A normally weighted die has a weight of 16.67% for each face. No matter what result the first die rolls, the second one has a 16.67% chance of rolling the same number. Therefore, the average chance of a (total of) 7 is (16.67 + 16.67 + 16.67 + 16.67 + 16.67 + 16.67) / 6, or, 16.67%, or, 1 in 6.
Consider your example: Die #1 has the following weights:
1: 0%
2: 20%
3: 20%
4: 20%
5: 20%
6: 20%
In your example, if die 2 rolls a 6, there’s a 0% chance of a (total of) 7, instead of the normal 16.67%, but if die 2 rolls a 2, 3, 4, 5 or 6, it has a 20% chance of totaling 7, instead of the normal 16.67%.
The average chance, therefore, (0 + 20 + 20 + 20 + 20 + 20) / 6, or, 16.67%, or, 1 in 6.
KoboldCoterie@pawb.social 1 month ago
Doesn’t actually matter.
A normally weighted die has a weight of 16.67% for each face. No matter what result the first die rolls, the second one has a 16.67% chance of rolling the same number. Therefore, the average chance of a (total of) 7 is (16.67 + 16.67 + 16.67 + 16.67 + 16.67 + 16.67) / 6, or, 16.67%, or, 1 in 6.
Consider your example: Die #1 has the following weights:
In your example, if die 2 rolls a 6, there’s a 0% chance of a (total of) 7, instead of the normal 16.67%, but if die 2 rolls a 2, 3, 4, 5 or 6, it has a 20% chance of totaling 7, instead of the normal 16.67%.
The average chance, therefore, (0 + 20 + 20 + 20 + 20 + 20) / 6, or, 16.67%, or, 1 in 6.