* If you want to pre-define the champion, then your maths is perfect: If you have two crystals and you're hoping to pull and Awaken Corvus in particular, then the odds of pulling Corvus back to back from two crystals is 1/250 X 1/250.
So if I pulled Corvus from my first pull, and I decided I wanted to pull a specific but different champ on my second pull -- say, Doom -- then my odds would be the same, right?
Just got 3 3* longshots from 6 total event cavs. coincidence? idk. Either way that opening was pain, 2 4*s and 4 3*s from 6 cavs, absolute stinker I can't lie.
I don't believe your calculations. I gave you the reasoning . Pulling a champ twice in a row has to be lower than pulling it once. That is logic. Can you please answer me this if you do not believe the maths which you clearly don't. In your time of playing mcoc, have you ever! Seen someone open two crystals and get the same champs twice, then open 3 crystals and get the same champ 3 times. I doubt that you have...
it's all good man, like i said i can just give you the numbers but i can't force you to believe them.
If there's 250 champs, the odds of pulling any 6* twice in a row is 1/250. That's not my opinion, that's just a fact. If there's 250 champs, the odds of pulling any 6* once in a row is 250/250, aka 100%. If there's 250 champs, the odds of pulling a specific 6* (say corvus) in your next crystal is 1/250. If there's 250 champs, the odds of pulling a specific 6* (say corvus) in your next 2 crystals is (1/250)^2.
Those are all facts, you can accept it or not, won't change it
They are not the facts. I am not clueless , 1/250 is the chance from opening 1 crystal, then to open a second crystal has the same 1/250. Because there are 2 events of 1/250, the probability is much lower for the second crystal to be the same. I am wasting my time explaining this.
Assuming 250 different champions, the odds of pulling one specific champ is one in 250. The odds of pulling that specific champ twice in a row is 1/250 x 1/250. But there are 250 different ways to pull two of the same champion in a row: one for each different champion. So the odds of pulling the same champion twice in a row is one in 250, or 1/250 x 1/250 x 250.
This is an extrapolation of the fundamental counting principle, which is the foundation of statistics and probability. I'm not going to do it for 250, but I'll illustrate the principle with (six sided) dice. The odds of rolling the same number twice in a row is one in six, not one in 36. Calculation would say the odds of rolling one specific number twice in a row is one in 36, and there are six different numbers, so the odds of rolling the same number twice is 1/36 x 6 = 1/6.
But if you don't trust the calculations, you can just list all possible ways to roll a dice twice, and just visually count the number of times you get two of the same number in a row. Here we go:
There are thirty six different ways to roll dice twice. There are six ways to roll a duplicate. Thus the odds of doing this are six in thirty six, or one in six. That's the definition of probability.
Because each crystal opening is rolled independently, the odds of a champion being a particular champ after rolling that champ are identical to the odds of rolling that champion initially. Someone might argue that the rolls aren't independent because they are generated by random number generator, but that argument fails due to the nature of modern pRNGs. Modern pRNGs are tested to determine if they pass so-called randomness tests across huge numbers of iterations. One of those tests is the correlation test. This is a test to determine if, basically, the RNG is biased to generate the same results repeatedly *or* are anti-biased to generate a different result more often than random chance would dictate duplicate results. Modern pRNGs generally pass these tests (at least within the scope of how they are used in a game like this) and thus the fact that the game uses software pRNGs essentially guarantees that sequential crystal openings will behave as if they were statistically independent to a statistically high degree (certainly far higher than a player could detect a variance from).
It is also worth noting that given the number of crystals that players open in this game, the odds of a player opening two crystals in a row and actually *seeing* two consecutive openings is low. There's a pretty good chance that in between those two openings were other crystals being opened. The sixth anniversary video stated that over 29 billion crystals were opened by players over the history of the game. That is an average of 150 crystals per second. No player is likely to ever *see* two "consecutive" crystal openings. They are consecutive to them, but they are just two out of the hundreds or thousands of crystals opened at that time, and probably not actually rolled "consecutively."
