. Those of us with nothing and don't mind the costumes etc basically pick up something every time. I acquired all those mounts and costumes for a lot less than had I bought them from the cr store (a lot of luck played a huge part, I know). It's all those people in the middle that stand to lose the most or those who just want a specific item or 2.
    Edited by Prof_Bawbag on December 5, 2016 10:09PM
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  • bellanca6561n
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    Solid work!

    I wonder how people would have felt had the studio published these odds upfront as most state lotteries have to.

  • Prof_Bawbag
    Prof_Bawbag
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    Solid work!

    I wonder how people would have felt had the studio published these odds upfront as most state lotteries have to.

    Because it's not gambling in a legal sense. To be considered gambling in that sense requires the prize to have some monetary value. Pixels in a game have no monetary value and as such they're not bound by the laws and regulations that lotteries, bookies, casinos etc are.

    This is the case in the UK anyway. Not sure about other countries laws.
    Edited by Prof_Bawbag on December 5, 2016 10:16PM
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  • Slurg
    Slurg
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    Dominoid wrote: »
    Valethar wrote: »
    Translation: Crown crates are a blatant ripoff, and they should have stuck to populating the store at reasonable prices instead.

    They're actually a pretty good deal if you don't care what you get - if you just want a variety of virtual goodies. If you want something in particular, it would certainly be better to be able to buy it outright.

    Thanks for putting these numbers up. This helps explain why some people are really happy with the crates while others are very unhappy.

    (I want specific legendary and epic items and they are in the boxes where I can't buy them outright, so I'm one of the unhappy ones.)
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  • KingYogi415
    KingYogi415
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    50% chance of getting an Apex, of 15 boxes.

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  • driosketch
    driosketch
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    If you want a particular Apex mount, you will need to open 39 crates on average to get the exact mount you want or 400 gems to outright purchase said mount - whichever comes first.
    If you got all your crowns on sale in 5500 packs, the apex mount you want should cost you on average almost $60. This feels right given the one player who spent just under $400 to get everything.

    Put another way, the apex mount you want will use up your crowns from 9 months of subscribing, on average give or take.
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  • Enodoc
    Enodoc
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    Nice work! This is the sort of thing I was hoping might result from my spreadsheet :)
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  • ArchMikem
    ArchMikem
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    Dominoid wrote: »
    [*] If you want a particular Apex mount, you will need to open 39 crates on average to get the exact mount you want or 400 gems to outright purchase said mount - whichever comes first.

    So then the 400 gems.
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  • Crimsonwolf666
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    Opened 46 crates.....no apex mount at all...:(
  • Maegi
    Maegi
    4800 crowns worth of crates, no apex. Blatant scam.
  • ArchMikem
    ArchMikem
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    Opened 46 crates.....no apex mount at all...:(
    Maegi wrote: »
    4800 crowns worth of crates, no apex. Blatant scam.

    All I can say is ZOS appreciates your patronage.
    CP1,000+ Master Explorer - AvA Tribune - Console Peasant
  • Stopnaggin
    Stopnaggin
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    Solid work!

    I wonder how people would have felt had the studio published these odds upfront as most state lotteries have to.

    The argument here is you are not buying crates, you are buying crowns, trading crowns for crates. While I still see this as gambling, that's not how the laws work.

    Think about going to Chuckie Cheese, you pay money to play games, but you get tickets to exchange for stuff. Had you have just spent money for a chance to win those prizes it would be considered gambling.

    Yeah I don't like em either, got 15 and nothing spectacular, won't be spending anymore crowns on them.
  • Recremen
    Recremen
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    Stopnaggin wrote: »
    Solid work!

    I wonder how people would have felt had the studio published these odds upfront as most state lotteries have to.

    The argument here is you are not buying crates, you are buying crowns, trading crowns for crates. While I still see this as gambling, that's not how the laws work.

    Think about going to Chuckie Cheese, you pay money to play games, but you get tickets to exchange for stuff. Had you have just spent money for a chance to win those prizes it would be considered gambling.

    Yeah I don't like em either, got 15 and nothing spectacular, won't be spending anymore crowns on them.

