Could someone help me calculate the odds of this?

Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
edited June 2021 in General Discussion

So this is my 6* cosmic roster. There are 13 of them. In total I have 35 unique 6*s (about 3 are duped). So I have opened about 36 6*s so far (2 were nexuses) and have pulled a whopping 13 cosmics...

This isn't quite a rant post, but either way, feel free to leave a lol reaction at my abysmal luck. This meme-tier ratio pretty much reflects my entire 6* luck, lmao. As you can see, I haven't leveled them up because it would probably take literally 1000 cosmic iso to do so (don't have such funds).
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Comments

  • The_Sentry06The_Sentry06 Member Posts: 7,803 ★★★★★
    Rank up Venom even though you are done with Variants.
  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    The_Sentry06 said:

    Rank up Venom even though you are done with Variants.

    Honestly I wish I had a gem. However, I could rank him and Angela back-to-back since I have (very nearly) enough T4 cosmics for both. But since Angela would take less iso to be completely leveled, I'm leaning towards her first. Also she would see more immediate use than Venom since variants are done for me as you mentioned.
  • UnknownUnknown
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  • PulyamanPulyaman Member Posts: 2,365 ★★★★★
    I have 63 6 star champs.
    Science 11
    Mutant 12
    Cosmic 14
    Tech 11
    Mystic 11
    Skill 4
    The skill ratio is pretty screwed. Only skill champ that I did not choose was elsa from my latest nexus. It was between corvus dupe, elsa or km dupe and I chose corvus. Before that my nexus was km, elsa and sabretooth dupe and I chose km because I like him better. I dread forming another skill t5cc.
  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    Zan0 said:

    I would need all 6 of your nexus options to make a correct calculation

    First was from a lucky cav (the second one I ever bought). Was between Aarkus, og cap and terrax (before the buff). I chose Aarkus (cosmic, and I'm glad I did. He's such an underrated workhorse).

    Second one was from 7.1 exploration. Was to choose between Hela, awakening psylocke, and getting Karnak. I picked Hela (cosmic) and I should have probably picked psylocke dupe (since I have apoc now, but didn't have him then).

    Haven't opened a nexus this year just yet.
  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    edited June 2021
    Crcrcrc said:

    I've got 10 science and 22 total, count your blessings

    Oof... The good thing is that science class has less duds than cosmic.
    ItsDamien said:

    Out of 60 total 6* pulls, 18 of them have been Mutant.

    Now that... That is a jackpot right there! Mutant class is so good, that it's quite literally impossible to have that amount of mutant 6*s, and not have at least 1/2+ extremely useful ones.
  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    odishika123 said:

    Kill_Grey said:


    So this is my 6* cosmic roster. There are 13 of them. In total I have 35 unique 6*s (about 3 are duped). So I have opened about 36 6*s so far (2 were nexuses) and have pulled a whopping 13 cosmics...

    This isn't quite a rant post, but either way, feel free to leave a lol reaction at my abysmal luck. This meme-tier ratio pretty much reflects my entire 6* luck, lmao. As you can see, I haven't leveled them up because it would probably take literally 1000 cosmic iso to do so (don't have such funds).

    No offence oga
    But this is 10 times better than my roster
    Boss, how that one dey possible sef? 😂
  • ItsDamienItsDamien Member Posts: 5,626 ★★★★★
    Kill_Grey said:

    Crcrcrc said:

    I've got 10 science and 22 total, count your blessings

    Oof... The good thing is that science class has less duds than cosmic.
    ItsDamien said:

    Out of 60 total 6* pulls, 18 of them have been Mutant.

    Now that... That is a jackpot right there! Mutant class is so good, that it's quite literally impossible to have that amount of mutant 6*s, and not have at least 1/2+ extremely useful ones.
    Oh I have plenty of good mutants in that. But I also have some duds. My last mutant was actually a dupe on Bishop before his buff was announced so.... maybe there's a sign?

    Problem is.... t4 mutant is a struggle to come across right now.
  • UnknownUnknown
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  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    Zan0 said:

    Kill_Grey said:

    Zan0 said:

    I would need all 6 of your nexus options to make a correct calculation

    First was from a lucky cav (the second one I ever bought). Was between Aarkus, og cap and terrax (before the buff). I chose Aarkus (cosmic, and I'm glad I did. He's such an underrated workhorse).

    Second one was from 7.1 exploration. Was to choose between Hela, awakening psylocke, and getting Karnak. I picked Hela (cosmic) and I should have probably picked psylocke dupe (since I have apoc now, but didn't have him then).

    Haven't opened a nexus this year just yet.
    So you've rolled the 6 star die 40 times and gotten cosmic 14 times

    That comes out to 0.2% probability

    But I really don't like to throw things like these probabilities out there lol
    So it's a 1 in 500 odds?
  • UnknownUnknown
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  • DawsManDawsMan Member Posts: 2,169 ★★★★★
    Yeah I have ton of skill and mutant (bad ones) and only one tech, one science,
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  • Agent_X_zzzAgent_X_zzz Member Posts: 4,498 ★★★★★
    I have both r3 Hela and Venom, both fun.
  • DawsManDawsMan Member Posts: 2,169 ★★★★★
    Agent_X_zzz said:

    I have both r3 Hela and Venom, both fun.