In a game with millions of players (over time) this sort of things almost certainly happens all the time. It would be rare to happen to one individual player, but the odds of it happening to someone and then having them post about it is practically a certainty.
Could be worse. We could be discussing the Monty Haul problem.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
Do you know how many times a Random number generator can generate the same number again in a row ? The RNG they use in software are Pseudo RNG algorithms. Nothing can be truly random. They tend to generate the same numbers in a row more often than they should, the outcome is more likely to happen that it should. Strange but that's how it is.
This is mostly false. No random number generator in general use has this flaw to a detectable degree.
In fact, something like the exact opposite is true. Genuinely random sequences contain more consecutive numbers than people intuitively believe should be there. This is so strong of a psychological error that they've done experiments where people are asked to attempt to generate random sequences of numbers and they are trivial to pick out of a set of otherwise randomly generated sequences specifically because they lack repeats at the proper statistical rate.
So it isn't that pRNGs generate repeats more often than they should, it is that people think pRNGs should generate fewer repeats than statistics otherwise dictates they must.
Could be worse. We could be discussing the Monty Haul problem.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
We should totally discuss the Monty Hall problem. At least more folks than just Glads would learn something from this thread.
* If you want to pre-define the champion, then your maths is perfect: If you have two crystals and you're hoping to pull and Awaken Corvus in particular, then the odds of pulling Corvus back to back from two crystals is 1/250 X 1/250.
So if I pulled Corvus from my first pull, and I decided I wanted to pull a specific but different champ on my second pull -- say, Doom -- then my odds would be the same, right?
I'm not entirely sure what you're asking, so I'm going to lay out a couple different answers. I'm also assuming that there are 250 champs in the crystal pool. It's not exactly that in the basic, I'm sure. And many crystals have different sized pools, so adjust as needed for each crystal.
If you've got two crystals and, before you open them, you decide that you want Corvus in the first and Doom in the second, then your odds are (1/250)*(1/250). This is true of any two specific rolls. If you want Night Thrasher followed by Darkhawk, it's (1/250)*(1/250). If you're a masochist and you want Groot followed by OG Iron man, it's (1/250)*(1/250). And if you want Corvus followed by Corvus, it's (1/250)*(1/250).
But that's not exactly what you've described. If you've already opened your Corvus, then the odds that you get Corvus followed by Doom is just 1/250. The odds that you get Corvus followed by any particular champ is 1/250. You've already got Corvus, so the odds that Corvus precedes whomever is your second pull is 100%. It's a fact that you already got him. So the odds that you get that specific champ you want second, after securing your first pick in your first crystal, is 1/250.
Could be worse. We could be discussing the Monty Haul problem.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
MCOC Monty Hall problem: Groots behind two doors and a Ghost behind the third?
Could be worse. We could be discussing the Monty Haul problem.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
MCOC Monty Hall problem: Groots behind two doors and a Ghost behind the third?
The Monty Haul Mythic Nexus crystal. Guaranteed to have exactly one 6* champ option, the rest are 3*.
Game shows you three hidden options. You get to pick one. Before the game shows you what you picked, it opens one option that definitely contain a 3* champ. Then it gives you the option to keep your choice or switch.
Those who switch will have an enormous edge over those who stick. But the people who do stick will be so convinced they are correct to stick many will do so no matter how horrible their results are, then they will descend into crystal manipulation madness convinced the game is cheating them. Meanwhile the people who understand the actual probabilities will be getting 6* champs twice as often as those who stick.
You balance the cost of the crystal as costing about 50% of the relative cost of a 6* crystal. Those who switch come out ahead. Those who don't come out behind. Good math wins. Bad math loses.
Could be worse. We could be discussing the Monty Haul problem.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
MCOC Monty Hall problem: Groots behind two doors and a Ghost behind the third?
