That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

The first crystal doesn't factor into the odds though. It's just once you open a crystal, what are the odds that the next crystal will be the same, which is just 1/250.

Of course it does, it's like winning the lotto twice you have the same odds for the first and the second game. When u combine the odds for winning it twice its much lower. I do this stuff for a job

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

The first crystal doesn't factor into the odds though. It's just once you open a crystal, what are the odds that the next crystal will be the same, which is just 1/250.

Of course it does, it's like winning the lotto twice you have the same odds for the first and the second game. When u combine the odds for winning it twice its much lower. I do this stuff for a job

If you do this for your job you would know that the first one only comes into play when you are chasing a specific result. When dealing with random odds with no specific aim, the first result doesn’t factor into the equation.

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

The first crystal doesn't factor into the odds though. It's just once you open a crystal, what are the odds that the next crystal will be the same, which is just 1/250.

Of course it does, it's like winning the lotto twice you have the same odds for the first and the second game. When u combine the odds for winning it twice its much lower. I do this stuff for a job

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

The first crystal doesn't factor into the odds though. It's just once you open a crystal, what are the odds that the next crystal will be the same, which is just 1/250.

Of course it does, it's like winning the lotto twice you have the same odds for the first and the second game. When u combine the odds for winning it twice its much lower. I do this stuff for a job

What are the odds that a nexus crystals will have three of the same champ at different rarities? About one in fifty thousand. However, that was a *submitted* opening. So the question is really, out of all of the players out there, what are the odds of one of them seeing this and then submitting it to Prof Hoff. There are probably hundreds of thousands of players opening nexus crystals, and across all of them there are probably hundreds of thousands of crystals being opened every day. If only one percent of them are players that are in some way active in the player community, and only one percent of them would be inclined to submit a rare opening to Prof Hoff, I would expect him to get an opening like that least once every couple of years.

Rare events are rare, but if you wait long enough they eventually happen.

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

The first crystal doesn't factor into the odds though. It's just once you open a crystal, what are the odds that the next crystal will be the same, which is just 1/250.

Of course it does, it's like winning the lotto twice you have the same odds for the first and the second game. When u combine the odds for winning it twice its much lower. I do this stuff for a job

That's alarming. Because they are correct: when you are calculating the odds of a dup, the first opening doesn't matter. If can be any champion X, and the odds of a dup are the odds of the second opening also being X.

You're analogizing to a situation that is statistically different. When we calculate the odds of winning the lottery twice we are calculating the odds of two separate low probability events happening consecutively. But when we are calculating the odds of a dup, we aren't calculating the odds of two specific low probability events happening. We are calculating the odds of a correlation.

When in doubt, always reduce to first principles. The odds of pulling two identical champions out of two crystals is defined to be the number of ways to pull a pair of duplicates divided by the total number of ways to open two crystals in total. The fundamental counting principle states that when there are N ways for the first event to happen and M ways for the second event to happen and they are independent events, the total number of ways for the two events to happen is NxM. Therefore, if we assume 220 champs in the crystal, there are 220x220 = 48400 possible ways to open two crystals.

There are exactly 220 ways to pull duplicate champions. The fundamental way to determine this is to list them and count them, but I'm not going to do that. It is trivially easy to determine that the 220 ways to pull dups is when the first crystal is the first champion and the second crystal also drops that first champion, or with the first crystal drops the second champion in the crystal and the second crystal also drops that second champion, and so on.

Therefore, the odds of pulling a dup are exactly 220 divided by 48400. That would be 220/48400 or 1/220. That is the definition of probability.

The reason why the first drop doesn't matter, and the way this is typically taught in school, is to look at a simplification. The odds of any particular champion dropping from the first crystal are identical. Therefore, if we look at the general case where the first crystal drops some unspecified champion X, the odds of the second crystal duplicating the first is one out of 220. There are 220 possibilities, and only one of them duplicates the first crystal. Because this line of reasoning works no matter what the first crystal produces, and because the odds of any particular champ dropping from the first crystal is identical, the odds of pulling two of the same champ must be identical to the odds of pulling a duplicate of the first given the first has already been rolled. QED.

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

The first crystal doesn't factor into the odds though. It's just once you open a crystal, what are the odds that the next crystal will be the same, which is just 1/250.

Of course it does, it's like winning the lotto twice you have the same odds for the first and the second game. When u combine the odds for winning it twice its much lower. I do this stuff for a job

What are the odds of two consecutive coin flips resulting in heads ?

