Dice Math - what are the chances for these rolls?

[Meds]

(A)
0 0.077%
1 0.309%
2 0.772%
3 1.543%
4 2.701%
5 4.321%
6 6.173%
7 8.025%
8 9.645%
9 10.802%
10 11.265%
11 10.802%
12 9.645%
13 8.025%
14 6.173%
15 4.321%
16 2.701%
17 1.543%
18 0.772%
19 0.309%
20 0.077%

(B) What are the chances to roll a match (e.g. all 2s or all 5s)?
1/216

(C) What are the chances to roll one *specific* match?
1/1296

 

[jerichothebard]

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

oops, my bad. You're right...

that's a 16^18) chance, or
1:101,559,956,700,000

or, 1 in an hundred trillion, more or less.

which is a .0000000000000098 % chance. more or less



eewww... messy.

I retract my earlier statement about it being possible. It is still technically possible, of course, but I sincerly doubt it has ever actually, legitimately happened in the 30+ years of RPG history.

and if I DID see it happen, I still wouldn't believe it.

jtb

 

[Hardhead]

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.

The probability calculator linked to gave much lower chances, kind of. I put in 18d6 for the roll, and looked for the result of 108, but it said 0%. Apparently, it wouldn't calculate that low. The lowest percentage chance it gave was for 93, and it said the probability of that was .001%.

Is it wrong?

 

[SubMensa]

What's the chances of rolling six 18s using the old 2e 3d6 method?

Using the math presented before the odds that you would roll eighteen straight sixes in a row is:
1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6*1/6 or
1 in 34012224 or
0.0000029401194111858136651105202647142%
According to windows calculator. Now I dont have enough schoolin' to tell you exactly how much, but the odds of rolling five eighteens and one seventeen are considerably better.

Good luck!
Now I have never personally seen it happen, though I have witnessed somebody come close. I think it was all 18's with a 17 and 16. Lucky monkey, we all said he had sold his soul for good dice rolls. Me on the other hand, I'm lucky to break 16 in my stats with the new 4d6 drop lowest method.

 

[jerichothebard]

...1 in a hundred trillion, more or less.

The good news, is, of course, that super-loser man is equally as unlikely to be rolled.

Now, super-average man... (all 10's)...

let's see. there are 27 ways to make 10 on 3d6, out of 216 possible rolls.

1/x = (27/216)^6
1/x = .0000038147
x = 262,144


So, super-average man has a 1:262,144 chance of being rolled randomly on 3d6.

still pretty darn unlikely, but far MORE likely that super-hero man!

 

[reiella]

The good news, is, of course, that super-loser man is equally as unlikely to be rolled.

Now, super-average man... (all 10's)...

let's see. there are 27 ways to make 10 on 3d6, out of 216 possible rolls.

1/x = (27/216)^6
1/x = .0000038147
x = 262,144


So, super-average man has a 1:262,144 chance of being rolled randomly on 3d6.

still pretty darn unlikely, but far MORE likely that super-hero man!

I can't help myself .

So pretty much every generic human was roughly 1 in 250,000 (rounded for nice quirkiness).

 

[Nightfall]

"Chance favors the prepared mind"

"Chaos is essential the stock market only with fewer investors."

"Time and tide wait for no man, but chaos just screws with you"

Just some thinking when it comes to trying to determine percentages.

 

[orsal]

The probability calculator linked to gave much lower chances, kind of. I put in 18d6 for the roll, and looked for the result of 108, but it said 0%. Apparently, it wouldn't calculate that low. The lowest percentage chance it gave was for 93, and it said the probability of that was .001%.

Is it wrong?

No, it rounds all numbers to the nearest .001%, and the probability of 18 6's in a row, rounded to the nearest .001%, is 0.000%.

 

[Agback]

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?

As you can readily confirm, the number of combinations where the faces total to each sum is as follows:

0 1
1 4
2 10
3 20
4 35
5 56
6 80
7 104
8 125
9 140
10 146
11 140
12 125
13 104
14 80
15 56
16 35
17 20
18 10
19 4
20 1

So the number of combinations summing to each total or less is

0 1
1 5
2 15
3 35
4 70
5 126
6 206
7 310
8 435
9 575
10 721
11 861
12 986
13 1090
14 1170
15 1226
16 1261
17 1281
18 1291
19 1295
20 1296

For the associated probabilities, divide by the total number of combinations (6^4). The results are approximately:

0 0.077%
1 0.386%
2 1.157%
3 2.701%
4 5.401%
5 9.722%
6 15.895%
7 23.920%
8 33.565%
9 44.367%
10 55.633%
11 66.435%
12 76.080%
13 84.105%
14 90.278%
15 94.599%
16 97.299%
17 98.843%
18 99.614%
19 99.923%
20 100.000%

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

Six different combinations count as matches. P = 6/1296 = 1/216 which is approximately 0.46296%.

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

Each specific match is one combination out of 1296, so P = 1/1296, which is approximately 0.07716%.

Regards,


Agback

 

[The Cardinal]

thanks guys!