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Guide Forgery Chest Mythic Probability

Discussion in 'Wynncraft' started by Verle, Feb 23, 2021.

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  1. Verle

    Verle Atlas Devotee HERO

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    Motivation
    Now, you may be thinking, hasn't this been done before? And you'd be right - there are (as far as I'm aware) two posts that address the question of the expected number of Mythics from the Forgery chest after a certain number of runs. However, both posts make the same error, so I thought I'd put my response to them in a new post.

    For formality's sake, let n be the number of complete (all dungeons) Forgery runs, and p the probability of getting a Mythic from a complete Forgery run chest (p = 0.01).
    In essence, they start by stating that the probability of not getting a Mythic in any chest is equal to (1-p)^n = 0.99^n, which is true. Then, the probability of getting one Mythic is defined as the complement of that, being 1 - 0.99^n. However, this is actually the probability of getting one Mythic or more.

    So, what number of Mythics can you actually expect after
    n runs?

    Method & Results

    Let's denote the random variable associated with the number of Mythics obtained as X. We can gain some insight from the Probability Mass Function (PMF) of X. Basically, you can feed the number of Mythics (given a certain number of runs) to the PMF, and it will tell you how probable it is for that to occur.

    X follows a Binomial distribution; its PMF takes the form of
    PDF.PNG .


    For a Binomial distribution, the expected value (thus mean number of Mythics) can easily be found through n*p. Thus, after 100 runs, you'll have gained 1 Mythic on average. However, note that at 100 runs, there is still a 36.6% chance of 0 Mythics, and a 26.4% chance of 2 or more Mythics.

    In the figure below, the probability of getting a certain number of Mythics is shown for the cases of 50, 100, 200 and 300 runs (as also considered by the most recent post).​

    Forgery.png
    Conclusion
    In short, the number of Mythics you can expect after n complete Forgery runs is equal to n*p, where p = 0.01. Based on this, you can estimate the cost per Mythic as (n*[run cost])/(n*p) = [run cost]/p and determine whether running the Forgery for Mythics is worthwhile, but that's somewhat outside of the scope of this post. In any case, thank you for reading :)
     
    Last edited: Feb 26, 2021
  2. TMoney1909

    TMoney1909 Well-Known Adventurer CHAMPION

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    Hmmm interesting.
     
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  3. PikaPrince

    PikaPrince Famous Adventurer HERO

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    I can't be the only who saw the words Binomial Distribution, saw a graph and was "Idk what's going on but I'm sure he's correct"
     
  4. Horizon

    Horizon Well-Known Adventurer HERO

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    Ah, Binomial Distribution, from calling Dream out to solving if Forgery is worth farming for Mythics, there's nothing it cannot do.
     
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  5. coolname2034

    coolname2034 Formerly known as NPCGrian HERO

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    This was on the test I failed a few months ago
     
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  6. highrescucumber

    highrescucumber <- iron deficiency CHAMPION

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    idk what this says but its telling me i can get mythics and thats good enough for me! very interesting though
     
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  7. Verle

    Verle Atlas Devotee HERO

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    Sorry I didn't really go into what a Binomial distribution is, though as has been mentioned -
    There are quite some videos that explain what a Binomial distribution is and how it relates to the Dream cheating accusations (e.g. https://www.youtube.com/watch?v=rbhx3UNpV64), so feel free to check that out if you're interested.
     
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  8. btdmaster

    btdmaster Famous Adventurer VIP Item Team

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    I mean, in my post explaining how to get the chance on the one thread it wasn't an error, it was intentional. If I phrased it incorrectly that's on me, my bad (did I? I don't particularly remember) but I just didn't really think that most people would care about the specific chance of getting 2, 3 etc. so I just did the chance of getting one or more.
    Plus, the chance of getting multiple are rather small especially when compounded with wynn's active player base (and considering how many are the available level, and will actually run forgery chest that many times) it likely won't happen to any player for a long time

    also this video is epic would recommend. I used it as a guide for myself the other day cause I was pissed about some rates in a game
     
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  9. Skidooskei

    Skidooskei King of the Lollipops CHAMPION

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    That’s a dream epic exposed word so I’m sure they’re fine
     
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  10. PikaPrince

    PikaPrince Famous Adventurer HERO

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    I actually know binomial distribution cuz Im taking stats but doing math outside of class hurts my brain
     
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  11. Potatomancer

    Potatomancer Budget Wither

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    isnt 50 runs a lot?
     
  12. Mistrise Mystic

    Mistrise Mystic Surfing winds and chasing windfalls HERO

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    Without dungeon bombs? Yes
    With dungeon bombs? Yesish
     
  13. ghoti0315

    ghoti0315 buff assassin CHAMPION

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    50 runs of forgery chests be like 350 dungeon runs, assuming that you do a run per 6 mins you spend 2100 mins, which is 1.46 (1.458333...) days worth of time of doing dungeons. Of course we consider 200+ runs because more chance of mythic (and it is near statistically impossible for no mythic). You have to farm 5.833 days straight of it, with keys or dungeon bombs and the chance of sudden restarts.

    With that absurd amount of time I could go ingredient/emerald farming with totems and loot gear for money just to buy an unrolled mythic (i believe it is a thing). It may be slower, however this method is more stable and at least less boring for me.

    (thats why I asked for a forgery chest rework in the other thread)
     
  14. Computekk

    Computekk Steampunk Virtuoso

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    Tell me you used a graphing calculator and didn’t actually use the whole formula cause u can find the info in 2-var stats I think
     
  15. Retathrah

    Retathrah Retired Nostalgia Hunter, Tired Metalworker CHAMPION

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    My math wasn’t perfect in all fairness, and the mythic portion was more of a panicked endnote for the Main goal of the XP sums to get to 106. I was more concerned about whether or not you’d get a mythic than how many considering most of us have maybe seen 1 in our total playtime, less so of it’s viability. But still, good on you for showing this might be a marginally competitive strategy compared to loot running
     
  16. Verle

    Verle Atlas Devotee HERO

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    It wasn't my intention at all to call anyone out with this thread - sorry for coming across a bit harsh. The difference isn't that significant when the number of runs is small, and indeed you need to spend a lot of time on Forgery runs for a decent chance at a Mythic. There were simply a few misleading statements in the original posts which I wanted to address - e.g. "33 STACKS of LE for a 95% chance to find ONE mythic", when on average you'll have gotten 3 Mythics by 300 runs (still not very cost-effective, but that's beside the point).

    I just used the whole equation in MATLAB since that also allows me to create figures easily :)
     
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