Dr. Zola

1/4

Check the sample space. Possible outcomes are

{ HH,HT,TH,TT } where T is Tails and H is Heads. So HH reads Head Head which is Head followed by Head.

There are 4 outcomes each if which are equally likely. In that your desirable out come is just 1 out of the sample space. So 1/4

@DrZola i just realized you might have been directing the question at OP and not actually asking this. Sorry if it's the former

It was actually more of a rhetorical question.

If the question is “what are the odds of pulling the same champ twice in two consecutive 6* crystals?” then the answer would be 1/220 (assuming 220 champs). But if the question is “what are the odds of pulling two 6* Blue Cykes in two consecutive 6* crystals?” then I like your mathematical approach.

What are the odds of two consecutive coin flips resulting in heads ?

Dr. Zola

1/4

Check the sample space. Possible outcomes are

{ HH,HT,TH,TT } where T is Tails and H is Heads. So HH reads Head Head which is Head followed by Head.

There are 4 outcomes each if which are equally likely. In that your desirable out come is just 1 out of the sample space. So 1/4

@DrZola i just realized you might have been directing the question at OP and not actually asking this. Sorry if it's the former

It was actually more of a rhetorical question.

If the question is “what are the odds of pulling the same champ twice in two consecutive 6* crystals?” then the answer would be 1/220 (assuming 220 champs). But if the question is “what are the odds of pulling two 6* Blue Cykes in two consecutive 6* crystals?” then I like your mathematical approach.

Dr. Zola

The meta question is: what’s the correct question to ask? Is it “what are the odds of a dup” or “what are the odds of two Cyclops?” It seems arbitrary, but it is not. Here’s why.

If you ask “what are the odds of two Cyclops” then the answer is one in 48400. But the follow up question is “is that unusual?” and the answer is no, it is not. Because the odds of any two specific champs coming up are exactly the same. If you see two specific champs: a blue cyclops and another blue cyclops, then the odds of seeing that are 48400, but the odds of seeing literally any other specific combination is exactly the same. Two blue cyclops in a row is *literally* not noteworthy, because all other combinations have exactly the same odds to happen. There is nothing special about Cyclops, Cyclops compared to Hulkbuster, Archangel. I could just as easily post a picture of me pulling HB and AA and ask “what are the odds of that happening” and the answer would be the same: one in 48400.

If you ask “what are the odds of a duplicate pull?” then the odds of that happening are one in 220. And that is noteworthy, because the odds of a dup are far lower than the odds of non dups. The blue Cyclops is not the only way to pull a dup, but there’s only 220 ways to do that out of 48400 possible openings. That is noteworthy.

What are the odds of two consecutive coin flips resulting in heads ?

Dr. Zola

1/4

Check the sample space. Possible outcomes are

{ HH,HT,TH,TT } where T is Tails and H is Heads. So HH reads Head Head which is Head followed by Head.

There are 4 outcomes each if which are equally likely. In that your desirable out come is just 1 out of the sample space. So 1/4

@DrZola i just realized you might have been directing the question at OP and not actually asking this. Sorry if it's the former

It was actually more of a rhetorical question.

If the question is “what are the odds of pulling the same champ twice in two consecutive 6* crystals?” then the answer would be 1/220 (assuming 220 champs). But if the question is “what are the odds of pulling two 6* Blue Cykes in two consecutive 6* crystals?” then I like your mathematical approach.

Dr. Zola

The meta question is: what’s the correct question to ask? Is it “what are the odds of a dup” or “what are the odds of two Cyclops?” It seems arbitrary, but it is not. Here’s why.

If you ask “what are the odds of two Cyclops” then the answer is one in 48400. But the follow up question is “is that unusual?” and the answer is no, it is not. Because the odds of any two specific champs coming up are exactly the same. If you see two specific champs: a blue cyclops and another blue cyclops, then the odds of seeing that are 48400, but the odds of seeing literally any other specific combination is exactly the same. Two blue cyclops in a row is *literally* not noteworthy, because all other combinations have exactly the same odds to happen. There is nothing special about Cyclops, Cyclops compared to Hulkbuster, Archangel. I could just as easily post a picture of me pulling HB and AA and ask “what are the odds of that happening” and the answer would be the same: one in 48400.

