Comment on Odds of rolling a 7 with a weighted die
KoboldCoterie@pawb.social 1 day agoNo, it wouldn’t, as long as only one of the dice is weighted.
If it has a 95% chance to roll a 6, and a 5% chance to roll any other number, or a 100% chance to roll a 6, or a 0% chance to roll a 6, the chance is still 1 in 6 to roll a 7 with two dice (where either zero or one is weighted).
meco03211@lemmy.world 22 hours ago
Added an example
KoboldCoterie@pawb.social 22 hours 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.