Calculating probability of intersecting sets (Dice rolls arranged in a grid)












0












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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.



I want to compare this system to the standard method of simply rolling 6 scores and using just those. 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.



I want to know 2 things:




  1. How do the bell curves/at-leasts for the SUM of all scores compare between the two methods

  2. How do the bell curves/at-leasts for the number of 18s you're likely to get compare between the two methods.


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.






probability dice







share|cite|improve this question









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  • 1




    $begingroup$
    Seems like it would be easy enough to code up a simulation and run it a few million times.
    $endgroup$
    – amd
    Jan 8 at 2:06
















0












$begingroup$


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.



I want to compare this system to the standard method of simply rolling 6 scores and using just those. 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.



I want to know 2 things:




  1. How do the bell curves/at-leasts for the SUM of all scores compare between the two methods

  2. How do the bell curves/at-leasts for the number of 18s you're likely to get compare between the two methods.


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.






probability dice







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    Seems like it would be easy enough to code up a simulation and run it a few million times.
    $endgroup$
    – amd
    Jan 8 at 2:06














0












0








0





$begingroup$


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.



I want to compare this system to the standard method of simply rolling 6 scores and using just those. 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.



I want to know 2 things:




  1. How do the bell curves/at-leasts for the SUM of all scores compare between the two methods

  2. How do the bell curves/at-leasts for the number of 18s you're likely to get compare between the two methods.


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.






probability dice







share|cite|improve this question









$endgroup$




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.



I want to compare this system to the standard method of simply rolling 6 scores and using just those. 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.



I want to know 2 things:




  1. How do the bell curves/at-leasts for the SUM of all scores compare between the two methods

  2. How do the bell curves/at-leasts for the number of 18s you're likely to get compare between the two methods.


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.






probability dice




probability dice






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 7 at 2:12









Isaac ReefmanIsaac Reefman

1013




1013








  • 1




    $begingroup$
    Seems like it would be easy enough to code up a simulation and run it a few million times.
    $endgroup$
    – amd
    Jan 8 at 2:06














  • 1




    $begingroup$
    Seems like it would be easy enough to code up a simulation and run it a few million times.
    $endgroup$
    – amd
    Jan 8 at 2:06








1




1




$begingroup$
Seems like it would be easy enough to code up a simulation and run it a few million times.
$endgroup$
– amd
Jan 8 at 2:06




$begingroup$
Seems like it would be easy enough to code up a simulation and run it a few million times.
$endgroup$
– amd
Jan 8 at 2:06










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