If you ask “what are the odds of a duplicate pull?” then the odds of that happening are one in 220. And that is noteworthy, because the odds of a dup are far lower than the odds of non dups. The blue Cyclops is not the only way to pull a dup, but there’s only 220 ways to do that out of 48400 possible openings. That is noteworthy.

More entertaining statistic questions than have been posted in foums:

What are the odds that a post containing that phrase ("What are the odds") includes this exact scenario? What are the odds that the first champion is a previously unowned champ, then gets the dupe? What are the odds that DNA gives up explaining statistics to start a Youtube channel and actually make money explaining algebra through gaming? What are the odds that I get bored and stop naming scenarios?

Pretty high. I'm lazy, but I have a proposal to write and probably also could be grinding out EQ or something.

What are the odds of two consecutive coin flips resulting in heads ?

Dr. Zola

1/4

Check the sample space. Possible outcomes are

{ HH,HT,TH,TT } where T is Tails and H is Heads. So HH reads Head Head which is Head followed by Head.

There are 4 outcomes each if which are equally likely. In that your desirable out come is just 1 out of the sample space. So 1/4

@DrZola i just realized you might have been directing the question at OP and not actually asking this. Sorry if it's the former

It was actually more of a rhetorical question.

If the question is “what are the odds of pulling the same champ twice in two consecutive 6* crystals?” then the answer would be 1/220 (assuming 220 champs). But if the question is “what are the odds of pulling two 6* Blue Cykes in two consecutive 6* crystals?” then I like your mathematical approach.

Dr. Zola

The meta question is: what’s the correct question to ask? Is it “what are the odds of a dup” or “what are the odds of two Cyclops?” It seems arbitrary, but it is not. Here’s why.

If you ask “what are the odds of two Cyclops” then the answer is one in 48400. But the follow up question is “is that unusual?” and the answer is no, it is not. Because the odds of any two specific champs coming up are exactly the same. If you see two specific champs: a blue cyclops and another blue cyclops, then the odds of seeing that are 48400, but the odds of seeing literally any other specific combination is exactly the same. Two blue cyclops in a row is *literally* not noteworthy, because all other combinations have exactly the same odds to happen. There is nothing special about Cyclops, Cyclops compared to Hulkbuster, Archangel. I could just as easily post a picture of me pulling HB and AA and ask “what are the odds of that happening” and the answer would be the same: one in 48400.

If you ask “what are the odds of a duplicate pull?” then the odds of that happening are one in 220. And that is noteworthy, because the odds of a dup are far lower than the odds of non dups. The blue Cyclops is not the only way to pull a dup, but there’s only 220 ways to do that out of 48400 possible openings. That is noteworthy.

Precisely—and that’s my point.

An even better question would be “what are the odds of disappointment with this upcoming pull?”😉 Statistics, emotions, context, roster, progression and more all rolled into one question. My guess is it’s always > zero.

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

It is not 0.004%. It is 0.4%. 1 / 250 = 0.004 x 100%

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

It is not 0.004%. It is 0.4%. 1 / 250 = 0.004 x 100%

@Glads were you serious about doing this as a job?

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

It is not 0.004%. It is 0.4%. 1 / 250 = 0.004 x 100%

@Glads were you serious about doing this as a job?

That’s almost your off of getting a single champ from the basic but to get the same champ twice in a row is a lot lower of a odd I’m not great at maths but ik that it ain’t that low of a probability

Nope, AverageDesi is right. Because the question isn’t “before opening this crystal, what are the odds I pull two Blue Cyclops,” but rather “after opening the first crystal, what are the odds I pull this same champion again?”

The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.

I completely agree with you there are 2 chances of 1/250, as you have 2 crystals the point is its consecutive. If you open a crystals and duplicate a champ u have in your roster that's a .004% chance as it's consecutive that's a .000016% chance I argued this a while back no one believes the maths

It is not 0.004%. It is 0.4%. 1 / 250 = 0.004 x 100%

@Glads were you serious about doing this as a job?

Frankly, i do not believe the odds are that small given that not all of the champs are in every crystal. That may be the line but I happen to believe they are packed with certain champs for kabams own reasons and cycled, just the same as a featured crystals. All 200 plus champs are "available" but not in every crystal. Therefore the odds of the double dupe increase.

