Has this happened to anyone?

2

Comments

  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    edited February 2018
    If you understand what I was talking about in the first place, why are you arguing it? I was talking about the odds of each individual outcome, and they're not affected by the others because each Crystal is a separate outcome. Regardless of statistical calculations, each outcome is generated individually. If someone wants to elaborate and make it much more complex, that's entirely up them. The main point is, if you have 10 Crystals at 0.02%, that's what you have.
    This is becoming an off-topic discussion about statistics and I'm really not interested in continuing it. Some believe there is a mathematical explanation for everything. Some believe it's a question of chance. Some are in the middle. I don't go to any extreme in my line of thinking.
  • There is somebody on the team (who you might occasionally see in the Forums) that pulled Black Panther (the original) from a 4-Star Crystal 7 times in a row. It's statistically very uncommon, but it can happen!

    This is a story that gets told around the office a lot and gets bigger each time. It was actually the first 9 4-stars I acquired out of 24 were Black Panther. Not 7 in a row, but I did have some consecutive BPs. At the time we checked and I was one of the fastest (top 10) to a max sig 4-Star based on number of 4-Stars to achieve it.

    Notes:

    * This was before Black Panther was buffed. (Increased bleed stuff)
    * You couldn't link a special 2 out of his medium or light attack because of the start up animation (later fixed)
    * This was before Deep Wounds mastery existed.
    * You can tell by my avatar who I really wanted as a 4-star.
    * I still don't have a 4-Star or 5-Star Iron Man T_T
    * I still work here.


    Well then, shame on Miike for bringing back a bad memory ;)
    But more importantly that confirms that there were definitely a lot less champs in the crystal at the time then.
  • My first 7 5 star pulls we’re HE, Ronan, MK, SL, MK, Ronan, HE. It was a palindrome of 5 star pulls, still waiting on that SL dupe though
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    edited February 2018
    Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    You are wrong. The chance to pull a specific champ out of 60 is 1.7% yes, but the chance to pull the same champion 7 times in a row is not 1.7%. Which is what is being discussed currently, consecutive pulls of the same champion. This is elementary to middle school level math.

    EDIT: Should never trust your math either, 1/60 is 1.66% not .02%
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    edited February 2018
    Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    You are wrong. The chance to pull a specific champ out of 60 is .02% yes, but the chance to pull the same champion 7 times in a row is not .02%. Which is what is being discussed currently, consecutive pulls of the same champion. This is elementary to middle school level math.

    The Crystal on the server doesn't understand that. It just generates a random outcome based on the selections. Which means every Crystal you open has an equal chance of being any Champ.
  • Primmer79Primmer79 Posts: 2,739 Guardian
    edited February 2018
    Edit: not worth it
  • Speeds80Speeds80 Posts: 1,158 ★★★
    So ignoring the theory which I put about the algorithm, which I don’t really care about just mentioning it as it had been brought up in forums and I thought was very interesting (sorry DNA I can’t find the original convos but it’s popped up 2 or 3 times and it’s a support ticket reply where someone was querying this exact occurrence and the support staff said that (summarised) The algorithm for determining champs is very complicated and that part of it had been designed to make duping a champion more common as duped champs are usually sought after and that it had been designed with the player in mind)

    Gw. Do you just not acknowledge simple odds statistics? Or are unaware of them, for round figures the odds of pulling a said champ are closer to .001 (there are closer to 100 champs than 50 available) h3rzyxnrhi6g.png
    So the odds of pulling any champ back to back are 1/100 or, the odds of 3 in a row are 1/100 x 1/100 or 0.01 x 0.01... 0.0001
    The odds of 4 in a row, (yes this is literally statistics maths which I studied in school) are 0.01 x 0.01 x 0.01 0.000001 and so on. I would definitely suggest 6 in a row maybe a bug in the algorithm as it’s odds are 0.0000000001 if using the rounded 100 champ figure (several of the 112 champs aren’t in the basic crystal)
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    You are wrong. The chance to pull a specific champ out of 60 is .02% yes, but the chance to pull the same champion 7 times in a row is not .02%. Which is what is being discussed currently, consecutive pulls of the same champion. This is elementary to middle school level math.

