
♫ Eric Herman ♫
United States West Richland Washington
I like elephants. I like how they swing through trees.

10 GG if someone can give me the percentages for the following list... I'm looking for the probabilities of getting combinations of ranges (i.e., 13, 45) on multiple dice, for a skill check type of thing.
EDIT: I found a few of these... but it's the combination of different ranges that I'd like some help with in particular.
2 dice: (13) + (13) = 25% 2 dice: (13) + (45) 2 dice: (13) + 6 2 dice: (45) + (45) = 11% 2 dice: (45) + 6 2 dice: 6 + 6 = 3%
3 dice: (13) + (13) = 50% 3 dice: (13) + (45) 3 dice: (13) + 6 3 dice: (45) + (45) = 26% 3 dice: (45) + 6 3 dice: 6 + 6 = 7%
4 dice: (13) + (13) = 69% 4 dice: (13) + (45) 4 dice: (13) + 6 4 dice: (45) + (45) = 41% 4 dice: (45) + 6 4 dice: 6 + 6 = 13%
5 dice: (13) + (13) = 81% 5 dice: (13) + (45) 5 dice: (13) + 6 5 dice: (45) + (45) = 54% 5 dice: (45) + 6 5 dice: 6 + 6 = 20%
6 dice: (13) + (13) = 89% 6 dice: (13) + (45) 6 dice: (13) + 6 6 dice: (45) + (45) = 65% 6 dice: (45) + 6 6 dice: 6 + 6 = 26%
7 dice: (13) + (13) = 94% 7 dice: (13) + (45) 7 dice: (13) + 6 7 dice: (45) + (45) = 74% 7 dice: (45) + 6 7 dice: 6 + 6 = 33%

Paul Dale
Australia Moggill Queensland
Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn
When will the die stop rolling? What face finishes showing?

How about these:
2 dice: (13) + (13) = 1 / 4 = 25.0000 % 2 dice: (13) + (45) = 1 / 3 = 33.3333 % 2 dice: (13) + 6 = 1 / 6 = 16.6667 % 2 dice: (45) + (45) = 1 / 9 = 11.1111 % 2 dice: (45) + 6 = 1 / 9 = 11.1111 % 2 dice: 6 + 6 = 1 / 36 = 2.7778 %
3 dice: (13) + (13) = 1 / 2 = 50.0000 % 3 dice: (13) + (45) = 7 / 12 = 58.3333 % 3 dice: (13) + 6 = 1 / 3 = 33.3333 % 3 dice: (45) + (45) = 7 / 27 = 25.9259 % 3 dice: (45) + 6 = 1 / 4 = 25.0000 % 3 dice: 6 + 6 = 2 / 27 = 7.4074 %
4 dice: (13) + (13) = 11 / 16 = 68.7500 % 4 dice: (13) + (45) = 20 / 27 = 74.0741 % 4 dice: (13) + 6 = 101 / 216 = 46.7593 % 4 dice: (45) + (45) = 11 / 27 = 40.7407 % 4 dice: (45) + 6 = 31 / 81 = 38.2716 % 4 dice: 6 + 6 = 19 / 144 = 13.1944 %
5 dice: (13) + (13) = 13 / 16 = 81.2500 % 5 dice: (13) + (45) = 1085 / 1296 = 83.7191 % 5 dice: (13) + 6 = 185 / 324 = 57.0988 % 5 dice: (45) + (45) = 131 / 243 = 53.9095 % 5 dice: (45) + 6 = 215 / 432 = 49.7685 % 5 dice: 6 + 6 = 763 / 3888 = 19.6245 %
6 dice: (13) + (13) = 57 / 64 = 89.0625 % 6 dice: (13) + (45) = 581 / 648 = 89.6605 % 6 dice: (13) + 6 = 1687 / 2592 = 65.0849 % 6 dice: (45) + (45) = 473 / 729 = 64.8834 % 6 dice: (45) + 6 = 1729 / 2916 = 59.2936 % 6 dice: 6 + 6 = 12281 / 46656 = 26.3224 %
7 dice: (13) + (13) = 15 / 16 = 93.7500 % 7 dice: (13) + (45) = 43561 / 46656 = 93.3663 % 7 dice: (13) + 6 = 8323 / 11664 = 71.3563 % 7 dice: (45) + (45) = 179 / 243 = 73.6626 % 7 dice: (45) + 6 = 10423 / 15552 = 67.0203 % 7 dice: 6 + 6 = 7703 / 23328 = 33.0204 %
8 dice: (13) + (13) = 247 / 256 = 96.4844 % 8 dice: (13) + (45) = 16745 / 17496 = 95.7076 % 8 dice: (13) + 6 = 213781 / 279936 = 76.3678 % 8 dice: (45) + (45) = 5281 / 6561 = 80.4908 % 8 dice: (45) + 6 = 19219 / 26244 = 73.2320 % 8 dice: 6 + 6 = 663991 / 1679616 = 39.5323 %
9 dice: (13) + (13) = 251 / 256 = 98.0469 % 9 dice: (13) + (45) = 181405 / 186624 = 97.2035 % 9 dice: (13) + 6 = 37525 / 46656 = 80.4291 % 9 dice: (45) + (45) = 16867 / 19683 = 85.6932 % 9 dice: (45) + 6 = 48655 / 62208 = 78.2134 % 9 dice: 6 + 6 = 2304473 / 5038848 = 45.7341 %
10 dice: (13) + (13) = 1013 / 1024 = 98.9258 % 10 dice: (13) + (45) = 2473273 / 2519424 = 98.1682 % 10 dice: (13) + 6 = 8440421 / 10077696 = 83.7535 % 10 dice: (45) + (45) = 17635 / 19683 = 89.5951 % 10 dice: (45) + 6 = 3106939 / 3779136 = 82.2129 % 10 dice: 6 + 6 = 10389767 / 20155392 = 51.5483 %
11 dice: (13) + (13) = 509 / 512 = 99.4141 % 11 dice: (13) + (45) = 59737601 / 60466176 = 98.7951 % 11 dice: (13) + 6 = 13074743 / 15116544 = 86.4929 % 11 dice: (45) + (45) = 163835 / 177147 = 92.4853 % 11 dice: (45) + 6 = 17219543 / 20155392 = 85.4339 % 11 dice: 6 + 6 = 12909191 / 22674816 = 56.9318 %
12 dice: (13) + (13) = 4083 / 4096 = 99.6826 % 12 dice: (13) + (45) = 14996345 / 15116544 = 99.2049 % 12 dice: (13) + 6 = 107339687 / 120932352 = 88.7601 % 12 dice: (45) + (45) = 502769 / 531441 = 94.6049 % 12 dice: (45) + 6 = 59887373 / 68024448 = 88.0380 % 12 dice: 6 + 6 = 1346704211 / 2176782336 = 61.8667 %
 Pauli
Edit: extended the results up to 12 dice. Edit the second: reduce fractions to their lowest terms.

