Originally Posted by Flooter
Doing it that way takes about an hour an a half to record 400 rolls. I've got some reading to do to analyze the data properly; it's here should anyone like to take a crack at it.


5
20
3
16
10
4
2
10
10
16
3
16
3
9
17
1
4
9
12
1
3
11
8
3
10
11
9
8
17
2
1
10
13
6
8
19
19
11
6
2
19
1
17
16
4
15
16
20
14
11
8
20
14
16
5
18
3
11
7
4
4
9
20
15
19
8
17
6
18
6
5
4
16
17
20
20
7
3
18
19
4
6
6
8
17
16
13
12
12
4
13
12
17
18
9
13
18
7
8
6
16
17
5
4
1
12
7
12
2
13
2
19
1
7
8
16
6
3
20
20
12
10
4
4
9
17
19
7
11
9
12
16
8
19
2
18
16
12
3
13
9
8
12
8
9
6
19
6
19
10
5
11
20
10
14
17
15
12
3
4
16
3
10
9
5
19
17
14
5
19
15
4
12
1
2
20
12
10
14
8
3
16
14
11
17
16
8
2
20
7
11
14
19
15
15
4
18
13
9
15
14
7
2
11
8
16
11
18
8
15
7
2
4
8
16
4
19
3
13
9
11
11
19
9
9
17
4
9
13
15
19
9
15
13
9
19
17
4
17
18
10
12
3
2
15
18
6
12
13
3
1
2
10
9
16
12
13
19
13
15
12
19
12
10
12
2
19
16
6
2
19
14
19
11
7
3
20
6
6
11
6
8
6
6
2
16
12
15
1
13
6
6
7
15
11
4
11
7
2
20
19
1
10
8
2
18
3
9
8
10
15
5
20
5
13
8
10
6
16
4
20
11
17
14
5
8
19
20
13
4
16
20
17
10
15
11
15
15
7
4
18
4
9
13
14
3
7
9
1
1
19
10
8
20
8
2
10
2
13
15
2
14
10
9
19
18
13
10
4
8
19
16
9
7
11
8
11
6
15
14
12
16
15
12
2
12
9
2
17
1
1
20
17
20
10
17
10
13
6
14
The average of this set of numbers is 10.72 +/- 0.28, so it is statistically consistent with the expected average of 10.5.

For the actual distribution of rolls, we use a chi-squared test. A d20 results in 20-1=19 degrees of freedom, and for a 95% confidence level gives a critical value of 30.14. We compare this to the chi-squared of the sample, which I calculated to be 20. 20 is less than 30.14, meaning that this overall distribution is indistinguishable from an even distribution at the 95% confidence level (ignoring the order of rolls).
- The most discrepant single value is 5: it only appears 10 times and it should appear 20 -> 2.2-sigma difference. Every other value is within ~1.5-sigma.

Plotting the rolls as a function of time...visually it looks okay(?), but I'm not sure how to easily statistically quantify this. I want the excel function:
> go through the 400 cells and if a cell's value is between 1-10, how likely is it that the following cell's value is between 11-20? [or use slightly different ranges]
A perfect rng system should give 50%, but Larian's self-described Weighted Dice should give >50%.