    The Crystal on the server doesn't understand that. It just generates a random outcome based on the selections. Which means every Crystal you open has an equal chance of being any Champ.

    A coin doesn't understand how many times it's going to get flipped either. It just knows it has a 50% chance to land on heads or tails. The chance to flip a coin and land heads 10 times in a row is not 50% though.
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.
  • 420sam420sam Posts: 526 ★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Neither does statistics, lol. That is why they are saying that the probability of it happening is ridiculously low. Give it up man! You were right, but now you are very wrong.
  • SnaggleSnaggle Posts: 226
    There is somebody on the team (who you might occasionally see in the Forums) that pulled Black Panther (the original) from a 4-Star Crystal 7 times in a row. It's statistically very uncommon, but it can happen!

    "Statistically very uncommon"
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.
  • Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    You are wrong. The chance to pull a specific champ out of 60 is .02% yes, but the chance to pull the same champion 7 times in a row is not .02%. Which is what is being discussed currently, consecutive pulls of the same champion. This is elementary to middle school level math.

    The Crystal on the server doesn't understand that. It just generates a random outcome based on the selections. Which means every Crystal you open has an equal chance of being any Champ.

    Jesus. You don't understand statistics. Yes you are correct that each time the chance is the same. But because of odds and rng the chance of pulling the same champ multiple times in a row is much less.

    If the chance for me to pull X is set at a hypothetical .1%
    The chance for me to pull X 10 times in a row is not .1%
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.

    I was making a point but it was stretched to hell over a conversation on Probability.
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.

    I was making a point but it was stretched to hell over a conversation on Probability.

    That's because the topic of this thread is probability.
    This is the weirdest thing that happened to me:
    A week ago, I opened a 4 star crystal and got a Daredevil Classic
    A few days ago, I opened another 4 star crystal and duped my Daredevil Classic
    Today, I opened another 4 star crystal and got ANOTHER Daredevil classic!!!
    Has anything like this ever happened to you?

    The OP is not talking about pulling a 4-star daredevil classic once. He is talking about how weird it was to pull a 2nd and 3rd daredevil classic consecutively, which is a question of probability.
  • There is somebody on the team (who you might occasionally see in the Forums) that pulled Black Panther (the original) from a 4-Star Crystal 7 times in a row. It's statistically very uncommon, but it can happen!

    This is a story that gets told around the office a lot and gets bigger each time. It was actually the first 9 4-stars I acquired out of 24 were Black Panther. Not 7 in a row, but I did have some consecutive BPs. At the time we checked and I was one of the fastest (top 10) to a max sig 4-Star based on number of 4-Stars to achieve it.

    Notes:

    * This was before Black Panther was buffed. (Increased bleed stuff)
    * You couldn't link a special 2 out of his medium or light attack because of the start up animation (later fixed)
    * This was before Deep Wounds mastery existed.
    * You can tell by my avatar who I really wanted as a 4-star.
    * I still don't have a 4-Star or 5-Star Iron Man T_T
    * I still work here.


    I am glad you corrected this. Your corrected account sounds far more plausible then Miike saying 7 times in a row can happen and did happen (the odds are just too far out there for this to be considered likely to have happened at all).

    That being said I really hope you get an Iron Man soon... cannot believe you have no gotten one yet after all this time!
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.

    I was making a point but it was stretched to hell over a conversation on Probability.

    That's because the topic of this thread is probability.
    This is the weirdest thing that happened to me:
    A week ago, I opened a 4 star crystal and got a Daredevil Classic
    A few days ago, I opened another 4 star crystal and duped my Daredevil Classic
    Today, I opened another 4 star crystal and got ANOTHER Daredevil classic!!!
    Has anything like this ever happened to you?

    The OP is not talking about pulling a 4-star daredevil classic once. He is talking about how weird it was to pull a 2nd and 3rd daredevil classic consecutively, which is a question of probability.

