If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
I’m sorry but unfortunately u can still play and never get the 4 star but if you is a arena grind u can’t miss them as a 4 star anymore
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
No, they dont. Thats a horrible analogy. I like my odds with a 50% chance rather than 0.5. Also that’s an absurd amount of 4* shards you’re talking about, of course that would increase the chances significantly to pull the missing champion you’re after. Also another awful comparison between 2*s and 4*s. 2*s consist of exclusive champions that are found in rarer crystals, whereas the 4* hero crystal has a more expanded roster. 3*s are the same, just more common. I’m still missing 3* og spidey and moon knight, and I’ve been playing for almost 3 years on this account, that’s just how RNG works.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
Have you opened more premium hero crystals or more 4* crystals?
Again your last point is completely stupid. I doubt that most of the players have opened more than 2,000-3,000 4* crystals. So why you say 1 million crystals?
I've always considered it logical to take things to the extremes and work backwards, or simply and work forwards. No one like the coin analogy, and you don't like a million crystals.
Why don't we try a dice then, similar to a crystal but down to 6 options instead of 200 (less some number that exclusives).
Odds are 17% you'll roll any particular number on any particular roll, so how many tries is it going to take to roll 1 for example. Well, we can calculate the odds of an event given a particular set of trials. Given 10 trials, you'll roll a 1 at least once 83% of the time. 100 times though? Virtually 100% (99.99999919% to be precise).
So apply this to Sabretooth, in a crystal with 200, odds of .5%, significantly less than the 17% we started with in the dice example.
100 trials in this situation results in a mediocre 39% 250 trials = 71% 500 trials = 91% 1000 trials = 99.335% 1500 trials = 99.946% 2000 trials = 99.996% 2500 trials = 99.9996%
and so forth.
How many 4* crystals and 4* equivalents has an endgamer opened? That's going to be a very difficult question to answer. Between legendary, Ultimate, PHC, Cavs, GMCs and 4* crystals it's pretty hard to say. Maybe it's not close to 2500, could be 1000 to 5000 reasonably, but the point is that with an overwhelming number of trials, you will get Sabretooth.
This doesn't even take into account dual class crystals which allow for increased odds as well.
Should my math be wrong, I'd love to know. I find probability fascinating.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
You sir, are truly a specimen.
Just a dude that likes probability. Not sure why the name calling tbh, just a math discussion.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
You sir, are truly a specimen.
Just a dude that likes probability. Not sure why the name calling tbh, just a math discussion.
For how much you like math, it’s interesting how little you understand it. You really think somebody has opened up 1 mil 4* crystals?
I don't believe I ever said that. I do believe that if anyone ever had opened 1 million 4* crystals, they are a 100% lock to have every 4* champ in basics.
I’ve open more than 100 skill/mutant class crystals still no sabretooth isn’t easy still with only two classes i’ll probably wait a few more months trying or i’ll try and do it with oldman logan but i know that will cost me a ton more units than using sabretooth
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
Have you opened more premium hero crystals or more 4* crystals?
Again your last point is completely stupid. I doubt that most of the players have opened more than 2,000-3,000 4* crystals. So why you say 1 million crystals?
I've always considered it logical to take things to the extremes and work backwards, or simply and work forwards. No one like the coin analogy, and you don't like a million crystals.
Why don't we try a dice then, similar to a crystal but down to 6 options instead of 200 (less some number that exclusives).
Odds are 17% you'll roll any particular number on any particular roll, so how many tries is it going to take to roll 1 for example. Well, we can calculate the odds of an event given a particular set of trials. Given 10 trials, you'll roll a 1 at least once 83% of the time. 100 times though? Virtually 100% (99.99999919% to be precise).
So apply this to Sabretooth, in a crystal with 200, odds of .5%, significantly less than the 17% we started with in the dice example.
100 trials in this situation results in a mediocre 39% 250 trials = 71% 500 trials = 91% 1000 trials = 99.335% 1500 trials = 99.946% 2000 trials = 99.996% 2500 trials = 99.9996%
and so forth.
How many 4* crystals and 4* equivalents has an endgamer opened? That's going to be a very difficult question to answer. Between legendary, Ultimate, PHC, Cavs, GMCs and 4* crystals it's pretty hard to say. Maybe it's not close to 2500, could be 1000 to 5000 reasonably, but the point is that with an overwhelming number of trials, you will get Sabretooth.
This doesn't even take into account dual class crystals which allow for increased odds as well.
Should my math be wrong, I'd love to know. I find probability fascinating.
The direct way to calculate this quickly is with logarithms. The math goes like this. Suppose we want to know how many crystals to open before the odds of missing a single champ are one in a billion. The equation looks like this:
(199/200)^n = 1/1000000000
We then log both sides:
n log (199/200) = log (1/1000000000) = -9 n = -9 / log (199/200) ~= 4134
For one in a million odds, it takes about 2756 crystals. For one in a billion odds, it takes about 4134 crystals. Somewhere between those two, most players will have every champ (at least of the champs that have been in the crystal long enough for these pulls to matter). Scarlet Witch has been in the crystals since basically forever. Most people who have opened thousands of 4* crystals have the bulk or all of those openings containing that champion (outside dual crystals of the wrong class and the occasional special crystal). So it comes down to how many crystals a player has opened.
If you didn’t and you’ve just never pulled a 3-4 year old champion, then you’ve just been doing something wrong all this time and it’s still your fault
I play for 4 years and I still don't have 4* Scarlet Witch. Am I doing something wrong?
If you have 1 Carinas challenge left, and ALL other content complete (act 6 and abyss exploration), you're doing or did something wrong.
