Dice Math - what are the chances for these rolls?

[The Cardinal]

maybe somebody around here will be so nice and calculate the probabilities for the following dice rolls for me:


(A) When rolling 4D5 (i.e. the added results of 4 six-sided dice, each numbered from 0-5) or 4d6-4 - what are the chances to roll at or below
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20?

(B) What are the chances to roll a match (e.g. all 2s or all 5s)?


(C) What are the chances to roll one *specific* match?

 

[d4]

i don't feel like working out the table for (A), but i can handle (B) and (C) easily enough, because it's the same answer.

the chances of rolling 2-2-2-2 or 5-5-5-5 or (for example) 3-0-2-4 is the chances of rolling one side (1/6) taken to the power of how many times you are rolling; so (1/6)*(1/6)*(1/6)*(1/6) or (1/1296).

edit: well, it's 7:30 AM on a saturday morning, so i realize i may have misinterpreted the question or done the math wrong. no doubt someone else will come along to fix it up for me.

 

[shawnsse]

maybe somebody around here will be so nice and calculate the probabilities for the following dice rolls for me:


(A) When rolling 4D5 (i.e. the added results of 4 six-sided dice, each numbered from 0-5) or 4d6-4 - what are the chances to roll at or below
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20?

(B) What are the chances to roll a match (e.g. all 2s or all 5s)?


(C) What are the chances to roll one *specific* match?

(A) Estimated Answer: (Don't quote me if I'm wrong)
0 & 20 ~ 0.077%
1 & 19 ~ 0.154%
2 & 18 ~ 0.463%
3 & 17 ~ 1.851%
4 & 16 ~ 6.944%
5 & 15 ~ 11.111%
6 & 14 ~ 22.222%
7 & 13 ~ 33.333%
8 & 12 ~ 44.444%
9 & 11 ~ 55.556%
10 ~ 66.667%

(B) 1/6*1/6*1/6*1/6 =0.077% (1/1296)

(C) If i understand your question correctly, the answer is same as (B)

Shawn

 

[Dalamar]

Let's see... I had a refreshment lesson of propabilities just yesterday. I'm not going to count 'em all since that would be a lot of work, but I'll tackle some of 'em.

First, the chance to roll at or under 20 is, surprise surprise, 100%, since there is no possible way that you could roll over 20 with dice like that.

The chance to roll equal to or under 0 (or any specific pairing for that matter) is, as d4 pointed out, (1/6)^4=1/1296 (0,77%)

The chance to roll equal to or under 1 is the chance mentioned above plus the chance to roll a single 1 (1,0,0,0 or 0,1,0,0 etc), which is the chance we used above times four (there are four different places where the 1 can be), so it comes out as 5*1/1296=5/1296 (3,86%)

The chance to roll equal to or under 2 is the above-mentioned chance plus the chance to roll either a single 2 (again four different combinations of the first chance) or two 1s (1,1,0,0 or 1,0,1,0 etc., 6 different combinations) so the chance is 13*1/1296=13/1296 (1,00%)

The chance to roll equal to or under 3 is the above-mentioned chance plus the chance for a single 3 (four combinations), a 1 and a 2 (twelve combinations), or three 1s (four combinations), for a grand total of 33*1/1296=11/432 (2,55%)

And then I don't want to go on with that. The chance to get all of a kind (all 2s, all 5s) is 6/1296=1/216 (4,63%)

Edit - And no, I didn't count these values for over and hour and miss the post above because of that, I just ate right after I had clicked the Quick Reply button.

 

[physicscarp]

I found this really neat dice probability generator online. It should be able to handle anything you need to do.

Dice Probability Generator

Carp

 

[Hardhead]

I found this really neat dice probability generator online. It should be able to handle anything you need to do.

Dice Probability Generator

Carp

Thanks, that's a neat link. But I have a question it couldn't answer for me. What's the chances of rolling six 18s using the old 2e 3d6 method?

 

[jerichothebard]

Thanks, that's a neat link. But I have a question it couldn't answer for me. What's the chances of rolling six 18s using the old 2e 3d6 method?

1:1296

each attribute has a 1:216 chance of being an 18; there are six attributes, so that's 1: (216*6) = 1:1296, or 0.077% of the time.

in other words, rare enough that I would have to see it to believe it, but not impossible.

You are, incidentally, exactly as likely to roll super-loser man (straight 3's) as super-hero man (straight 18's).

super-average man (straight 10's or straight 11's), however, stands a 27:1296 chance, or 2.08%, of being rolled randomly 3d6.

 

[Sammael]

(1/6)^18, or 9.84e-15

 

[Sammael]

The probability of rolling six 18s is the same as the probability of rolling eighteen 6s.

 

[Altamont Ravenard]

1:1296

each attribute has a 1:216 chance of being an 18; there are six attributes, so that's 1: (216*6) = 1:1296.

in other words, rare enough that I would have to see it to believe it, but not impossible.

Um I believe the probability is MUCH lower than that. It's not (1/216)*6 but rather (1/216)^6.

AR