    Actually. all the OP asked was if it's happened to anyone. I don't even care at this point. It's rare but it happens.
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    Speeds80 wrote: »
    So ignoring the theory which I put about the algorithm, which I don’t really care about just mentioning it as it had been brought up in forums and I thought was very interesting (sorry DNA I can’t find the original convos but it’s popped up 2 or 3 times and it’s a support ticket reply where someone was querying this exact occurrence and the support staff said that (summarised) The algorithm for determining champs is very complicated and that part of it had been designed to make duping a champion more common as duped champs are usually sought after and that it had been designed with the player in mind)

    Gw. Do you just not acknowledge simple odds statistics? Or are unaware of them, for round figures the odds of pulling a said champ are closer to .001 (there are closer to 100 champs than 50 available) h3rzyxnrhi6g.png
    So the odds of pulling any champ back to back are 1/100 or, the odds of 3 in a row are 1/100 x 1/100 or 0.01 x 0.01... 0.0001
    The odds of 4 in a row, (yes this is literally statistics maths which I studied in school) are 0.01 x 0.01 x 0.01 0.000001 and so on. I would definitely suggest 6 in a row maybe a bug in the algorithm as it’s odds are 0.0000000001 if using the rounded 100 champ figure (several of the 112 champs aren’t in the basic crystal)

    I've already talked about the Support Ticket. Responses from Support aren't always the best. They tend to be generic and sometimes misinformed. That's not exclusive to this company. It's an issue that happens with Support in general.
    I would be surprised to see Support have access to the information on the algorithms altogether. That's not generally information that Support has access to. What you have is a generic response, which is not uncommon.
    I'm not getting into the Probability anymore.
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.

    I was making a point but it was stretched to hell over a conversation on Probability.

    That's because the topic of this thread is probability.
    This is the weirdest thing that happened to me:
    A week ago, I opened a 4 star crystal and got a Daredevil Classic
    A few days ago, I opened another 4 star crystal and duped my Daredevil Classic
    Today, I opened another 4 star crystal and got ANOTHER Daredevil classic!!!
    Has anything like this ever happened to you?

    The OP is not talking about pulling a 4-star daredevil classic once. He is talking about how weird it was to pull a 2nd and 3rd daredevil classic consecutively, which is a question of probability.

    Actually. all the OP asked was if it's happened to anyone. I don't even care at this point. It's rare but it happens.

    You are right it is rare but happens. I don't know how many champions are in the 4-star exactly but let's say 90. It's about a (1/90) X (1/90) = ~.012% chance to happen.
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.

    I was making a point but it was stretched to hell over a conversation on Probability.

    That's because the topic of this thread is probability.
    This is the weirdest thing that happened to me:
    A week ago, I opened a 4 star crystal and got a Daredevil Classic
    A few days ago, I opened another 4 star crystal and duped my Daredevil Classic
    Today, I opened another 4 star crystal and got ANOTHER Daredevil classic!!!
    Has anything like this ever happened to you?

    The OP is not talking about pulling a 4-star daredevil classic once. He is talking about how weird it was to pull a 2nd and 3rd daredevil classic consecutively, which is a question of probability.

    Actually. all the OP asked was if it's happened to anyone. I don't even care at this point. It's rare but it happens.

    You are right it is rare but happens. I don't know how many champions are in the 4-star exactly but let's say 90. It's about a (1/90) X (1/90) = ~.012% chance to happen.

    I wouldn't argue with that theoretically, but with a random outcome, anything can happen. Lol. It's not the Math I'm questioning. ;)
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    We're talking about two different subjects. Can you calculate the probability of something occurring using Mathematics? Yes. You're correct. The point I'm making is the pool doesn't have independent capacity and doesn't operate that way when we're talking about equal chance at any Champ. It doesn't take into account previously generated outcomes. Each one generated is literally the result of a random generated outcome of the possibilities.

    Me and everyone else talking about statistics are on the same page. I think you're the only one on your own subject.

    I was making a point but it was stretched to hell over a conversation on Probability.

    That's because the topic of this thread is probability.
    This is the weirdest thing that happened to me:
    A week ago, I opened a 4 star crystal and got a Daredevil Classic
    A few days ago, I opened another 4 star crystal and duped my Daredevil Classic
    Today, I opened another 4 star crystal and got ANOTHER Daredevil classic!!!
    Has anything like this ever happened to you?

    The OP is not talking about pulling a 4-star daredevil classic once. He is talking about how weird it was to pull a 2nd and 3rd daredevil classic consecutively, which is a question of probability.

