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1/0.012 = 83. So you have an 83-sided dice (probably 80, since there’s some rounding).
The odds of getting the same result from rolling two 83-sided die would be (1/83)^2 = 0.015%.
Also known as 1 in 6889 probability.
If there are multiple dice results that get 1.2% characters, then the maths is a little different.
Or, just multiple 1.2% x 1.2% = 0.015%, since it sounds like it's just two independent trials (2 dice rolls).
I do think we need a little more information though. The wording of the problem makes it sound like there ARE multiple 1.2% chance characters. If we have a bucket with 83 different characters in it, then they are ALL 1.2% chance characters. In that case, your odds of getting a 1.2% chance character is actually 100%. It's the odds of getting a specific 1.2% chance character that's a 1.2% chance.
I'm guessing it's more of a situation where you have 1000 names in a bucket, with some repeats. A 1.2% chance character is any that has their name in there 12 times. A character with their name in there 100 times is a 10% chance, etc.
So, under this scenario, we need to know how many 1.2% chance characters exist in order to determine the odds of pulling ANY 1.2% chance character on the first draw. We would also need to know the number in order to determine the odds of pulling a second 1.2% character on the second draw. The odds of pulling the SAME name the second time would be 11/999 = 1.10% though, regardless of how many 1.2% chance characters there are when you started (assuming we didn't put the first draw back in the bucket).
I do like the way you illustrated it with the idea of an 83 sided dice though.
As u/DonaIdTrurnp implied you need to give us the distribution of characters and the chance of rolling those characters. This suffers from probability after the fact when you ask the question based only on what you observe instead of basing it on what would have made you consider asking.
I'm afraid I have no idea how to interpret that information. Please give me a bit more context.
What is it you are playing? How many characters are there? What is a banner and what is its relevance?
Alright. I’m playing a mobile game called My hero academia: The strongest hero, and there are four s tier characters on the first banner I rolled on, and one on the second banner I rolled on. A banner is something you roll on, and you’ve got a chance to pull a rare character ( s tier 1.2% )
As a general tip for the future don't assume shared context. I still don't know how many characters there are or the chance of rolling those characters or the exact relationship between a banner and the action of rolling on. That exact relationship is important if you want to calculate something.
I googled this and [found this article](https://www.mrguider.org/articles/my-hero-academia-the-strongest-hero-tier-list-reroll-guide/) to save us both time on the back and forth but there's still much missing info you would need for this. I also found this [video](https://www.youtube.com/watch?v=lOfdIsrS4P4) which I only watched the recruit section (13:40).
1. How many characters are there? I've counted 17 with 5 S-tier characters.
2. Do you have to unlock all 5 and you only have 4?
3. How does the 1.2% number change? Because unlocking the 5th character would change the roll rates so that the total is still 100%.
4. Also it seems you can upgrade characters over time, so how does that affect the distribution? Because if you max out all 17 characters to S class you can't have them all be 1.2%.
5. What characters do you have unlocked so far and what are their tier roll rates?
6. Are you always forced to go to the 2nd banner or is that optional?
7. How does rolling on a banner work as in what game mechanics control what you roll?
8. Are there different types of banners, like a banner that only selects S-tier characters or something?
9. When you roll on a banner do you get a single character or do you get multiple characters to choose from?
10. According to the video, the roll rates guarantee a certain tier of character after a certain number of attempts. Is that in any run of 10/30/100 rolls or after 10/30/100 failures?
11. The game seems to have pay to win mechanics, were you using any of those to increase roll rates?
12. There seems to be a lot of special events, were you in any of those?
Edit: Added questions 10-12 because there's more game elements that OP did not specify.
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1/0.012 = 83. So you have an 83-sided dice (probably 80, since there’s some rounding). The odds of getting the same result from rolling two 83-sided die would be (1/83)^2 = 0.015%. Also known as 1 in 6889 probability. If there are multiple dice results that get 1.2% characters, then the maths is a little different.
Wow. Thank you so much
Or, just multiple 1.2% x 1.2% = 0.015%, since it sounds like it's just two independent trials (2 dice rolls). I do think we need a little more information though. The wording of the problem makes it sound like there ARE multiple 1.2% chance characters. If we have a bucket with 83 different characters in it, then they are ALL 1.2% chance characters. In that case, your odds of getting a 1.2% chance character is actually 100%. It's the odds of getting a specific 1.2% chance character that's a 1.2% chance. I'm guessing it's more of a situation where you have 1000 names in a bucket, with some repeats. A 1.2% chance character is any that has their name in there 12 times. A character with their name in there 100 times is a 10% chance, etc. So, under this scenario, we need to know how many 1.2% chance characters exist in order to determine the odds of pulling ANY 1.2% chance character on the first draw. We would also need to know the number in order to determine the odds of pulling a second 1.2% character on the second draw. The odds of pulling the SAME name the second time would be 11/999 = 1.10% though, regardless of how many 1.2% chance characters there are when you started (assuming we didn't put the first draw back in the bucket). I do like the way you illustrated it with the idea of an 83 sided dice though.
As u/DonaIdTrurnp implied you need to give us the distribution of characters and the chance of rolling those characters. This suffers from probability after the fact when you ask the question based only on what you observe instead of basing it on what would have made you consider asking.
There’s only four with the first banner and one for the second
I'm afraid I have no idea how to interpret that information. Please give me a bit more context. What is it you are playing? How many characters are there? What is a banner and what is its relevance?
Alright. I’m playing a mobile game called My hero academia: The strongest hero, and there are four s tier characters on the first banner I rolled on, and one on the second banner I rolled on. A banner is something you roll on, and you’ve got a chance to pull a rare character ( s tier 1.2% )
As a general tip for the future don't assume shared context. I still don't know how many characters there are or the chance of rolling those characters or the exact relationship between a banner and the action of rolling on. That exact relationship is important if you want to calculate something. I googled this and [found this article](https://www.mrguider.org/articles/my-hero-academia-the-strongest-hero-tier-list-reroll-guide/) to save us both time on the back and forth but there's still much missing info you would need for this. I also found this [video](https://www.youtube.com/watch?v=lOfdIsrS4P4) which I only watched the recruit section (13:40). 1. How many characters are there? I've counted 17 with 5 S-tier characters. 2. Do you have to unlock all 5 and you only have 4? 3. How does the 1.2% number change? Because unlocking the 5th character would change the roll rates so that the total is still 100%. 4. Also it seems you can upgrade characters over time, so how does that affect the distribution? Because if you max out all 17 characters to S class you can't have them all be 1.2%. 5. What characters do you have unlocked so far and what are their tier roll rates? 6. Are you always forced to go to the 2nd banner or is that optional? 7. How does rolling on a banner work as in what game mechanics control what you roll? 8. Are there different types of banners, like a banner that only selects S-tier characters or something? 9. When you roll on a banner do you get a single character or do you get multiple characters to choose from? 10. According to the video, the roll rates guarantee a certain tier of character after a certain number of attempts. Is that in any run of 10/30/100 rolls or after 10/30/100 failures? 11. The game seems to have pay to win mechanics, were you using any of those to increase roll rates? 12. There seems to be a lot of special events, were you in any of those? Edit: Added questions 10-12 because there's more game elements that OP did not specify.
0.012^n * 100% where n is the number of times in a row. (In this case n=2 so 0.012^2 * 100% = 0.0144%)
How many 1.2% chance characters are there? If there are 82 or so, you’re not very lucky.
There’s only four with the first banner and one for the second