Question About Dice Rolls

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Well, I suppose since I started this mess, I should make a contribution

I did 4d6 in excel, and came up with the following. The first column is the total damage, the second is the number of ways to get it (totals 1296), and the third is the percentages.

4 - 1 - 0.08%
5 - 4 - 0.31%
6 - 10 - 0.77%
7 - 20 - 1.54%
8 - 35 - 2.70%
9 - 56 - 4.32%
10 - 80 - 6.17%
11 - 104 - 8.02%
12 - 125 - 9.65%
13 - 140 - 10.80%
14 - 146 - 11.27%
15 - 140 - 10.80%
16 - 125 - 9.65%
17 - 104 - 8.02%
18 - 80 - 6.17%
19 - 56 - 4.32%
20 - 35 - 2.70%
21 - 20 - 1.54%
22 - 10 - 0.77%
23 - 4 - 0.31%
24 - 1 - 0.08%

The results for 13-15 are very close to Aldeth's, but not quite right, but it may be a rounding difference. To get less than 9, it's actually 126, again close to Aldeth's 128. I know I'm not actually helping with the math here, but right now, I'm too busy to try.

 

Hey splunge,

I think your distribution looks to be about right. I'm not saying this because I'm a math whiz or "Excel whiz" but rather because I remember seeing a similar distribution ("normal distribution"?) in the 1st edition AD&D PHB (or DMG) ... I guess in the later editions they felt it was too geeky for the average gamer to handle

 

I'd love to contribute something worthwhile to this thread but as seeing all that maths takes me back to my school days I'll just settle for posting those smilies and leave it at that.

 

I just redid my math, and Splunge is correct. It should be 10.80%, not 10.50%. I didn't both redoing the rest of the calculations though. How did you do that with Excel? It seems like that if doing it with 6 dice wasn't too bad, doing it with 10 wouldn't be that bad either. I'm just hoping to discover a trend. My gut instinct is that the more dice you include the chances for getting the most common roll would go down, simply because there are far more possibilities. Regardless of how many dice you roll, the greatest chance is going to be the average of the highest and lowest possible total. However, with 6 dice you're dividing that percentage among 30 possible end results, whereas with 10 dice you're dividing the percentage among 50 possible end results.

 

In excel, I just had 1 column for each die; 1st column has 1, paired up to 1-6 in second column, etc. Do cell ref's to the cell above, (or +1 when it changes from 1 to 2, 2 to 3, etc.). Copy and paste. You'll end up with one row for each possible combiation. Then add each row across to get total damage. Then list each possible damage total, do a Countif function, and total it up. Pretty easy, but the spreadsheet is pretty big. I did it for 6d6, but I can't do more, because it uses 46,656 rows, and I only have 65,536 available. Here are the results:

6 - 1 - 0.002%
7 - 6 - 0.013%
8 - 21 - 0.045%
9 - 56 - 0.120%
10 - 126 - 0.270%
11 - 252 - 0.540%
12 - 456 - 0.977%
13 - 756 - 1.620%
14 - 1,161- 2.488%
15 - 1,666 - 3.571%
16 - 2,247 - 4.816%
17 - 2,856 - 6.121%
18 - 3,431 - 7.354%
19 - 3,906 - 8.372%
20 - 4,221 - 9.047%
21 - 4,332 - 9.285%
22 - 4,221 - 9.047%
23 - 3,906 - 8.372%
24 - 3,431 - 7.354%
25 - 2,856 - 6.121%
26 - 2,247 - 4.816%
27 - 1,666 - 3.571%
28 - 1,161 - 2.488%
29 - 756 - 1.620%
30 - 456 - 0.977%
31 - 252 - 0.540%
32 - 126 - 0.270%
33 - 56 - 0.120%
34 - 21 - 0.045%
35 - 6 - 0.013%
36 - 1 - 0.002%

 

I just want to point out that you are all completely nuts. If my calculations are correct, you need to get out more!

 

I see now why I'm a Physical Education major. As Homer would say DOH!