I've recently come across a stat rolling method used by some tabletop gamers that involves rolling 36 stat scores, placing them in a 6x6 grid, and selecting a row, column or diagonal of 6 values to use as your 6 scores. Lets call this method B.
I want to compare this system to the standard method of simply rolling 6 scores and using just those. As this is the original, we'll call it method A. With both methods each individual score is achieved by rolling 4 six-sided dice and adding the three highest values. I want to be able to compare these two methods with similar graphs/metrics to this anydice article.
The standard method obviously returns just one array of stats, so we need just one array to compare from the grid method.
I want to know 2 things:
- How do the bell curves/at-leasts for the SUM of all scores compare between the two methods
- For this the standard method's results should be compared to the array from the grid with the highest sum of scores; eg. Chance Method A yields at least x for the total sum of scores, compared to chance Method B yields at least one array with at least x for the total sum of scores.
- How do the bell curves/at-leasts for the number of 18s you're likely to get compare between the two methods.
- For this the standard method's results should be compared to the array that yields the highest number of 18s; eg. Chance Method A yields x scores of 18 compared to chance Method B yields at least one array with x scores of 18.
How do I calculate these probabilities?
I understand that for each roll, the probability of any specific result is the number of ways that result can be achieved divided by the number of possible results, so getting a 6 on a 6 sided dice is 1 in 6 (16.67%), getting an 18 on 3 6 sided dice (3d6) is 1 in 216 etc (0.4%), and the actual way of getting a single result, 4d6 drop lowest, can return a score of 18 by rolling 6 on any three dice, and anything on the other; so 21 in 1296 (1.62%).
What is getting me, though, is how I work out the number of possibilities and number of desired outcomes when 36 results are randomly entered into a 6x6 grid, and only certain sets (14) of 6 of these outcomes can be combined.
I'm not sure how to reliably test any hypothesis I may have, and even if I do formulate an idea and check it against some test tries I'd really want to get the actual principles of it.