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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[–] 2 points 1 year ago* (last edited 1 year ago) (8 children)

That'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.

E: consider a die weighted to favor 6. Standard dice have opposite faces add up to 7. If this die favors 6 to the extent it never rolls a 1, any time a 6 is rolled on the second die can never result in a total roll of 7.

E2: I has the dumb. Apologies.

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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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  • [–] 2 points 1 year ago (2 children)

    So long as you roll the weighted die first, the odds the unweighted die lands on the number you need is 1/6. If you roll the unweighted die first though, your odds of getting the needed number are no longer 1/6.

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  • [–] 4 points 1 year ago

    The odds that the first die landed on the correct number are 1 in 6, though, so if you're considering the throw of both dice as a whole, the chance is still 1 in 6 regardless of which die you throw first. (If you're rolling the unweighted die first and then evaluating the chance of getting a 7 based on that outcome, then you're correct.)

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