    Do you run odin with hela? That's the only way I would r3 a hela.
  • HendrossHendross Member Posts: 965 ★★★
    An approximate, simplified answer would be; the probability of pulling 13 or more cosmics from 35 crystals assuming classes were equally distributed (.166 each) and not adjusting for featured or nexus.

    The answer is ~ 0.28%, less probably than getting any 1 specific champ from the 6star basic pool (0.625% @ 160 champs)
  • flygamerflygamer Member Posts: 345 ★★
    edited June 2021
    Right there with you! About 40 6* pulls, only 3 tech and 4 science and mystic, but all these cosmic and dupes.

  • AndyBeardoAndyBeardo Member Posts: 180 ★
    edited June 2021
    Given that you picked 2 cosmics out of Nexus Crystals (and there were other classes available) you would have to ignore these two.
    Then it would be 11 out of maybe 34 or 35 (make sure you don't ignore any duped 6* in other classes).
    Cosmic is the class with the most 6* heroes (37 as of today, see auntm.ai), so the odds are at least a bit in favor of cosmic champs. So maybe 7 to 9 out of 35 would be relatively common. 11 is a lot.

    The exact odds are impossible to know because you didn't get all your 6* champs at the same time so with the addition of new 6*s the odds changed.

    But basically, it would work like that: You had a glass full of 193 M&Ms in six colors of which 37 were light blue. You take one of those M&Ms out with your eyes shut, open your eyes, add +1 in the respective color's chart on a notebook and put the M&M back into the glass (you can pull the same champ over and over again). You do the same thing 35 times.The result? I wish I still knew how to calculate that.
  • Hammerbro_64Hammerbro_64 Member Posts: 7,463 ★★★★★
    It is 100% chance of that exact outcome happening because it happened according to the sacred timeline
  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    DawsMan said:

    Agent_X_zzz said:

    I have both r3 Hela and Venom, both fun.

    Do you run odin with hela? That's the only way I would r3 a hela.
    Same here. Don't have Odin at any rarity, and I missed him from the featured as well.
  • rivetrivet Member Posts: 256 ★
    I am going to ignore the nexus, and calculate the probability of pulling 13 cosmic champion out of 36 pulls, assuming all 6 classes are equal likely for each pull. First, you need to calculate the number of possible ways of selecting 13 pulls or locations out of 36 pulls to be your cosmic pulls, this is equal to “36 choose 13”=36!/13!/23!; now for each way, the probability of the 13 pulls being cosmic is (1/6)^13, the probability of the remaining 23 pulls being non-cosmic is (5/6)^23, now the finally answer of pulling 13 cosmic out of 36 pulls is to multiply that 3 terms together, which is around 0.22%. Note that if you are referring to probability of any class (not specific of cosmic) being 13 out of 36 pull, that probability needs to multiply by 6.
  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    Hendross said:

    An approximate, simplified answer would be; the probability of pulling 13 or more cosmics from 35 crystals assuming classes were equally distributed (.166 each) and not adjusting for featured or nexus.

    The answer is ~ 0.28%, less probably than getting any 1 specific champ from the 6star basic pool (0.625% @ 160 champs)

    I actually forgot to add that about 3 of these are from the featured.
    AndyBeardo said:


    The exact odds are impossible to know because you didn't get all your 6* champs at the same time so with the addition of new 6*s the odds changed.

    Also yes, this is completely accurate. I actually forgot to think about that. Regardless, it's probably about a year ago I got my first featured, and there have probably been about 3 featured crystal cycles since then adding new champs to the basics. Notwithstanding, the odds are truly impossible to calculate because I definitely can't say for sure at what times I opened all my 6*s..
  • UnknownUnknown
    edited June 2021
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  • Kill_GreyKill_Grey Member Posts: 8,666 ★★★★★
    edited June 2021
    DNA3000 said:

    I could calculate this in closed form, but since I'm currently working on some scripting, I decided to just python 1000 trials and see what I got:

    Trials: 1000
    Successes: 24
    Success rate: 2.4 %

    That's how often a simulated opening of 36 crystals with equal chance at one of six classes generated a set where at least 13 of them were of the same class.



    Uncommon, but not extraordinarily rare. There were a few 14s in the data, so that's not super rare either.
    And this is the stuff that conspiracy theories are made of. A legitimately randomly generated result that some people would never believe was random if it happened to them.

    Wow, so this basically entails that RNG odds aren't as "simple" as a result obtainable from something like binomial distribution or Poisson distribution (well, Poisson would require an absolutely immense amount of crystals as a sample size anyways, and that's borderline impossible with 6*s of anyone's roster at this point in time we are.); But it rather seems that a simulated environment would reveal an answer closer to the truth (more or less). At least that's what I understood.

    Regardless, the odds turned out to be fairly high in the end as per this calculation. Appears that there's a multitude of summoners with a similar condition to mine in-game. I feel this weird 6* ratio is going to continue anyways considering my luck. Just gonna hope the majority gets buffed.

    Thanks to all who commented. To those with a similar situation, hopefully our pulls would even out in due time. To those who calculated, thanks for the insight. Have a great day, all.
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