A magic square is a type of number grid where the sum of the numbers in each row, column and diagonal add up to the same number. Wikipedia contains an extensive entry on magic squares with many examples. We can use a 6x6 magic square to balance ability score arrays. There are several examples of 6x6 magic squares, but here is just one:
MagicCol 1 Col 2 Col 3 Col 4 Col 5 Col 6 Total Square Row 1132218271120 111 Row 231 436 929 2 111 Row 3122114231625 111 Row 430 3 53234 7 111 Row 5172610191524 111 Row 683528 1 633 111 Total111 111 111 111 111 111
We could use the magic square with a spreadsheet, but we don’t need to. Instead, copy the magic square to your battle mat. Leave enough spacebetween each number for a 3 x 5 index card.
Then create 36 ability scores. The traditional 4d6 keep 3 method will work fine for this. Write each score on a separate index card and sort the cards from highest to lowest.
Finally, place your cards on the battle mat. Place the first card on the space with the 1, the second card on the space with the 2, etc. When you are done, you will end up with a grid that looks something like this:
MagicCol 1 Col 2 Col 3 Col 4 Col 5 Col 6 Total Square Row 114121311151277 Row 2916 815 917. 74 Row 314121412131176 Row 491616 9 91675 Row 513111512131175 Row 616 8101716 976 Total757576767576
Players may now choose their ability score array from any row or column. They may even choose their scores from either diagonal. The total of all their ability scores will be around 75 points +/- 1 or 2.
Try it with your own set of scores and let me know how it works out!
If you want a fixed attribute total, there are a large number of solutions (for example, 18 cards, deal 3 per stat), but not all distributions of X points are equally useful.
If you want a fixed attribute total, there are a large number of solutions (for example, 18 cards, deal 3 per stat), but not all distributions of X points are equally useful.
True. The easiest, most direct way to get to a fixed attribute total is to decide on a total and any rules around what the array should look like. For example, "You have 75 points to distribute among 6 attributes. One attribute may be as low as 8 and one may be as high as 18. Everything else needs to be between 9 and 17." This isn't the easiest or most direct method, but it is interesting (to me at least) and it involves rolling dice.
BTW, I think the card method is also very cool and interesting.
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A magic square is a type of number grid where the sum of the numbers in each row, column and diagonal add up to the same number. Wikipedia contains an extensive entry on magic squares with many examples. We can use a 6x6 magic square to balance ability score arrays. There are several examples of 6x6 magic squares, but here is just one:
Magic Col 1 Col 2 Col 3 Col 4 Col 5 Col 6 Total
Square
Row 1 13 22 18 27 11 20 111
Row 2 31 4 36 9 29 2 111
Row 3 12 21 14 23 16 25 111
Row 4 30 3 5 32 34 7 111
Row 5 17 26 10 19 15 24 111
Row 6 8 35 28 1 6 33 111
Total 111 111 111 111 111 111
We could use the magic square with a spreadsheet, but we don’t need to. Instead, copy the magic square to your battle mat. Leave enough space between each number for a 3 x 5 index card.
Then create 36 ability scores. The traditional 4d6 keep 3 method will work fine for this. Write each score on a separate index card and sort the cards from highest to lowest.
Finally, place your cards on the battle mat. Place the first card on the space with the 1, the second card on the space with the 2, etc. When you are done, you will end up with a grid that looks something like this:
Magic Col 1 Col 2 Col 3 Col 4 Col 5 Col 6 Total
Square
Row 1 14 12 13 11 15 12 77
Row 2 9 16 8 15 9 17. 74
Row 3 14 12 14 12 13 11 76
Row 4 9 16 16 9 9 16 75
Row 5 13 11 15 12 13 11 75
Row 6 16 8 10 17 16 9 76
Total 75 75 76 76 75 76
Players may now choose their ability score array from any row or column. They may even choose their scores from either diagonal. The total of all their ability scores will be around 75 points +/- 1 or 2.
Try it with your own set of scores and let me know how it works out!
If you want a fixed attribute total, there are a large number of solutions (for example, 18 cards, deal 3 per stat), but not all distributions of X points are equally useful.
True. The easiest, most direct way to get to a fixed attribute total is to decide on a total and any rules around what the array should look like. For example, "You have 75 points to distribute among 6 attributes. One attribute may be as low as 8 and one may be as high as 18. Everything else needs to be between 9 and 17." This isn't the easiest or most direct method, but it is interesting (to me at least) and it involves rolling dice.
BTW, I think the card method is also very cool and interesting.