    Actually. all the OP asked was if it's happened to anyone. I don't even care at this point. It's rare but it happens.

    You are right it is rare but happens. I don't know how many champions are in the 4-star exactly but let's say 90. It's about a (1/90) X (1/90) = ~.012% chance to happen.

    I wouldn't argue with that theoretically, but with a random outcome, anything can happen. Lol. It's not the Math I'm questioning. ;)

    Yeah the math says it can happen at a .012% chance. Glad we're on the same page now.
  • I got 2 falcon in a row from 4 star crystal who was already awakened
  • Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    Nobody is saying it is. The odds of each opening being a certain thing is not (or should not be) affected by the previous events. So if someone pulled Black Panther seven times in a row and that has already happened, the odds of pulling Black Panther again are the same for that player as any other: one in however many champs are in the crystal.

    But the odds of pulling a sequence of seven pulls in a row are in fact multiplicative: that's a fundamental principle of statistics. If there were, say, 60 champs in the crystal, the odds of pulling Black Panther seven times in a row would be (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) ~= 0.000000000000357. That's one in 2,799,360,000,000. The odds of that specific event happening in the entire history of the game are very small.

    But statistics has many pitfalls. The odds of *any* sequence of seven openings has the exact same odds. In other words, the odds of pulling Black Panther, followed by Captain America, followed by Storm, then Luke Cage, then Star Lord, then Magik, then Storm again, are also one in about 2.8 trillion. If *every* sequence is equally rare, why is the seven BPs in a row considered more unlikely? Its because the previous sequence is not noteworthy. No one notices that one happening, and there are billions of combinations that are all different, but look equally uninteresting to the players. They don't notice those "rare" events. What makes 7 x BP interesting is that it is seven identical champs in a row. You have to ask whether the noteworthy thing that happened was seven BPs in a row or seven *identical* champs in a row.

    The odds of seven *anything* in a row is lower: it is basically (1/60)^6 instead of (1/60)^7, because the first one can be anything. Those odds become one in 46,656,000,000, or one in about 47 billion. That's still very rare, but not as rare.

    To determine if this is a statistical anomaly, we have to do at least one more step. One out of 47 billion sounds unlikely, but that depends on how many pulls have happened. Again: most sequence of pulls aren't reported because they aren't interesting. We are much more likely to hear about the interesting ones. If one person tries this and gets seven in a row, that's amazing. But if a million players are constantly opening crystals, what are the odds that *someone* gets lucky? That requires some estimates. If we assume that at least 500k players have opened at least seven 4* crystals, and on average the players that did have opened at least a hundred 4* crystals, then across the entire game the odds of seven pulls in a row happening at least once becomes a lot higher than one in 47 billion. Without doing the closed form math, it is probably approximately one in a thousand.

    That's not astronomically low, but it is unusual. And in fact, there are a lot of unusual events that happen when looking at crystal openings that aren't definitive on their own, but suggest the random openings are not completely random. They are *not* biased towards or away from individual rewards, but they seem to be more internally correlated than I would expect.

    For the mathematically educated: I believe there is a hint of evidence of a lower level of entropy in the random number sequences than you'd expect when analyzing n-way correlations. Not specifically in this example, but across a lot of other data.
  • GroundedWisdomGroundedWisdom Posts: 19,226 ★★★★★
    DNA3000 wrote: »
    Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    Nobody is saying it is. The odds of each opening being a certain thing is not (or should not be) affected by the previous events. So if someone pulled Black Panther seven times in a row and that has already happened, the odds of pulling Black Panther again are the same for that player as any other: one in however many champs are in the crystal.

    But the odds of pulling a sequence of seven pulls in a row are in fact multiplicative: that's a fundamental principle of statistics. If there were, say, 60 champs in the crystal, the odds of pulling Black Panther seven times in a row would be (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) ~= 0.000000000000357. That's one in 2,799,360,000,000. The odds of that specific event happening in the entire history of the game are very small.