## Comments

331★★★I do this stuff for a job

5,622★★★★★4,031★★★★★313★★★16,436GuardianRare events are rare, but if you wait long enough they eventually happen.

https://www.youtube.com/watch?v=rqHRQdmjdrg

16,436GuardianYou're analogizing to a situation that is statistically different. When we calculate the odds of winning the lottery twice we are calculating the odds of two separate low probability events happening consecutively. But when we are calculating the odds of a dup, we aren't calculating the odds of two

specificlow probability events happening. We are calculating the odds of a correlation.When in doubt, always reduce to first principles. The odds of pulling two identical champions out of two crystals is

definedto be the number of ways to pull a pair of duplicates divided by the total number of ways to open two crystals in total. The fundamental counting principle states that when there are N ways for the first event to happen and M ways for the second event to happen and they are independent events, the total number of ways for the two events to happen is NxM. Therefore, if we assume 220 champs in the crystal, there are 220x220 = 48400 possible ways to open two crystals.There are exactly 220 ways to pull duplicate champions. The fundamental way to determine this is to list them and count them, but I'm not going to do that. It is trivially easy to determine that the 220 ways to pull dups is when the first crystal is the first champion and the second crystal also drops that first champion, or with the first crystal drops the second champion in the crystal and the second crystal also drops that second champion, and so on.

Therefore, the odds of pulling a dup are exactly 220 divided by 48400. That would be 220/48400 or 1/220. That is the definition of probability.

The reason why the first drop doesn't matter, and the way this is typically taught in school, is to look at a simplification. The odds of any particular champion dropping from the first crystal are identical. Therefore, if we look at the general case where the first crystal drops some unspecified champion X, the odds of the second crystal duplicating the first is one out of 220. There are 220 possibilities, and only one of them duplicates the first crystal. Because this line of reasoning works no matter what the first crystal produces, and because the odds of any particular champ dropping from the first crystal is identical, the odds of pulling two of the same champ must be identical to the odds of pulling a duplicate of the first given the first has already been rolled. QED.

7,369★★★★★Dr. Zola

4,031★★★★★Check the sample space. Possible outcomes are

{ HH,HT,TH,TT }

where T is Tails and H is Heads. So HH reads Head Head which is Head followed by Head.

There are 4 outcomes each if which are equally likely. In that your desirable out come is just 1 out of the sample space. So 1/4

2,002★★★★★1,559★★★★4,031★★★★★7,369★★★★★If the question is “what are the odds of pulling the same champ twice in two consecutive 6* crystals?” then the answer would be 1/220 (assuming 220 champs). But if the question is “what are the odds of pulling two 6* Blue Cykes in two consecutive 6* crystals?” then I like your mathematical approach.

Dr. Zola

16,436GuardianIf you ask “what are the odds of two Cyclops” then the answer is one in 48400. But the follow up question is “is that unusual?” and the answer is no, it is not. Because the odds of any two specific champs coming up are exactly the same. If you see two specific champs: a blue cyclops and another blue cyclops, then the odds of seeing that are 48400, but the odds of seeing literally any other specific combination is exactly the same. Two blue cyclops in a row is *literally* not noteworthy, because all other combinations have exactly the same odds to happen. There is nothing special about Cyclops, Cyclops compared to Hulkbuster, Archangel. I could just as easily post a picture of me pulling HB and AA and ask “what are the odds of that happening” and the answer would be the same: one in 48400.

If you ask “what are the odds of a duplicate pull?” then the odds of that happening are one in 220. And that is noteworthy, because the odds of a dup are far lower than the odds of non dups. The blue Cyclops is not the only way to pull a dup, but there’s only 220 ways to do that out of 48400 possible openings. That is noteworthy.

28★3,170★★★★2,353★★★★★What are the odds that a post containing that phrase ("What are the odds") includes this exact scenario?

What are the odds that the first champion is a previously unowned champ, then gets the dupe?

What are the odds that DNA gives up explaining statistics to start a Youtube channel and actually make money explaining algebra through gaming?

What are the odds that I get bored and stop naming scenarios?

7,369★★★★★An even better question would be “what are the odds of disappointment with this upcoming pull?”😉 Statistics, emotions, context, roster, progression and more all rolled into one question. My guess is it’s always > zero.

Dr. Zola

16,436Guardian7,369★★★★★Dr. Zola

16,436Guardian410★★★(That’ll keep the math trolls busy for a while; everyone run!)

7,369★★★★★Dr. Zola

404★★★4,031★★★★★5,622★★★★★3,406★★★★★16,436Guardian4,031★★★★★3,159★★★★Therefore the odds of the double dupe increase.

61★