The Monty Haul Mythic Nexus crystal. Guaranteed to have exactly one 6* champ option, the rest are 3*.
Game shows you three hidden options. You get to pick one. Before the game shows you what you picked, it opens one option that definitely contain a 3* champ. Then it gives you the option to keep your choice or switch.
Those who switch will have an enormous edge over those who stick. But the people who do stick will be so convinced they are correct to stick many will do so no matter how horrible their results are, then they will descend into crystal manipulation madness convinced the game is cheating them. Meanwhile the people who understand the actual probabilities will be getting 6* champs twice as often as those who stick.
You balance the cost of the crystal as costing about 50% of the relative cost of a 6* crystal. Those who switch come out ahead. Those who don't come out behind. Good math wins. Bad math loses.
Don't forget to account for the people who create superstitious method of opening the crystal ("always switch if it shows you the door on the left!" ) and stumble into the right answer some of the time.
Bonus points: the more likely you are to believe in crystal conspiracies, the more likely I believe you will be to stick. You'll think the game is trying to trick you into switching, so switching must be bad.
This punishes conspiracy theorists with cold hard math. All they would have to do is let go of their conspiracy theories and they would start to win. But most won't.
Could be worse. We could be discussing the Monty Haul problem.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
MCOC Monty Hall problem: Groots behind two doors and a Ghost behind the third?
The Monty Haul Mythic Nexus crystal. Guaranteed to have exactly one 6* champ option, the rest are 3*.
Game shows you three hidden options. You get to pick one. Before the game shows you what you picked, it opens one option that definitely contain a 3* champ. Then it gives you the option to keep your choice or switch.
Those who switch will have an enormous edge over those who stick. But the people who do stick will be so convinced they are correct to stick many will do so no matter how horrible their results are, then they will descend into crystal manipulation madness convinced the game is cheating them. Meanwhile the people who understand the actual probabilities will be getting 6* champs twice as often as those who stick.
You balance the cost of the crystal as costing about 50% of the relative cost of a 6* crystal. Those who switch come out ahead. Those who don't come out behind. Good math wins. Bad math loses.
Don't forget to account for the people who create superstitious method of opening the crystal ("always switch if it shows you the door on the left!" ) and stumble into the right answer some of the time.
True, but anything short of always switching will always underperform, and by a large enough margin that it wouldn't take very long for the statistical likelihood of that underperformance being realized getting very high very quickly.
Or, if we want this probability to converge faster, we could increase the crystals to five choices, or even ten choices.
I don't believe your calculations. I gave you the reasoning . Pulling a champ twice in a row has to be lower than pulling it once. That is logic. Can you please answer me this if you do not believe the maths which you clearly don't. In your time of playing mcoc, have you ever! Seen someone open two crystals and get the same champs twice, then open 3 crystals and get the same champ 3 times. I doubt that you have...
I don't think you are getting the point. If you name a specific champ and want to know the odds of pulling that champ twice in a row you are doing it right. But that isn't what is happening. The first champ is what it is. It could be any champ. Let's say you pulled 6* Diablo. Now you want to know what the odds are that the next champ will also be Diablo. The odds are 1/250 or however many champs are in the crystal. Only the second crystal matters for this calculation. You could also say if you open a crystal, every subsequent pull has a 1/250 chance to have the same outcome. That's very different from saying "what are my odds that the next two crystals will both be Diablo."
Math is hard, because math is about two different things: adding numbers up, and knowing which ones to add up. It is not easy to learn how to add numbers up. Many people who learn how to do this forget that is just the crust of the pizza. Without all the toppings, it is just bread.
You have a 1/250 chance of pulling a specific champ. So if you are trying to pull two of a specific champ it would be (1/250)^2.
However, you have 1/1 chance of pulling any champ, and then a 1/250 chance of pulling that same champ again, which makes it a 1/250 chance of pulling two of any champ.