    But statistics has many pitfalls. The odds of *any* sequence of seven openings has the exact same odds. In other words, the odds of pulling Black Panther, followed by Captain America, followed by Storm, then Luke Cage, then Star Lord, then Magik, then Storm again, are also one in about 2.8 trillion. If *every* sequence is equally rare, why is the seven BPs in a row considered more unlikely? Its because the previous sequence is not noteworthy. No one notices that one happening, and there are billions of combinations that are all different, but look equally uninteresting to the players. They don't notice those "rare" events. What makes 7 x BP interesting is that it is seven identical champs in a row. You have to ask whether the noteworthy thing that happened was seven BPs in a row or seven *identical* champs in a row.

    The odds of seven *anything* in a row is lower: it is basically (1/60)^6 instead of (1/60)^7, because the first one can be anything. Those odds become one in 46,656,000,000, or one in about 47 billion. That's still very rare, but not as rare.

    To determine if this is a statistical anomaly, we have to do at least one more step. One out of 47 billion sounds unlikely, but that depends on how many pulls have happened. Again: most sequence of pulls aren't reported because they aren't interesting. We are much more likely to hear about the interesting ones. If one person tries this and gets seven in a row, that's amazing. But if a million players are constantly opening crystals, what are the odds that *someone* gets lucky? That requires some estimates. If we assume that at least 500k players have opened at least seven 4* crystals, and on average the players that did have opened at least a hundred 4* crystals, then across the entire game the odds of seven pulls in a row happening at least once becomes a lot higher than one in 47 billion. Without doing the closed form math, it is probably approximately one in a thousand.

    That's not astronomically low, but it is unusual. And in fact, there are a lot of unusual events that happen when looking at crystal openings that aren't definitive on their own, but suggest the random openings are not completely random. They are *not* biased towards or away from individual rewards, but they seem to be more internally correlated than I would expect.

    For the mathematically educated: I believe there is a hint of evidence of a lower level of entropy in the random number sequences than you'd expect when analyzing n-way correlations. Not specifically in this example, but across a lot of other data.

    I hear what you're saying.
  • HulksmasshhHulksmasshh Posts: 742 ★★★
    DNA3000 wrote: »
    Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    Nobody is saying it is. The odds of each opening being a certain thing is not (or should not be) affected by the previous events. So if someone pulled Black Panther seven times in a row and that has already happened, the odds of pulling Black Panther again are the same for that player as any other: one in however many champs are in the crystal.

    But the odds of pulling a sequence of seven pulls in a row are in fact multiplicative: that's a fundamental principle of statistics. If there were, say, 60 champs in the crystal, the odds of pulling Black Panther seven times in a row would be (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) ~= 0.000000000000357. That's one in 2,799,360,000,000. The odds of that specific event happening in the entire history of the game are very small.

    But statistics has many pitfalls. The odds of *any* sequence of seven openings has the exact same odds. In other words, the odds of pulling Black Panther, followed by Captain America, followed by Storm, then Luke Cage, then Star Lord, then Magik, then Storm again, are also one in about 2.8 trillion. If *every* sequence is equally rare, why is the seven BPs in a row considered more unlikely? Its because the previous sequence is not noteworthy. No one notices that one happening, and there are billions of combinations that are all different, but look equally uninteresting to the players. They don't notice those "rare" events. What makes 7 x BP interesting is that it is seven identical champs in a row. You have to ask whether the noteworthy thing that happened was seven BPs in a row or seven *identical* champs in a row.

    The odds of seven *anything* in a row is lower: it is basically (1/60)^6 instead of (1/60)^7, because the first one can be anything. Those odds become one in 46,656,000,000, or one in about 47 billion. That's still very rare, but not as rare.

    To determine if this is a statistical anomaly, we have to do at least one more step. One out of 47 billion sounds unlikely, but that depends on how many pulls have happened. Again: most sequence of pulls aren't reported because they aren't interesting. We are much more likely to hear about the interesting ones. If one person tries this and gets seven in a row, that's amazing. But if a million players are constantly opening crystals, what are the odds that *someone* gets lucky? That requires some estimates. If we assume that at least 500k players have opened at least seven 4* crystals, and on average the players that did have opened at least a hundred 4* crystals, then across the entire game the odds of seven pulls in a row happening at least once becomes a lot higher than one in 47 billion. Without doing the closed form math, it is probably approximately one in a thousand.