Lol. What exactly I am doing wrong? If there was a challenge with a 4* Scarlet Witch, I would have made numerous threads as well (maybe not numerous, but I would ask many times for a way to get this champs). There are over 200 4* champs. It's still an RNG thing whether you like it or not.
You can choose to believe that if you want. There's a point when the number of pulls has reached a point where the RNG becomes a total non factor, and anyone who has completed essentially all content in the game will be at a place where they have every 4*. It's just math.
It's just math? I don't see any math here. If you open 2.000 4* crystal there is still a chance of you not getting a Scarlet Witch. It's a small chance, but it's a chance
It's an irrelevant chance. I COULD flip a coin 10000 times and never land tails, but no one in their right mind is going to say its actually possible. By the same token, if you have an overwhelming number of pulls, the RNG becomes completely irrelevant.
this is a truly awful comparison, as the chances aren’t the same.
Odds work the same way, but ok. How about 2*, or 3*? How many endgamers are missing these champions? At some point, your number of pulls overwhelm the RNG factor.
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
Have you opened more premium hero crystals or more 4* crystals?
Again your last point is completely stupid. I doubt that most of the players have opened more than 2,000-3,000 4* crystals. So why you say 1 million crystals?
I've always considered it logical to take things to the extremes and work backwards, or simply and work forwards. No one like the coin analogy, and you don't like a million crystals.
Why don't we try a dice then, similar to a crystal but down to 6 options instead of 200 (less some number that exclusives).
Odds are 17% you'll roll any particular number on any particular roll, so how many tries is it going to take to roll 1 for example. Well, we can calculate the odds of an event given a particular set of trials. Given 10 trials, you'll roll a 1 at least once 83% of the time. 100 times though? Virtually 100% (99.99999919% to be precise).
So apply this to Sabretooth, in a crystal with 200, odds of .5%, significantly less than the 17% we started with in the dice example.
100 trials in this situation results in a mediocre 39% 250 trials = 71% 500 trials = 91% 1000 trials = 99.335% 1500 trials = 99.946% 2000 trials = 99.996% 2500 trials = 99.9996%
and so forth.
How many 4* crystals and 4* equivalents has an endgamer opened? That's going to be a very difficult question to answer. Between legendary, Ultimate, PHC, Cavs, GMCs and 4* crystals it's pretty hard to say. Maybe it's not close to 2500, could be 1000 to 5000 reasonably, but the point is that with an overwhelming number of trials, you will get Sabretooth.
This doesn't even take into account dual class crystals which allow for increased odds as well.
Should my math be wrong, I'd love to know. I find probability fascinating.
The direct way to calculate this quickly is with logarithms. The math goes like this. Suppose we want to know how many crystals to open before the odds of missing a single champ are one in a billion. The equation looks like this:
(199/200)^n = 1/1000000000
We then log both sides:
n log (199/200) = log (1/1000000000) = -9 n = -9 / log (199/200) ~= 4134
For one in a million odds, it takes about 2756 crystals. For one in a billion odds, it takes about 4134 crystals. Somewhere between those two, most players will have every champ (at least of the champs that have been in the crystal long enough for these pulls to matter). Scarlet Witch has been in the crystals since basically forever. Most people who have opened thousands of 4* crystals have the bulk or all of those openings containing that champion (outside dual crystals of the wrong class and the occasional special crystal). So it comes down to how many crystals a player has opened.
I honestly contemplated tagging you because I knew you'd have the answer. Thanks for the explainer.
Comments
If you had 1 million 4* crystals, you will absolutely receive every single 4* champion available in the pool. If you have 1 4* crystal, you will most likely not receive a specific 4* champion. Somewhere between these two extremes is a point where you have become 99.999999% to receive every champion. I'd wager you need fewer pulls then you think to achieve this.
Why don't we try a dice then, similar to a crystal but down to 6 options instead of 200 (less some number that exclusives).
Odds are 17% you'll roll any particular number on any particular roll, so how many tries is it going to take to roll 1 for example. Well, we can calculate the odds of an event given a particular set of trials. Given 10 trials, you'll roll a 1 at least once 83% of the time. 100 times though? Virtually 100% (99.99999919% to be precise).
So apply this to Sabretooth, in a crystal with 200, odds of .5%, significantly less than the 17% we started with in the dice example.
100 trials in this situation results in a mediocre 39%
250 trials = 71%
500 trials = 91%
1000 trials = 99.335%
1500 trials = 99.946%
2000 trials = 99.996%
2500 trials = 99.9996%
and so forth.
How many 4* crystals and 4* equivalents has an endgamer opened? That's going to be a very difficult question to answer. Between legendary, Ultimate, PHC, Cavs, GMCs and 4* crystals it's pretty hard to say. Maybe it's not close to 2500, could be 1000 to 5000 reasonably, but the point is that with an overwhelming number of trials, you will get Sabretooth.
This doesn't even take into account dual class crystals which allow for increased odds as well.
Should my math be wrong, I'd love to know. I find probability fascinating.
(199/200)^n = 1/1000000000
We then log both sides:
n log (199/200) = log (1/1000000000) = -9
n = -9 / log (199/200) ~= 4134
For one in a million odds, it takes about 2756 crystals. For one in a billion odds, it takes about 4134 crystals. Somewhere between those two, most players will have every champ (at least of the champs that have been in the crystal long enough for these pulls to matter). Scarlet Witch has been in the crystals since basically forever. Most people who have opened thousands of 4* crystals have the bulk or all of those openings containing that champion (outside dual crystals of the wrong class and the occasional special crystal). So it comes down to how many crystals a player has opened.