For several weeks now I have been contemplating what appears to be a statistical paradox. Since my highest math skills consist of discretely copying Brian C.'s answers over his shoulder in Algebra class some yeas ago, I thought I would pose my muse to the board and see if one of you can answer it satisfactorily. Forgive the muddled language: it is a bit tricky to explain.
When D&D requires a percentile dice roll, say 25% or less, ordinarily you roll a d10 for the 10s column and a d10 for the ones column. Nothing strange about that, right? Its in the rules, right?
Well, consider this. If you roll your dice one at a time something odd appears to happen.
First, you roll the 10s column. In order to make your percentage, you have to roll a 1 or a 2. Statistically, you have a 1/5 or 20% chance of doing this.
Irrespective of whether you roll a million more dice after your first roll, the threshold you always need to pass through is 1 in 5. It must always pass through 20% on its way to whatever final roll you are trying to make. This initial chance can neither be lessened or increased by rolling the "1's" column, because the first roll is already tabulated by the time you roll the second.
Oddly, as it happens, the "1s" column appears even to *lessen* your chance of making your 25% because, if after the 10s roll (i.e. the 20% threshold), if you've gotten a "2", you've still only got a fifty-fifty chance of making your "1s" roll (i.e. 1-5 vs. 6-10).
Your 25% roll suddenly looks like 20% that only succeeds three fourths of the time.
Where did I go wrong?
When D&D requires a percentile dice roll, say 25% or less, ordinarily you roll a d10 for the 10s column and a d10 for the ones column. Nothing strange about that, right? Its in the rules, right?
Well, consider this. If you roll your dice one at a time something odd appears to happen.
First, you roll the 10s column. In order to make your percentage, you have to roll a 1 or a 2. Statistically, you have a 1/5 or 20% chance of doing this.
Irrespective of whether you roll a million more dice after your first roll, the threshold you always need to pass through is 1 in 5. It must always pass through 20% on its way to whatever final roll you are trying to make. This initial chance can neither be lessened or increased by rolling the "1's" column, because the first roll is already tabulated by the time you roll the second.
Oddly, as it happens, the "1s" column appears even to *lessen* your chance of making your 25% because, if after the 10s roll (i.e. the 20% threshold), if you've gotten a "2", you've still only got a fifty-fifty chance of making your "1s" roll (i.e. 1-5 vs. 6-10).
Your 25% roll suddenly looks like 20% that only succeeds three fourths of the time.
Where did I go wrong?
