Any mathematicians in the house?

Skydad23Skydad23 Member Posts: 556 ★★★
edited July 2023 in General Discussion
I would really like to know the odds this.

There are 38 science champs you can get in the science abyss nexus Crystal I have 37 of those champs I am trying to get Hulk the one Champion I do not have.

I opened eight science nexus abyss crystals
So that’s 10 different champions in each Crystal so basically 80 shots at getting him. Of course I did not get him. What are the odds of having 80 shots at some thing? And not actually getting the one single one you do not have????? I would love to know the odds of that

Comments

  • GroundedWisdomGroundedWisdom Member Posts: 36,646 ★★★★★
    @DNA3000
  • Skydad23Skydad23 Member Posts: 556 ★★★
    AverageDesi said:

    You didn't have just 80 shots. You had more than that since the pool would adjust. Although since the pool is large enough, this can be expected

    P(Not getting Hulk in 8Abyss Nexus crystals)= P(Not getting Hulk in one abyss Nexus Crystal)^8= 0.726 ^8= 0.086

    ≈ 8.6%. . Not too shabby tbh

    Are you saying I had an 8% chance to get him or not to get him?

    There are 38 science champions in the crystal you get 10 shots in each crystal that’s more than a 25% chance in each crystal and when you stack on the odds that the one I would not get is the one of the 38 I did not have having all 37 others percentage seems astronomical to not get that one?

  • PikoluPikolu Member, Guardian Posts: 8,022 Guardian
    Skydad23 said:

    AverageDesi said:

    You didn't have just 80 shots. You had more than that since the pool would adjust. Although since the pool is large enough, this can be expected

    P(Not getting Hulk in 8Abyss Nexus crystals)= P(Not getting Hulk in one abyss Nexus Crystal)^8= 0.726 ^8= 0.086

    ≈ 8.6%. . Not too shabby tbh

    Are you saying I had an 8% chance to get him or not to get him?

    There are 38 science champions in the crystal you get 10 shots in each crystal that’s more than a 25% chance in each crystal and when you stack on the odds that the one I would not get is the one of the 38 I did not have having all 37 others percentage seems astronomical to not get that one?

    You actually have a 1/38 + 1/37 + ... + 1/29 chance of getting hulk per abyss nexus which comes out to 29% chance per nexus.
  • PikoluPikolu Member, Guardian Posts: 8,022 Guardian
    edited July 2023
    MarvelNoob said:

    This is what I think (Just a highschooler).
    1/38 chance each attempt, 80 attempts.
    1/38 ≈ 2.6%. (Each attempt)
    2.6%(.0026) x 80 ≈ 2.1(210%)

    So you had a 210% chance of getting your one champ, but you didn't. Thats if every champ had an equal chance of dropping and it's an average. So this is an outlier right? Sorry I'm trying my best with this math.

    You have a 29% chance per nexus. See my previous post on how you get that. Then to find the chance of it not happening after 8 independent events, you do (1-.29)^8 which is a little more than 6%

    What you did wrong was had 1/38 over 80 attempts, when it is 1/38 over a decreasing pool size, over 8 tries.
  • TheNepperTheNepper Member Posts: 24 ★
    I am a mathematician. I did not see the correct answer yet, so:

    For 1 crystal the chance that you do not get him is: 37/38 * 36/38 * ... * 28/38 which is roughly 0.2013 (20.13% chance).

    For 8 crystals it is: 0.2013^8 = 0.000002696 (which is 0.00027%) that is extremely low chance.
  • TheNepperTheNepper Member Posts: 24 ★
    edited July 2023
    Just to point out the 29% theory is not that bad, the problem is that those odds are not independent, you would need to have used inclusion-exclusion principle if you calculate the odds of pulling him instead of the odds of not pulling him.

    See when you say 1/38 + 1/37 + ... you ignore the fact that it is impossible to pull him more times in 1 crystal (also production must be used instead of addition)
  • PikoluPikolu Member, Guardian Posts: 8,022 Guardian
    TheNepper said:

    Just to point out the 29% theory is not that bad, the problem is that those odds are not independent, you would need to have used inclusion-exclusion principle if you calculate the odds of pulling him instead of the odds of not pulling him.

