It's the difference between flipping a coin and coming up heads twice. Each individual flip is a 50/50 chance. How many times can you keep betting on heads without losing. Would you you bet $100 that you could flip a coin on heads 10 times in row if I gave you 10:1 odds.

You have it mixed up. It's more like:

I throw a coin and it lands on heads. Now, would you bet any amount of money on that it will not land on heads again? The cumulative odds are in your favor after all.

That's not what is being discussed. If you open a crystal and get Spider-Gwen, the odds of pulling Spider-Gwen again are the same as pulling Spider-Gwen at all: about one in 150 or so. But the odds of pulling SG twice in a row are not the same thing as the odds of pulling her a second time *after* you pull her once.

In one sense, probability is a measure of uncertainty. If you have two crystals, before you open either of them they could be anything. The odds of the first one being SG are one in a 150, and the odds of the second one being SG are also one in 150. But the moment you open the first one and see it is SG, the odds of that crystal being SG are now 100% and the odds of it being anything else is zero. The odds of getting two SGs in a row have risen from one in 22500 to one in 150.

Probability is not retroactive. The odds of history happening after it has happened is 100%, and the odds of anything else happening is zero.

If this is what you mean by "cumulative odds" then that's your point of confusion. Probability calculations do not combine the odds of the future happening and the odds of the past happening. Once the past happens, those odds no longer affect probability calculations.

Here's a situation that is sometimes used to explain what probability actually is. Suppose you're playing blackjack against the dealer. The dealer shows Ace. What are the odds that the down card is a ten? This is something you can calculate in your head. Except the dealer is required to look at that card when showing Ace. To him, there are no odds. He knows whether it is a ten or not. Does that mean you can't calculate the odds of it being a ten, because that card is not unknown anymore? No: whether the dealer sees the card or not only matters to him. It doesn't matter to you, because you don't have that information. There is still a calculable probability of that card being a ten, even though technically speaking the value of that card isn't "unknown." It is known. Just not by you. Relative to you, it will still be the case that a certain number of times when you are in this situation that card will be a ten, and at all other times it won't be, and that's what statistics calculates.

Before the dealer peeked, he would have calculated the same odds as you. But once he peeks, those odds disappear for him. The card no longer has a chance of being a ten: it either is or isn't. But only for him.

In this case, I would say the odds of pulling a 6* Cable would be greater since the pool is smaller, but both outcomes are independent. It's not as if the computer takes into account that you just pulled him.

The odds of having to revisit this explanation again within the next 90 days are almost definitely 100%.

The first time I explained this situation in the context of a game, I was doing it on Fidonet. I'm pretty sure I've done it over a hundred times on USENET. I did it so many times on a couple game forums it was enshrined as an official FAQ once. Statistical calculations are probably the single most misunderstood game mechanical subject in all of gaming.

Which is weird because I always thought probability and statistics was a required math subject for anyone who has graduated high school much less undergraduate college. Either you had to take it, or you had to take more sophisticated math that presumes it. I don't expect people to have command of the more sophisticated stuff, but I would think most people would at least be able to recognize it again when it is presented.

I recall a section in a stat course about leading people to mathematically incorrect conclusions with seemingly logical statistical gibberish and/or playing on their incorrect assumptions and feelings to get a desired response.

I know intellectually that the pulls are random and 1 champ is as likely as another, but if someone offered me money for getting multiple Vision or Magneto in my next PHC pops, I’m immediately thinking about what I’m going to buy. It’s human nature to feel like events are definitely not isolated and as random as they can possibly be and there are a host of influences on outcomes even one as passive as “I’m the observer, and I’m me, so maybe I’ll beat the odds.”

The odds of having to revisit this explanation again within the next 90 days are almost definitely 100%.

The first time I explained this situation in the context of a game, I was doing it on Fidonet. I'm pretty sure I've done it over a hundred times on USENET. I did it so many times on a couple game forums it was enshrined as an official FAQ once. Statistical calculations are probably the single most misunderstood game mechanical subject in all of gaming.

Which is weird because I always thought probability and statistics was a required math subject for anyone who has graduated high school much less undergraduate college. Either you had to take it, or you had to take more sophisticated math that presumes it. I don't expect people to have command of the more sophisticated stuff, but I would think most people would at least be able to recognize it again when it is presented.

I recall a section in a stat course about leading people to mathematically incorrect conclusions with seemingly logical statistical gibberish and/or playing on their incorrect assumptions and feelings to get a desired response.

