Inspired by DnD. This is driving me nuts.
Say you have to roll a certain target number or higher, x, on a 20 sided dice to win. You have a modifier, z, which you can either add to the number you roll, y, or subtract from the target number x.
When I work it out with real numbers, the probability of sucess is the same regardless of whether you choose to add your modifier to the number you roll, or subtract it from the threshold number you need to achieve. Both cases have the same fail states. It makes intuitive sense, however I'm unable to generalize why this is true.
Can anyone demonstrate why this is true? I feel like I am missing something very straightforward here lol.
Pic related is an example of what I mean.
Say you have to roll a certain target number or higher, x, on a 20 sided dice to win. You have a modifier, z, which you can either add to the number you roll, y, or subtract from the target number x.
When I work it out with real numbers, the probability of sucess is the same regardless of whether you choose to add your modifier to the number you roll, or subtract it from the threshold number you need to achieve. Both cases have the same fail states. It makes intuitive sense, however I'm unable to generalize why this is true.
Can anyone demonstrate why this is true? I feel like I am missing something very straightforward here lol.
Pic related is an example of what I mean.
