As mentioned by others: No matter how it’s weighed, and no matter what it lands on, there’s a 1/6 probability that the other dice will land on the number you need to get seven. The probability of getting seven is independent of the “first” dice.
Comment on Odds of rolling a 7 with a weighted die
meco03211@lemmy.world 7 hours agoThat’s if it’s perfectly weighted. If it’s weighted to roll a 6, it might not always land on 6. This would lower the chance of rolling a 7 depending on what the overall probability profile is on the weighted die.
KoboldCoterie@pawb.social 6 hours ago
No, 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 2 hours ago
Added an example
KoboldCoterie@pawb.social 2 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.