    See when you say 1/38 + 1/37 + ... you ignore the fact that it is impossible to pull him more times in 1 crystal (also production must be used instead of addition)

    Fair enough, haven't taken stats in 5 years and forget some of these things 🤣
  • AverageDesiAverageDesi Member Posts: 5,260 ★★★★★
    Skydad23 said:

    AverageDesi said:

    You didn't have just 80 shots. You had more than that since the pool would adjust. Although since the pool is large enough, this can be expected

    P(Not getting Hulk in 8Abyss Nexus crystals)= P(Not getting Hulk in one abyss Nexus Crystal)^8= 0.726 ^8= 0.086

    ≈ 8.6%. . Not too shabby tbh

    Are you saying I had an 8% chance to get him or not to get him?

    There are 38 science champions in the crystal you get 10 shots in each crystal that’s more than a 25% chance in each crystal and when you stack on the odds that the one I would not get is the one of the 38 I did not have having all 37 others percentage seems astronomical to not get that one?

    You had an 8.6% chance of not getting Hulk at all
  • AverageDesiAverageDesi Member Posts: 5,260 ★★★★★
    TheNepper said:

    I am a mathematician. I did not see the correct answer yet, so:

    For 1 crystal the chance that you do not get him is: 37/38 * 36/38 * ... * 28/38 which is roughly 0.2013 (20.13% chance).

    For 8 crystals it is: 0.2013^8 = 0.000002696 (which is 0.00027%) that is extremely low chance.

    Why have you kept the denominator as 38 itself? If the numerator is decreasing, surely the denominator should too?
  • TheNepperTheNepper Member Posts: 24 ★
    edited July 2023
    AverageDesi said:


    Why have you kept the denominator as 38 itself? If the numerator is decreasing, surely the denominator should too?

    Yupp, you are totally right my bad. Also now that I think of it, my answer is totally incorrect :| (because the 'order' of the 10 does not matter)

    So to correct myself, this is how to calc it, exactly as you have said before:

    I will use the notation (n k) for n choose k (which is n! / (k! * (n-k)!) )
    - For 1 crystal the chance you don't get him is: (37 10) / (38 10) = 0.7368 (73.68%)
    - For 8 crystals it is: 0.7368^8 = 0.0869 (8.69%)

    P.S. I'll think about myself now... :pensive:
  • I_tell_no_tales_1I_tell_no_tales_1 Member Posts: 1,198 ★★★★
    Pikolu said:

    Skydad23 said:

    AverageDesi said:

    You didn't have just 80 shots. You had more than that since the pool would adjust. Although since the pool is large enough, this can be expected

    P(Not getting Hulk in 8Abyss Nexus crystals)= P(Not getting Hulk in one abyss Nexus Crystal)^8= 0.726 ^8= 0.086

    ≈ 8.6%. . Not too shabby tbh

    Are you saying I had an 8% chance to get him or not to get him?

    There are 38 science champions in the crystal you get 10 shots in each crystal that’s more than a 25% chance in each crystal and when you stack on the odds that the one I would not get is the one of the 38 I did not have having all 37 others percentage seems astronomical to not get that one?

    You actually have a 1/38 + 1/37 + ... + 1/29 chance of getting hulk per abyss nexus which comes out to 29% chance per nexus.
    That's not how it works for crystals
    Otherwise people wouldn't have had to open 30-40 crystals and then still come to forums to complain about not getting
    the champion they desire

    It's 1/38 for each crystal
    So he just had 2.6 % chance of getting hulk in each crystal
    And he will have 2.6% chance of getting hulk in each crystal even if he opens 100 abyss nexus

    But still it's quite sad that you couldn't get him
    I really love playing my r2 hulk in BGs
    But give me that 6* Juggs Kabam
  • Skydad23Skydad23 Member Posts: 556 ★★★
    I_tell_no_tales_1 said:

    Pikolu said:

    Skydad23 said:

    AverageDesi said:

    You didn't have just 80 shots. You had more than that since the pool would adjust. Although since the pool is large enough, this can be expected

    P(Not getting Hulk in 8Abyss Nexus crystals)= P(Not getting Hulk in one abyss Nexus Crystal)^8= 0.726 ^8= 0.086

    ≈ 8.6%. . Not too shabby tbh

    Are you saying I had an 8% chance to get him or not to get him?