Alec
United States Houston Texas

Just skimmed, but noticed this mistake immediately.
Quote: 2 dice: (45) + (45) = 4 / 36 = 11.1111 % 2 dice: (45) + 6 = 4 / 36 = 11.1111 %
Those can't have the same probability. The 2nd one should be 2/36.

Richard Linnell
United States Bedford NH
I really need a new badge, avatar, and overtext. GM me with any ideas....
This is the seahorse valley

Texjets281 wrote: Just skimmed, but noticed this mistake immediately. Quote: 2 dice: (45) + (45) = 4 / 36 = 11.1111 % 2 dice: (45) + 6 = 4 / 36 = 11.1111 % Those can't have the same probability. The 2nd one should be 2/36.
I think it should be 1/18............always reduce your fractions!

K Septyn
United States Unspecified Michigan
SEKRIT MESSAGE SSSHHHHHHHHH

Texjets281 wrote: Just skimmed, but noticed this mistake immediately. Quote: 2 dice: (45) + (45) = 4 / 36 = 11.1111 % 2 dice: (45) + 6 = 4 / 36 = 11.1111 % Those can't have the same probability. The 2nd one should be 2/36.
Die A shows 6 (1in6 chance) while Die B shows 4 or 5 (2in6) = 2in36
plus
Die B shows 6 (1in6 chance) while Die A shows 4 or 5 (2in6) = 2in36
equals
4in36 chance.
You can make a classic probability table as well if you like visual proofs:
Die A 1 2 3 4 5 6 1 o o o o o o D 2 o o o o o o i 3 o o o o o o e 4 o o o o o X 5 o o o o o X B 6 o o o X X o

PenumbraPenguin
Australia Sydney NSW

Texjets281 wrote: Just skimmed, but noticed this mistake immediately. Quote: 2 dice: (45) + (45) = 4 / 36 = 11.1111 % 2 dice: (45) + 6 = 4 / 36 = 11.1111 % Those can't have the same probability. The 2nd one should be 2/36.
Paul is assuming that the dice are indistinguishable. If this assumption is valid, then he is correct. Looking at the question, I would agree with this interpretation, because if the dice are distinct then you need more information to describe the problem for more than 2 dice.
To get 45 on both dice, you can have (4,4), (4,5), (5,4) or (5,5), for 4/36.
To get 45 on one die and 6 on the other, you can have (4,6), (5,6), (6,4) or (6,5), for 4/36.
If you want to get 45 on the red die and 6 on the blue die, then you have only two possibilities (4,6) and (5,6), so your odds are 2/36.

Paul Dale
Australia Moggill Queensland
Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn
When will the die stop rolling? What face finishes showing?

Nope, they are the same.
The four possibilities for (45) and 6 are:
4 6 5 6 6 4 6 5
There is no overlap or duplication so the final chance is 4 in 36
For (45) and (45) the possibilities are:
4 4 4 5 5 4 5 5
Again four of them.
 Pauli

DC
United States Grand Rapids Michigan

solidhavok wrote: I think it should be 1/18............always reduce your fractions!
I know that this is not the point, but I'm a college math instructor, and...
NO! DON'T REDUCE THOSE FRACTIONS!!
It is much clearer to write 2/36 than 1/18. 2/36 clearly says "out of all 36 ways to roll the dice, 2 of them give the result I want", whereas 1/18 says... nothing, at least until you UNreduce it. Similar for cards: Might as well leave everything over 52, because that's the most useful value anyhow.

Richard Linnell
United States Bedford NH
I really need a new badge, avatar, and overtext. GM me with any ideas....
This is the seahorse valley

Actually, in several card games, it is best to have the reduced fraction. Particularly in Poker, where the odds of what you can get need to be balanced against the ratio of money that you are going to have invested vs. the amount of money in the pot. Even without talking about the relative payoff vs. the odds, knowing that there are 3 cards out of 51 just seems clunkier to me than saying 1 in 17.
It also is easier for many people to digest smaller fractions that are more familiar to them, and generally easiest (IMHO) to digest percentages.
1/18 says exactly what it means to say  one out of every eighteen rolls will yield the desired result, on average. Which, of course, is the exact same thing as saying 2/36.