    At those kind of establishments you're actually playing games, though. For our purposes, this is like paying the purchase price of the game and then getting achievements (with their accompanying prizes) through play. It isn't guaranteed, it often requires at least a little bit of skill, but you are ultimately paying for gameplay. For the gambling boxes, you might be able to argue that you're paying to hear Pacrooti talk about peeing his pants in public (literally one of his lines), or that you're paying for trash consumables, but those sound a bit hard to defend. At any rate, you're definitely right regarding some layer of abstraction centering on the purchase of Crowns. As I recall from the TOS, Crowns are themselves considered a service, not a good, and they can be exchanged for other services like leasing costumes out (you do not actually "own" the costume) for a period of time. Apparently they are also leasing gambling boxes which have a chance at leasing costumes for use by your account, but idk how to tease any of that out legally as I am not a lawyer.
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  • necronomniconb14_ESO
    Solid work!

    I wonder how people would have felt had the studio published these odds upfront as most state lotteries have to.

    Because it's not gambling in a legal sense. To be considered gambling in that sense requires the prize to have some monetary value. Pixels in a game have no monetary value and as such they're not bound by the laws and regulations that lotteries, bookies, casinos etc are.

    This is the case in the UK anyway. Not sure about other countries laws.

    They have a money value through account sales. Though we shouldn't need a loophole in order to have laws written to protect the consumer through making it mandatory to inform them of their odds and statistics at regular periods of the actual results from other consumers. Good Guy China is doing this,.. China...

    Also, if a game is in China, the values will obviously be a little bit better for their version of games to avoid discouraging sales but if you assume the odds a hair worse for our version compared to their you can use the reported Chinese programmed odds to determine how big of a ripoff something likely is. I think it's in May that's supposed to begin for games in China with gambling involved. Government requiring odds given, along with the recorded results of players' actual gambling in the games so not just the intended programmed chances will be known.
    Edited by necronomniconb14_ESO on February 28, 2017 8:59PM
  • Jurand80
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    crates are bad mmmmkay?
  • Artemiisia
    Artemiisia
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    I didnt get the wolf I was hoping for, but I almost have 400 gems, and when I saw the next season spriggan theme I was happy I waited, rather have that wolf instead :D
    PC, EU server, Ebonheart Pact
  • Kagetenchu
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    Thanks for the math, just in time for wild hunt :D

    I tend to think of crown crates as grab bags. there is a pool of items and each bag has 4 or 5 items from the whole inside and if you get a repeat you return it for some tokens that you can use to get a specific item. (honestly i think vMA would work better with this system)

    EDIT: Crown Crates would be gambling if there was a chance of receiving nothing in the crate.
    Edited by Kagetenchu on February 28, 2017 9:06PM
  • SydneyGrey
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    Kagetenchu wrote: »
    EDIT: Crown Crates would be gambling if there was a chance of receiving nothing in the crate.
    If all you get are trash consumables and one hideous low-level thing you'd never use in a million years for a race you never play, then you've received nothing. These crates are absolutely gambling, whether you want to admit it or not.

    With that said, I like the "unknown grab-bag" factor, for the same reason I like blind box toys/collectibles. It's fun. I do plan to get some Wild Hunt crates just for the fun of it.

  • Kagetenchu
    Kagetenchu
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    SydneyGrey wrote: »
    Kagetenchu wrote: »
    EDIT: Crown Crates would be gambling if there was a chance of receiving nothing in the crate.
    If all you get are trash consumables and one hideous low-level thing you'd never use in a million years for a race you never play, then you've received nothing. These crates are absolutely gambling, whether you want to admit it or not.

    With that said, I like the "unknown grab-bag" factor, for the same reason I like blind box toys/collectibles. It's fun. I do plan to get some Wild Hunt crates just for the fun of it.

    True would like a way to refuse a collectable before it binds for crown hems. Looking at you argonian spike
  • THEDKEXPERIENCE
    THEDKEXPERIENCE
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    So wait ... what you're saying is that I got really lucky to get a lighting bear on my first ever crown crate?
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