    There are 38 science champions in the crystal you get 10 shots in each crystal that’s more than a 25% chance in each crystal and when you stack on the odds that the one I would not get is the one of the 38 I did not have having all 37 others percentage seems astronomical to not get that one?

    You actually have a 1/38 + 1/37 + ... + 1/29 chance of getting hulk per abyss nexus which comes out to 29% chance per nexus.
    That's not how it works for crystals
    Otherwise people wouldn't have had to open 30-40 crystals and then still come to forums to complain about not getting
    the champion they desire

    It's 1/38 for each crystal
    So he just had 2.6 % chance of getting hulk in each crystal
    And he will have 2.6% chance of getting hulk in each crystal even if he opens 100 abyss nexus

    But still it's quite sad that you couldn't get him
    I really love playing my r2 hulk in BGs
    But give me that 6* Juggs Kabam


    You’re forgetting the very important part that the one and 38 you’re choosing one of 10 getting a choice of 10 changes, if there is 40 of some thing and you open a box and there are 10 of that 40 in there with no duplicates and you get to pick one of the 10 that is 25% figuring this is one and 38 choosing one out of 10 the odds of each crystal is higher than 25%

  • TheNepperTheNepper Member Posts: 24 ★
    edited July 2023
    I_tell_no_tales_1 said:


    That's not how it works for crystals
    Otherwise people wouldn't have had to open 30-40 crystals and then still come to forums to complain about not getting
    the champion they desire

    It's 1/38 for each crystal
    So he just had 2.6 % chance of getting hulk in each crystal
    And he will have 2.6% chance of getting hulk in each crystal even if he opens 100 abyss nexus

    But still it's quite sad that you couldn't get him
    I really love playing my r2 hulk in BGs
    But give me that 6* Juggs Kabam

    By your logic if science class would only consist of 10 champs, you only had 1/10 chance of pulling your desired one with an abyss. :)
  • SummonerNRSummonerNR Member, Guardian Posts: 13,219 Guardian
    I_tell_no_tales_1 said:


    That's not how it works for crystals
    Otherwise people wouldn't have had to open 30-40 crystals and then still come to forums to complain about not getting
    the champion they desire

    It's 1/38 for each crystal
    So he just had 2.6 % chance of getting hulk in each crystal
    And he will have 2.6% chance of getting hulk in each crystal even if he opens 100 abyss nexus

    But still it's quite sad that you couldn't get him
    I really love playing my r2 hulk in BGs
    But give me that 6* Juggs Kabam

    You’re thinking of it as normal 1-champ crystals.
    It is a 10-CHOICE NEXUS.
    The potentials of all of the 10 choices of the Nexus (like the 3-choice Nexus's) are dependent on each other in that you will not be given the same champ for multiple of the 10 choices.

    So calculate that first (which is what the 38 and 10x calculations are first doing), and THEN proceed to do the (as you say) independent relation for the 8 of those such Nexus's.
  • SummonerNRSummonerNR Member, Guardian Posts: 13,219 Guardian
    If the consensus from prior replies is such as…
    (and just to further explain it in more understandable terms)..

    Odds of NOT getting in SLOT #1 of 10 choices of Nexus is 37/38
    And then of NOT getting in SLOT #2 is 36/37
    Etc, down to final SLOT being 28/29.

    Numerators going from 37, 36, 35 .. 28
    Denominators going from 38, 37, 36 .. 29
    Odds for Not getting for that particular Nexus boils down to (9 of the 10 numbers are same in Numer. and Denom.) 28/38.
    Which is 0.7368.. (73.68 chance of NOT getting in a single 10-choice Nexus)

    Then take that, as correctly said before, as an “8 factorial” (8 Nexus crystals).
    To become 0.0869 (8.7% chance you will NOT get him).

    Is that right ?