    That's not astronomically low, but it is unusual. And in fact, there are a lot of unusual events that happen when looking at crystal openings that aren't definitive on their own, but suggest the random openings are not completely random. They are *not* biased towards or away from individual rewards, but they seem to be more internally correlated than I would expect.

    For the mathematically educated: I believe there is a hint of evidence of a lower level of entropy in the random number sequences than you'd expect when analyzing n-way correlations. Not specifically in this example, but across a lot of other data.

    I hear what you're saying.

    Congrats you've been educated.
  • DaywalkerUKDaywalkerUK Posts: 98
    DNA3000 wrote: »
    Actually, that's not how the odds work. It's not additive or multiplicative. Let's say, if there are 60 Champs in the Crystal, you have a 1/60 chance of getting one specific Champ (0.02%). It's the same chance every Crystal you open. Each Crystal is a separate generated outcome. It's not increased or decreased by what you draw previously.

    Nobody is saying it is. The odds of each opening being a certain thing is not (or should not be) affected by the previous events. So if someone pulled Black Panther seven times in a row and that has already happened, the odds of pulling Black Panther again are the same for that player as any other: one in however many champs are in the crystal.

    But the odds of pulling a sequence of seven pulls in a row are in fact multiplicative: that's a fundamental principle of statistics. If there were, say, 60 champs in the crystal, the odds of pulling Black Panther seven times in a row would be (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) * (1/60) ~= 0.000000000000357. That's one in 2,799,360,000,000. The odds of that specific event happening in the entire history of the game are very small.

    But statistics has many pitfalls. The odds of *any* sequence of seven openings has the exact same odds. In other words, the odds of pulling Black Panther, followed by Captain America, followed by Storm, then Luke Cage, then Star Lord, then Magik, then Storm again, are also one in about 2.8 trillion. If *every* sequence is equally rare, why is the seven BPs in a row considered more unlikely? Its because the previous sequence is not noteworthy. No one notices that one happening, and there are billions of combinations that are all different, but look equally uninteresting to the players. They don't notice those "rare" events. What makes 7 x BP interesting is that it is seven identical champs in a row. You have to ask whether the noteworthy thing that happened was seven BPs in a row or seven *identical* champs in a row.

    The odds of seven *anything* in a row is lower: it is basically (1/60)^6 instead of (1/60)^7, because the first one can be anything. Those odds become one in 46,656,000,000, or one in about 47 billion. That's still very rare, but not as rare.

    To determine if this is a statistical anomaly, we have to do at least one more step. One out of 47 billion sounds unlikely, but that depends on how many pulls have happened. Again: most sequence of pulls aren't reported because they aren't interesting. We are much more likely to hear about the interesting ones. If one person tries this and gets seven in a row, that's amazing. But if a million players are constantly opening crystals, what are the odds that *someone* gets lucky? That requires some estimates. If we assume that at least 500k players have opened at least seven 4* crystals, and on average the players that did have opened at least a hundred 4* crystals, then across the entire game the odds of seven pulls in a row happening at least once becomes a lot higher than one in 47 billion. Without doing the closed form math, it is probably approximately one in a thousand.

    That's not astronomically low, but it is unusual. And in fact, there are a lot of unusual events that happen when looking at crystal openings that aren't definitive on their own, but suggest the random openings are not completely random. They are *not* biased towards or away from individual rewards, but they seem to be more internally correlated than I would expect.

    For the mathematically educated: I believe there is a hint of evidence of a lower level of entropy in the random number sequences than you'd expect when analyzing n-way correlations. Not specifically in this example, but across a lot of other data.

    I hear what you're saying.

    Congrats you've been educated.

    Unlikely
  • TheHoodedDormammuTheHoodedDormammu Posts: 677
    This is the weirdest thing that happened to me:
    A week ago, I opened a 4 star crystal and got a Daredevil Classic
    A few days ago, I opened another 4 star crystal and duped my Daredevil Classic
    Today, I opened another 4 star crystal and got ANOTHER Daredevil classic!!!
    Has anything like this ever happened to you?

    and... i just opened a another 4 star crystal and guess who i got?


    another Daredevil Classic.
    Thats 4 in a row
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