TLDR; (1/250)^2 chance to pull 2 of a specific champ. (1/250) chance to pull 2 of any champ.
you have the same odds of pulling ghost than kitty as you do juggs then rhino. it's also the same odds of pulling corvus twice or pulling iron patriot twice. if you flip a coin once, and it lands on heads, the coin doesn't somehow favor itself to land on heads again
popped 8 crystals 3 of those were white mags 3*... the odds of that per crystals drop rate is insane and not sure how its possible. people that understand basic math should understand how it shouldnt be happening this often in game
you have the same odds of pulling ghost than kitty as you do juggs then rhino. it's also the same odds of pulling corvus twice or pulling iron patriot twice. if you flip a coin once, and it lands on heads, the coin doesn't somehow favor itself to land on heads again
Yeah, but it's very much Human nature to say "It can't be heads again?!!!"
If the OP is still unconvinced when they get back on the thread, maybe we should direct them to one of the many threads complaining about how hard it is to Dupe champions because there are too many in the crystals...?
@DNA3000 could you elaborate on why the mcoc monthy hall switchers would have a better overall result? The closed door has a 50% of chance of having a six star and so does the other, why would switching be better?
@DNA3000 could you elaborate on why the mcoc monthy hall switchers would have a better overall result? The closed door has a 50% of chance of having a six star and so does the other, why would switching be better?
If anyone else is wondering it’s because your odds are locked in once you choose your first door. It’s 1/3 then, and removing the other option doesn’t suddenly make it 50/50 just because there’s only two options now.
To demonstrate this, imagine there were 100 doors, 1 with the prize and 99 with nothing. You randomly pick one, the host then opens 98 doors showing you nothing. He then asks you whether you want to swap.
The chances of you randomly picking the one door with the prize out of 100 is so low, that the host revealing 98 doors without a prize means that the final door he didn’t reveal likely has the prize in it.
The odds were locked in at 1% chance when you selected the first door. So the odds now that the other door contains the prize is 99%. Even though there are two options, it’s not 50/50.
I've been playing 6 years. Not only have I pulled the same champ back to back several times... I've pulled a champ 3 times in a row on 2 separate occasions.
Did it suck pulling Cyclops 3 times? Yes. Was it awesome to pull Corvus back to back to back? Absolutely!!!
@DNA3000 could you elaborate on why the mcoc monthy hall switchers would have a better overall result? The closed door has a 50% of chance of having a six star and so does the other, why would switching be better?
If anyone else is wondering it’s because your odds are locked in once you choose your first door. It’s 1/3 then, and removing the other option doesn’t suddenly make it 50/50 just because there’s only two options now.
To demonstrate this, imagine there were 100 doors, 1 with the prize and 99 with nothing. You randomly pick one, the host then opens 98 doors showing you nothing. He then asks you whether you want to swap.
The chances of you randomly picking the one door with the prize out of 100 is so low, that the host revealing 98 doors without a prize means that the final door he didn’t reveal likely has the prize in it.
The odds were locked in at 1% chance when you selected the first door. So the odds now that the other door contains the prize is 99%. Even though there are two options, it’s not 50/50.
Imagining it as 1000 doord is what finally made it intuitive for me
here is some simple math for you. I'm going to use a nice round 200 champ pool, not thing about start rarities for the same of simple math, as it depends on which crystal you are talking about.
Odds of getting same champ once in a row... well... let's see: 100%. Impossible not to.
Odds of getting same champ twice in a row: 1:200 or .5%
Odds of getting same champ three times in a row: 1:40000 or %.0025
Now obviously the math is a bit more complicated with say a featured cav, as you need to account for the odds of getting a certain starrage, and whether you are talking about the featured champ or some other random champ in the crystal... but the same approach to calculating the odds will apply.
So... take a look at that 0.5%: how many people here have some rarity immortal iron fist, or some other trophy champ that comes in and such rarities... or got the 6 star featured from the featured cav a couple times at some point... those have similar odds, and through sheer number of crystals opened... you got it.
