Its 1/6 to roll a 7 with two 6-sided dice. You can get weighted dice that make it more likely to land on a certain number.

Does having one weighted dice change the odds at all? My gut says no but reality is a tricky bitch and I'm convinced im wrong somehow.

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[–] 3 points 1 year ago (2 children)

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).

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  • [–] 1 point 1 year ago (1 child)
  • [–] 2 points 1 year 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 number needed to total 7. 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 1, 2, 3, 4, or 5, it has a 20% chance of totaling 7, instead of the normal 16.67%.

    The average chance, therefore, is (0 + 20 + 20 + 20 + 20 + 20) / 6, or, 16.67%, or, 1 in 6.

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