    ( @AverageDesi , where was your original 0.726 coming from, instead of 0.7368 above. Or just typo between switching apps doing calculations ??)
  • klobberintymeklobberintyme Member Posts: 1,641 ★★★★
    Chris_Summers said:

    Kabam rng… 0% chance of getting the one you want.

    EVER.

    She's the one that i wanted.




    Woo oo ooo, baby
  • AverageDesiAverageDesi Member Posts: 5,260 ★★★★★
    SummonerNR said:

    If the consensus from prior replies is such as…
    (and just to further explain it in more understandable terms)..

    Odds of NOT getting in SLOT #1 of 10 choices of Nexus is 37/38
    And then of NOT getting in SLOT #2 is 36/37
    Etc, down to final SLOT being 28/29.

    Numerators going from 37, 36, 35 .. 28
    Denominators going from 38, 37, 36 .. 29
    Odds for Not getting for that particular Nexus boils down to (9 of the 10 numbers are same in Numer. and Denom.) 28/38.
    Which is 0.7368.. (73.68 chance of NOT getting in a single 10-choice Nexus)

    Then take that, as correctly said before, as an “8 factorial” (8 Nexus crystals).
    To become 0.0869 (8.7% chance you will NOT get him).

    Is that right ?

    ( AverageDesi , where was your original 0.726 coming from, instead of 0.7368 above. Or just typo between switching apps doing calculations ??)

    Yeah typo
  • ChiliDogChiliDog Member Posts: 904 ★★★
    It's 0%, the game knows!!!....I kept yelling at it scorpion every time I rolled a 6* crystal or especially many science selectors. It's like when you talk about needing something and all of a sudden it pops up everywhere in your ads, even though you never searched on it....but in this case the opposite.

    It seems like 0%, but it isn't.

    I've been saving for the 2022 selector july 4th deal and bingo, crazy 100%!!!
  • UnknownUnknown
    This content has been removed.
  • DNA3000DNA3000 Member, Guardian Posts: 19,856 Guardian
    Pikolu said:

    Skydad23 said:

    AverageDesi said:

    You didn't have just 80 shots. You had more than that since the pool would adjust. Although since the pool is large enough, this can be expected

    P(Not getting Hulk in 8Abyss Nexus crystals)= P(Not getting Hulk in one abyss Nexus Crystal)^8= 0.726 ^8= 0.086

    ≈ 8.6%. . Not too shabby tbh

    Are you saying I had an 8% chance to get him or not to get him?

    There are 38 science champions in the crystal you get 10 shots in each crystal that’s more than a 25% chance in each crystal and when you stack on the odds that the one I would not get is the one of the 38 I did not have having all 37 others percentage seems astronomical to not get that one?

    You actually have a 1/38 + 1/37 + ... + 1/29 chance of getting hulk per abyss nexus which comes out to 29% chance per nexus.
    That's actually not correct. I get where you are going with this calculation but this is not the right way to account for not drawing duplicates, because you're ironically failing to account for the actual target draw duplicating, you're accounting for each non-target draw not duplicating only (as @TheNepper points out).

    This one is pretty simple. You get ten draws out of a pool of thirty eight. Each draw is unique (not duplicate) which means the crystal contains ten out of thirty eight of the possibilities. Therefore, the odds of the target being in the crystal is 10/38 ~= 26%, the odds of the target not being in the pool is 28/38 ~= 74%.

    The odds of missing the target after eight Nexus crystals is thus (28/38)^8 ~= 8.7%. The odds of landing the target after eight Nexus crystals is 91.3%. Alternatively, the odds of missing the target after eight Nexus crystals is about one in 11.5. If twenty three players do this, you'd expect on average two of them to miss with all eight Nexus crystals.

    This reproduces @AverageDesi 's calculations, except for the small typo (0.736, not 0.726), and @SummonerNR 's calculations except the per Nexus calculation is more straight forward.

    This is uncommon, but not extremely rare. In an alliance of thirty people, you'd expect to see two or three players suffer this fate.
  • JMORG1111JMORG1111 Member Posts: 184 ★★
    It's plausible. I had the same luck chasing Cosmic Ghost Rider for YEARS. Then, I stopped playing alliance wars, dropped out of an alliance and only played sparingly. Pulled him from a daily crystal. The game is funny like that.
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