Look, if the chance of pulling a champ is 1/250, then the chance of pulling him again in the next crystal should be almost impossible right? To me it's logic, but I could for sure be wrong..btw mates, sorry for the english spelling, I'm danish.
I love all the people that don't understand statistics on here. If your looking at the odds of pulling 2 champs individually, then it is 1/250. However that isn't what we are looking at, we are looking at both events dependently. The second event event can't happen without the first one. So if we look at the odds of pulling a 10 of clubs after drawing a 10 of hearts, then it is 1/52 (for the clubs) multiplied by 1/51 (for the hearts) because of the 1/52 chance, you get a clubs, there is still a 1/51 chance to pull the hearts so you multiply the odds together to reflect the accuracy of getting both cards. This is basic statistics I learned in high school.
Comments
This is an extrapolation of the fundamental counting principle, which is the foundation of statistics and probability. I'm not going to do it for 250, but I'll illustrate the principle with (six sided) dice. The odds of rolling the same number twice in a row is one in six, not one in 36. Calculation would say the odds of rolling one specific number twice in a row is one in 36, and there are six different numbers, so the odds of rolling the same number twice is 1/36 x 6 = 1/6.
But if you don't trust the calculations, you can just list all possible ways to roll a dice twice, and just visually count the number of times you get two of the same number in a row. Here we go:
1 1 < --- dup
1 2
1 3
1 4
1 5
1 6
2 1
2 2 < --- dup
2 3
2 4
2 5
2 6
3 1
3 2
3 3 < --- dup
3 4
3 5
3 6
4 1
4 2
4 3
4 4 < --- dup
4 5
4 6
5 1
5 2
5 3
5 4
5 5 < --- dup
5 6
6 1
6 2
6 3
6 4
6 5
6 6 < --- dup
There are thirty six different ways to roll dice twice. There are six ways to roll a duplicate. Thus the odds of doing this are six in thirty six, or one in six. That's the definition of probability.
Because each crystal opening is rolled independently, the odds of a champion being a particular champ after rolling that champ are identical to the odds of rolling that champion initially. Someone might argue that the rolls aren't independent because they are generated by random number generator, but that argument fails due to the nature of modern pRNGs. Modern pRNGs are tested to determine if they pass so-called randomness tests across huge numbers of iterations. One of those tests is the correlation test. This is a test to determine if, basically, the RNG is biased to generate the same results repeatedly *or* are anti-biased to generate a different result more often than random chance would dictate duplicate results. Modern pRNGs generally pass these tests (at least within the scope of how they are used in a game like this) and thus the fact that the game uses software pRNGs essentially guarantees that sequential crystal openings will behave as if they were statistically independent to a statistically high degree (certainly far higher than a player could detect a variance from).
It is also worth noting that given the number of crystals that players open in this game, the odds of a player opening two crystals in a row and actually *seeing* two consecutive openings is low. There's a pretty good chance that in between those two openings were other crystals being opened. The sixth anniversary video stated that over 29 billion crystals were opened by players over the history of the game. That is an average of 150 crystals per second. No player is likely to ever *see* two "consecutive" crystal openings. They are consecutive to them, but they are just two out of the hundreds or thousands of crystals opened at that time, and probably not actually rolled "consecutively."
What were the odds of this happening? About one in 7700.
https://forums.playcontestofchampions.com/en/discussion/comment/1493277/#Comment_1493277
In a game with millions of players (over time) this sort of things almost certainly happens all the time. It would be rare to happen to one individual player, but the odds of it happening to someone and then having them post about it is practically a certainty.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
In fact, something like the exact opposite is true. Genuinely random sequences contain more consecutive numbers than people intuitively believe should be there. This is so strong of a psychological error that they've done experiments where people are asked to attempt to generate random sequences of numbers and they are trivial to pick out of a set of otherwise randomly generated sequences specifically because they lack repeats at the proper statistical rate.