I know intellectually that the pulls are random and 1 champ is as likely as another, but if someone offered me money for getting multiple Vision or Magneto in my next PHC pops, I’m immediately thinking about what I’m going to buy. It’s human nature to feel like events are definitely not isolated and as random as they can possibly be and there are a host of influences on outcomes even one as passive as “I’m the observer, and I’m me, so maybe I’ll beat the odds.”

That's true, and I'll go even further. People misunderstand or misuse statistics all the time, and people get the wrong answers when they try to calculate things all the time. But that should be completely irrelevant to the question "what are the odds of pulling the same champion twice in two successive crystals." And more important, it should not have any bearing on whether to calculate and deliver the right answer.

There are many game developers and game studios that believe players shouldn't be given all the information about how the games they make work. They think if you tell players the numbers, they will stop focusing on playing the game and start focusing on the numbers, on numerical theorycraft, probably do it wrong, and end up misleading other players into all sorts of bad directions. Better to let everyone just figure everything out themselves.

And to an extent they are correct. Players do in fact do that. But does that validate the decision? Should game developers inform their players about what's going on in the games they play, or should they deliberately keep them in the dark for their own good? That's really the overarching question here. If anyone thinks that the OP's question is somehow subjective or doesn't have a clear cut answer, they are just wrong, period, the end. But if the real issue is whether they should be given the correct answer because they might not interpret the correct answer correctly, then you have to ask yourself if you're going to be someone that counters ignorance with education, or counters ignorance with more ignorance. I don't think there should be any question which side I've chosen.

Because if we're not going to tell players what the odds associated with crystal openings are, because we don't think everyone will use the answers in the right way, why tell them how the Parry mastery works, or how regeneration works, or what prestige is. People misunderstand or abuse that information all the time as well.

It is honestly weird to me, possibly because I'm simply too familiar with the math. When someone asks how to calculate prestige, we just tell them to add the correct numbers up. We don't tell them that prestige is just an abstract concept that doesn't really exist in the real world and don't worry about it because you'll just do something wrong with the information anyway. We don't tell them that while we can say what the prestige of a single champion is, we can't really say what the "cumulative prestige" of an account is.

But that is literally what I'm hearing in this thread. To me, calculating prestige and calculating crystal odds are both trivial calculation problems with no controversy inherent to the actual calculations, even though the topics themselves contain some controversy. That shouldn't, and doesn't impact the calculations themselves.

To simplify, probability = number of desired outcome / number of total possibilities

Assuming 150 possible champs, total possible outcomes for 2 successive pulls = 150 * 150= 22500.

Out of the 22500 possible outcomes, only 1 would be for a “specific” champ. Example is only 1 outcome would be for pulling Cable twice. So probability here is 1/22500.

But pulling any champ twice, number of desired outcome is 150 ( Cable-Cable, Antman-Antman, CapIW-CapIW, ...) so probability here is 150/22500 = 1/150

i opened 5 , 6 stars in last 2 months. They were electro electro yj red skull red skull. Now tell me what are the odds to happen this? Just suck it up and keep playing without getting emotionally drained. That's what i learned.

The odds of having to revisit this explanation again within the next 90 days are almost definitely 100%.

The first time I explained this situation in the context of a game, I was doing it on Fidonet. I'm pretty sure I've done it over a hundred times on USENET. I did it so many times on a couple game forums it was enshrined as an official FAQ once. Statistical calculations are probably the single most misunderstood game mechanical subject in all of gaming.

Which is weird because I always thought probability and statistics was a required math subject for anyone who has graduated high school much less undergraduate college. Either you had to take it, or you had to take more sophisticated math that presumes it. I don't expect people to have command of the more sophisticated stuff, but I would think most people would at least be able to recognize it again when it is presented.

Don't know what the odds are (looks like there are some serious math wiz's here to answer that), but it happens to me all the time. Pulled 5* GG last year 4 times in a row, pulled 2 Medusa's at the same time, Pulled three 4* and two 5* TM's within a week, Pulled then duped and then maxed 4* blue Cyclops in a 2 week time span (all while he was in the 4* featured arena lol). Pulled 4* Thor rags and Dr Voodoo side by side 3 times in a month, all 3 times pulling those 2 champions together, I could go on and on lol.

## Comments

18,799GuardianIn one sense, probability is a measure of uncertainty. If you have two crystals, before you open either of them they could be anything. The odds of the first one being SG are one in a 150, and the odds of the second one being SG are also one in 150. But the moment you open the first one and see it is SG, the odds of that crystal being SG are now 100% and the odds of it being anything else is zero. The odds of getting two SGs in a row have risen from one in 22500 to one in 150.

