This post has potentially manipulated dice roll results.
(For a 32!!) Roll 4d8 = 8 + 6 + 3 + 4= 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%
(For a 32!!) Roll 4d8 = 3 + 3 + 2 + 3= Unable to parse dice roll.
So an 18 with 4d6 drop lowest is 21 / 1296 = 1.62 %
A 17 with 4d6 drop lowest is 54 / 1296 = 4.17 %
and a 16 with 4d6 drop lowest is 94 / 1296 = 7.25 %
So, we can add the percentages for 17 + 18 to get the probability of at least a 17 ... 5.79 %
And we can add the percentages for 16 + 17 + 18 to get the probability of at least a 16 ... 13.04 %
But the real question is usually, what are the chances of getting an 18 as a skill out of six rolls? To get that, we compute the chance of not getting an 18 in six rolls, and subtract that from 100%.
1 - (1 - 0.0162) ^ 6 = 9.33 %
But this includes getting one 18, or two, or three, or four ...
What is the probability of getting just one 18?
(1 - 0.0162) ^ 5 x 0.0162 = 1.49 %
What is the probability of getting at least one 17 or better out of 6 skill rolls?
1 - (1 - 0.0579) ^ 6 = 30.08 %
And the probability of only one score of 17 or 18?
(1 - 0.0579) ^ 5 * 0.0579 = 4.30 %
What is the probability of getting at least one 16 or better out of 6 skill rolls?
1 - (1 - 0.1304) ^ 6 = 56.76 %
And the probability of getting only one score of 16, 17 or 18?
My online big sib is fry_doodles, they’re awesome!
My best friendos: TheGatoLover, Bananer28046, and I’m probably forgetting some… Arboreal Masterpiece and Sorlock Fanatic! Ace (part of the garlic bread cult), Demiaro, genderfluid, and a pan pancake! :3 Bye bye!
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4d8=15
7th Member of the High Roller Society
6+3+3+7=19
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
4d8=16
.
7th Member of the High Roller Society
4+6+2+4=16
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
4d8=17
.
7th Member of the High Roller Society
:4+1+6+6=17
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
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
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
(For a 32!!) Roll 4d8 = 8 + 6 + 3 + 4= 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
8+5+8+5=26
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
4d8 attempt: 4 + 5 + 5 + 6 = 20
Last to know and first to be blamed...
As a free action, can I regret my life choices?
Hi merlin!
4+7+7+8=26
And, for my last post, what are the chances of rolling a 24, on 4d8?
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
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?
4d8=19
7th Member of the High Roller Society
Gato, for ones with d6? yikes!
1 / 1296 = 0.077% chance.
(For a 32!!) Roll 4d8 = 3 + 3 + 2 + 3= Unable to parse dice roll.
So an 18 with 4d6 drop lowest is 21 / 1296 = 1.62 %
A 17 with 4d6 drop lowest is 54 / 1296 = 4.17 %
and a 16 with 4d6 drop lowest is 94 / 1296 = 7.25 %
So, we can add the percentages for 17 + 18 to get the probability of at least a 17 ... 5.79 %
And we can add the percentages for 16 + 17 + 18 to get the probability of at least a 16 ... 13.04 %
But the real question is usually, what are the chances of getting an 18 as a skill out of six rolls? To get that, we compute the chance of not getting an 18 in six rolls, and subtract that from 100%.
1 - (1 - 0.0162) ^ 6 = 9.33 %
But this includes getting one 18, or two, or three, or four ...
What is the probability of getting just one 18?
(1 - 0.0162) ^ 5 x 0.0162 = 1.49 %
What is the probability of getting at least one 17 or better out of 6 skill rolls?
1 - (1 - 0.0579) ^ 6 = 30.08 %
And the probability of only one score of 17 or 18?
(1 - 0.0579) ^ 5 * 0.0579 = 4.30 %
What is the probability of getting at least one 16 or better out of 6 skill rolls?
1 - (1 - 0.1304) ^ 6 = 56.76 %
And the probability of getting only one score of 16, 17 or 18?
(1 - 0.1304) ^ 5 x 0.1304 = 6.48 %
4d8=22
7th Member of the High Roller Society
(For a 32!!) Roll 4d8 = 2 + 1 + 7 + 1= 11
4+4+1+4=13
Hello! Call me Tana or 타나
My pronouns are Any/All/BOC
I will always support you. Because that is my way of showing how much I care
Current List of Children: Golden, Salem, Wes, Aspen, Link, SuperDog, and Foalin.
I have Autism. And, you would probably call me Trans, and a Pansexual pancake
Current Dice Code: [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] + [roll]1d6[/roll] = [roll][roll:-5]+[roll:-4]+[roll:-3]+[roll:-2]+[roll:-1][/roll]
(For a 32!!) Roll 4d8 = 4 + 4 + 2 + 4= 14
32 ATTEMPT:8+3+2+3=16
Heyo, I’m Starry, aka Aspen!
My hobbies: reading, crocheting, tennis, murder, arson, homicide :3 Pronouns: any!
My online big sib is fry_doodles, they’re awesome!
My best friendos: TheGatoLover, Bananer28046, and I’m probably forgetting some… Arboreal Masterpiece and Sorlock Fanatic! Ace (part of the garlic bread cult), Demiaro, genderfluid, and a pan pancake! :3 Bye bye!