So it isn't that pRNGs generate repeats more often than they should, it is that people think pRNGs should generate fewer repeats than statistics otherwise dictates they must.
If you've got two crystals and, before you open them, you decide that you want Corvus in the first and Doom in the second, then your odds are (1/250)*(1/250). This is true of any two specific rolls. If you want Night Thrasher followed by Darkhawk, it's (1/250)*(1/250). If you're a masochist and you want Groot followed by OG Iron man, it's (1/250)*(1/250). And if you want Corvus followed by Corvus, it's (1/250)*(1/250).
But that's not exactly what you've described. If you've already opened your Corvus, then the odds that you get Corvus followed by Doom is just 1/250. The odds that you get Corvus followed by any particular champ is 1/250. You've already got Corvus, so the odds that Corvus precedes whomever is your second pull is 100%. It's a fact that you already got him. So the odds that you get that specific champ you want second, after securing your first pick in your first crystal, is 1/250.
behind two doors and a Ghost behind the third?
Game shows you three hidden options. You get to pick one. Before the game shows you what you picked, it opens one option that definitely contain a 3* champ. Then it gives you the option to keep your choice or switch.
Those who switch will have an enormous edge over those who stick. But the people who do stick will be so convinced they are correct to stick many will do so no matter how horrible their results are, then they will descend into crystal manipulation madness convinced the game is cheating them. Meanwhile the people who understand the actual probabilities will be getting 6* champs twice as often as those who stick.
You balance the cost of the crystal as costing about 50% of the relative cost of a 6* crystal. Those who switch come out ahead. Those who don't come out behind. Good math wins. Bad math loses.
This punishes conspiracy theorists with cold hard math. All they would have to do is let go of their conspiracy theories and they would start to win. But most won't.
Or, if we want this probability to converge faster, we could increase the crystals to five choices, or even ten choices.
You have a 1/250 chance of pulling a specific champ. So if you are trying to pull two of a specific champ it would be (1/250)^2.
However, you have 1/1 chance of pulling any champ, and then a 1/250 chance of pulling that same champ again, which makes it a 1/250 chance of pulling two of any champ.
TLDR;
(1/250)^2 chance to pull 2 of a specific champ.
(1/250) chance to pull 2 of any champ.
If the OP is still unconvinced when they get back on the thread, maybe we should direct them to one of the many threads complaining about how hard it is to Dupe champions because there are too many in the crystals...?
To demonstrate this, imagine there were 100 doors, 1 with the prize and 99 with nothing. You randomly pick one, the host then opens 98 doors showing you nothing. He then asks you whether you want to swap.
The chances of you randomly picking the one door with the prize out of 100 is so low, that the host revealing 98 doors without a prize means that the final door he didn’t reveal likely has the prize in it.
The odds were locked in at 1% chance when you selected the first door. So the odds now that the other door contains the prize is 99%. Even though there are two options, it’s not 50/50.
Not only have I pulled the same champ back to back several times... I've pulled a champ 3 times in a row on 2 separate occasions.
Did it suck pulling Cyclops 3 times? Yes.
Was it awesome to pull Corvus back to back to back? Absolutely!!!
That's just how RNG works.
Odds of getting same champ once in a row... well... let's see: 100%. Impossible not to.
Odds of getting same champ twice in a row: 1:200 or .5%
Odds of getting same champ three times in a row: 1:40000 or %.0025
Now obviously the math is a bit more complicated with say a featured cav, as you need to account for the odds of getting a certain starrage, and whether you are talking about the featured champ or some other random champ in the crystal... but the same approach to calculating the odds will apply.
So... take a look at that 0.5%: how many people here have some rarity immortal iron fist, or some other trophy champ that comes in and such rarities... or got the 6 star featured from the featured cav a couple times at some point... those have similar odds, and through sheer number of crystals opened... you got it.
This statistically is no different.