Ability average scores

[Li Shenron]

Average of a 3d6 ability is easily 10.5

Has anybody calculated the average result of 4d6-lowest?
I get 12.25 (two decimals approx), but I would like to hear some confirmation!

Thanks

 

[bensei]

12.24459876543210

 

[Vinyafod]

I can confirm the average given by bensei plus the most likely stat to appear by rolling 4d6 dropping the lowest is a 13.
There are 1296 different combinations in which the dice can fall.
172 (13.27%) of these combinations sum up to a 13. Followed closely by 12 with 167 (12.89%) combinations and 14 with 160 (12.35%) possible combinations.

 

[Li Shenron]

Well... since it seems you have been calculating it all, can you post the % for all the possible result, from 3 to 18? That would be interesting, but I really can't afford all the computing

 

[Christian]

3 0.1%
4 0.3%
5 0.8%
6 1.6%
7 2.9%
8 4.8%
9 7.0%
10 9.4%
11 11.4%
12 12.9%
13 13.3%
14 12.3%
15 10.1%
16 7.3%
17 4.2%
18 1.6%

 

[Vinyafod]

As I said a total of 1296 combinations are possible... here we go:

Format: Stat -- no. of combinations -- percentage

3 -- 1 -- 0.08%
4 -- 4 -- 0.31%
5 -- 10 -- 0.77%
6 -- 21 -- 1.62%
7 -- 38 -- 2.93%
8 -- 62 -- 4.78%
9 -- 91 -- 7.02%
10 -- 122 -- 9.41%
11 -- 148 -- 11.42%
12 -- 167 -- 12.89%
13 -- 172 -- 13.27%
14 -- 160 -- 12.35%
15 -- 131 -- 10.11%
16 -- 94 -- 7.25%
17 -- 54 -- 4.17%
18 -- 21 -- 1.62%

 

[Nvvyn]

Whats the average roll for 5d6 and 6d6? just out of curiousity

 

[dcollins]

Kazam! A graph of the 4d6 (drop lowest) probablity distribution:

www.superdan.net/dndmisc/4d6curve.html

 

[Vinyafod]

5d6 drop lowest two gives 7776 possible dice combinations and the following results for each stat:

3 -- 1 -- 0.01%
4 -- 5 -- 0.06%
5 -- 15 -- 0.19%
6 -- 41 -- 0.53%
7 -- 90 -- 1.16%
8 -- 170 -- 2.19%
9 -- 296 -- 3.81%
10 -- 470 -- 6.04%
11 -- 665 -- 8.55%
12 -- 881 -- 11.33%
13 -- 1055 -- 13.57%
14 -- 1155 -- 14.85%
15 -- 1111 -- 14.29%
16 -- 935 -- 12.02%
17 -- 610 -- 7.84%
18 -- 276 -- 3.55%

So most likely stat is a 14. Stataverage is 13.43017

6d6 drop lowest 3 make 46656 combinations:

3 -- 1 -- 0.002%
4 -- 6 -- 0.01%
5 -- 21 -- 0.05%
6 -- 78 -- 0.17%
7 -- 207 -- 0.44%
8 -- 447 -- 0.96%
9 -- 914 -- 1.96%
10 -- 1677 -- 3.59%
11 -- 2706 -- 5.80%
12 -- 4135 -- 8.86%
13 -- 5646 -- 12.10%
14 -- 7056 -- 15.12%
15 -- 7770 -- 16.65%
16 -- 7551 -- 16.18%
17 -- 5535 -- 11.86%
18 -- 2906 -- 6.23%

Mos likely stat: 15
Average: 14.27379

 

[StGabriel]

averages for more dice

hit reply instead of edit, skip ahead