Probability is not retroactive. The odds of history happening after it has happened is 100%, and the odds of anything else happening is zero.

If this is what you mean by "cumulative odds" then that's your point of confusion. Probability calculations do not combine the odds of the future happening and the odds of the past happening. Once the past happens, those odds no longer affect probability calculations.

Here's a situation that is sometimes used to explain what probability actually is. Suppose you're playing blackjack against the dealer. The dealer shows Ace. What are the odds that the down card is a ten? This is something you can calculate in your head. Except the dealer is required to look at that card when showing Ace. To him, there are no odds. He knows whether it is a ten or not. Does that mean you can't calculate the odds of it being a ten, because that card is not unknown anymore? No: whether the dealer sees the card or not only matters to him. It doesn't matter to you, because you don't have that information. There is still a calculable probability of that card being a ten, even though technically speaking the value of that card isn't "unknown." It is known. Just not by you. Relative to you, it will still be the case that a certain number of times when you are in this situation that card will be a ten, and at all other times it won't be, and that's what statistics calculates.

Before the dealer peeked, he would have calculated the same odds as you. But once he peeks, those odds disappear for him. The card no longer has a chance of being a ten: it either is or isn't. But only for him.

5,017★★★★★36,298★★★★★2,320★★★★★I know intellectually that the pulls are random and 1 champ is as likely as another, but if someone offered me money for getting multiple Vision or Magneto in my next PHC pops, I’m immediately thinking about what I’m going to buy. It’s human nature to feel like events are definitely not isolated and as random as they can possibly be and there are a host of influences on outcomes even one as passive as “I’m the observer, and I’m me, so maybe I’ll beat the odds.”

18,799GuardianThere are many game developers and game studios that believe players shouldn't be given all the information about how the games they make work. They think if you tell players the numbers, they will stop focusing on playing the game and start focusing on the numbers, on numerical theorycraft, probably do it wrong, and end up misleading other players into all sorts of bad directions. Better to let everyone just figure everything out themselves.

And to an extent they are correct. Players do in fact do that. But does that validate the decision? Should game developers inform their players about what's going on in the games they play, or should they deliberately keep them in the dark for their own good? That's really the overarching question here. If anyone thinks that the OP's question is somehow subjective or doesn't have a clear cut answer, they are just wrong, period, the end. But if the real issue is whether they should be given the correct answer because they might not interpret the correct answer correctly, then you have to ask yourself if you're going to be someone that counters ignorance with education, or counters ignorance with more ignorance. I don't think there should be any question which side I've chosen.

Because if we're not going to tell players what the odds associated with crystal openings are, because we don't think everyone will use the answers in the right way, why tell them how the Parry mastery works, or how regeneration works, or what prestige is. People misunderstand or abuse that information all the time as well.

It is honestly weird to me, possibly because I'm simply too familiar with the math. When someone asks how to calculate prestige, we just tell them to add the correct numbers up. We don't tell them that prestige is just an abstract concept that doesn't really exist in the real world and don't worry about it because you'll just do something wrong with the information anyway. We don't tell them that while we can say what the prestige of a single champion is, we can't really say what the "cumulative prestige" of an account is.

But that is literally what I'm hearing in this thread. To me, calculating prestige and calculating crystal odds are both trivial calculation problems with no controversy inherent to the actual calculations, even though the topics themselves contain some controversy. That shouldn't, and doesn't impact the calculations themselves.

1,291★★★★200★84★23★To simplify, probability = number of desired outcome / number of total possibilities

Assuming 150 possible champs, total possible outcomes for 2 successive pulls = 150 * 150= 22500.

Out of the 22500 possible outcomes, only 1 would be for a “specific” champ. Example is only 1 outcome would be for pulling Cable twice. So probability here is 1/22500.

But pulling any champ twice, number of desired outcome is 150 ( Cable-Cable, Antman-Antman, CapIW-CapIW, ...) so probability here is 150/22500 = 1/150

1,175★★★i opened 5 , 6 stars in last 2 months. They were electro electro yj red skull red skull. Now tell me what are the odds to happen this? Just suck it up and keep playing without getting emotionally drained. That's what i learned.

8,611★★★★★Dr. Zola

500★★★36,298★★★★★973★★★1,396★★★★★18,799Guardian1,276★★★★But in about a 3 week span I pulled 6* sunspot back to back. Was pretty happy with that.

116★