The probability of rolling an 8 on an 8-sided die is 1/8.
Since each roll is an independent event, the probability of rolling an 8 four times in a row is found by multiplying the individual probabilities together:
I still see an 18 with 4d6 drop lowest as (4) x (1 x 1 x 1 x 6) / (1296) = 1.85%. One place said it was 21 / 1296 = 1.62%, and I can see how they get this number, I'm just not sure if it is right. But, if that is the right way, it's going to be harder for me to explain the formula for the rest.
I didn't even pay attention to this in depth and just assumed your 24/1296 solution was right, but obviously now that you say it, we have to exclude the case 6,6,6,6 from multiplying it by 4. therefore the formula should be ( (4)x(1x1x1x5)+1 )/(1296) which is 21/1296.
This makes a 17 interesting as well, because now we have to separate 2 cases again. Case 1: 6,6,5,X with X being one of {1,2,3,4} and Case 2: 6,6,5,5
Case 2 is easier to count the permutations. (6,6,5,5);(6,5,6,5);(6,5,5,6);(5,6,6,5);(5,6,5,6);(5,5,6,6). so 6 permutations Case 1 has 4!/2 =12 permutaions for each value that X can be.
So our final probability is ( (4)x(12)+(6) )/ (1296)=54/1296=1/24=4.17%
For the other numbers we will have to consider even more cases.
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
This post has potentially manipulated dice roll results.
:4+1+2+1=24
Rollback Post to RevisionRollBack
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
Case I: 6, 6, 4, A (6,6,4,A) (6,4,6,A) (6,4,A,6) (4,6,6,A) (4,6,A,6) (4,A,6,6) and the same number again with the 4 and the A switched making 12 permutations; A=3 so ...
12 x 3 = 36
Case II: 6, 5, 5, B (5,5,6,B) (5,6,5,B) (5,6,B,5) (6,5,5,B) (6,5,B,5) (6,B,5,5) and there are the same number again with the 6 and the B switched making 12 permutations; B=4 so ...
12 x 4 = 48
And the special cases (6,6,4,4) x 6 and (6,5,5,5) x 4 producing 10 extra cases.
Therefore, it appears we have (36 + 48 + 10) / 1296 = 7.25%
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
Hello! Call me Gato or Mother (Cat in Spanish) My pronouns are They/them, but they can fluctuate. I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic, but this community means the world to me; you cannot change that about me ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll] I have adopted Golden and Salem they are my D&D child.
4d8 attempt: 2 + 4 + 6 + 6 = 18
The probability of rolling an 8 on an 8-sided die is 1/8.
Since each roll is an independent event, the probability of rolling an 8 four times in a row is found by multiplying the individual probabilities together:
What is the probability of rolling a 6 four times in a row on a 6-sided dice?
The probability of rolling a 6-sided dice four times and having any three of those rolls result in a 6 is approximately 5/324 = 0.0154 = 1.54%.
Last to know and first to be blamed...
As a free action, can I regret my life choices?
(For a 32!!) Roll 4d8 = 1 + 2 + 3 + 6= 12
I don't know the spoiler trick.
Hope you have a good weekend.
I didn't even pay attention to this in depth and just assumed your 24/1296 solution was right, but obviously now that you say it, we have to exclude the case 6,6,6,6 from multiplying it by 4. therefore the formula should be ( (4)x(1x1x1x5)+1 )/(1296) which is 21/1296.
This makes a 17 interesting as well, because now we have to separate 2 cases again.
Case 1: 6,6,5,X with X being one of {1,2,3,4}
and Case 2: 6,6,5,5
Case 2 is easier to count the permutations. (6,6,5,5);(6,5,6,5);(6,5,5,6);(5,6,6,5);(5,6,5,6);(5,5,6,6). so 6 permutations
Case 1 has 4!/2 =12 permutaions for each value that X can be.
So our final probability is ( (4)x(12)+(6) )/ (1296)=54/1296=1/24=4.17%
For the other numbers we will have to consider even more cases.
4d8=13
7th Member of the High Roller Society
spare me, please
:2+6+6+5=19
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
okay :D
4d8=20
7th Member of the High Roller Society
6+3+4+2=15
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
4d8=13
7th Member of the High Roller Society
8+1+8+3=20
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
4d8=17
.
7th Member of the High Roller Society
4+6+2+4=16
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
4d8=17
.
7th Member of the High Roller Society
:4+1+2+1=24
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
Wow N-Nick, you're right on the mark with you're thinking. Yes, the 21 comes from a special case, where the extra 6 needs to be treated differently.
Deriving the expressions for the the other ones will be interesting.
(For a 32!!) Roll 4d8 = 6 + 1 + 5 + 7= 19
4+1+5+7=17
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
(For a 32!!) Roll 4d8 = 6 + 8 + 5 + 8= 27
Apologies Gato, but I'm going to geek out a bit.
So, let's look at the case for a 16 ...
Case I: 6, 6, 4, A (6,6,4,A) (6,4,6,A) (6,4,A,6) (4,6,6,A) (4,6,A,6) (4,A,6,6) and the same number again with the 4 and the A switched making 12 permutations; A=3 so ...
12 x 3 = 36
Case II: 6, 5, 5, B (5,5,6,B) (5,6,5,B) (5,6,B,5) (6,5,5,B) (6,5,B,5) (6,B,5,5) and there are the same number again with the 6 and the B switched making 12 permutations; B=4 so ...
12 x 4 = 48
And the special cases (6,6,4,4) x 6 and (6,5,5,5) x 4 producing 10 extra cases.
Therefore, it appears we have (36 + 48 + 10) / 1296 = 7.25%
Now, what are the chances of rolling 4 ones
Which has happened to me, twice
5+6+2+2=24
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
4d8 attempt: 5 + 1 + 7 + 6 = 19
Last to know and first to be blamed...
As a free action, can I regret my life choices?
Hi merlin!
7+4+8+8=27
And, for my last post, what are the chances of rolling a 24, on 4d8?
My pronouns are They/them, but they can fluctuate.
I am a teenage boy. I have ADHD, Depression, and anxiety. I'm also Genderfluid, Pansexual, and Aromantic,
but this community means the world to me; you cannot change that about me
ALL HAIL O_MERLIN_O. 4D8 ATTEMPT:[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]+[roll]1d8[/roll]=[roll][roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
I have adopted Golden and Salem they are my D&D child.
Had to consult an AI oracle (Gemini) for that one, as that's beyond my statistics background!
The probability of the dice values adding up to 24 when rolling an 8-sided dice four times is 161/4096, which is approximately 0.0393 (or 3.93%).
This is calculated by finding the number of successful outcomes (combinations that sum to 24) and dividing it by the total possible outcomes.
1. Total Possible Outcomes
Since the 8-sided die has 8 possible results for each of the 4 rolls, the total number of unique outcomes is: Total Outcomes = 8^4 = 4096
2. Number of Favorable Outcomes
We are looking for the number of integer solutions to the equation: x1 + x2 + x3 + x4 = 24
<skipping a metric ton of math, referred to as "Stars and Bars combined with the Principle of Inclusion-Exclusion (PIE)">
3. Final Probability
Probability = (Favorable Outcomes) / (Total Outcomes) = 161 / 4096
4d8 attempt: 7 + 1 + 5 + 5 = 18
Last to know and first to be blamed...
As a free action, can I regret my life choices?