The probability of rolling the same number on a die multiple times in a row & pre-rolling a number to change odds of the next roll.

Question

Specifically I’m asking about this situation that came up during a D&D game:

Say I’m rolling a 20 sided die, and I do not want to roll a 1. I know that the odds of rolling a 1 are 1/20.

I know that the chances of rolling a 1 twice in a row is (1/20 * 1/20), which is far a lower occurrence.

Say then, before I rolled my “real” roll, I rolled the die again and again until I landed on a 1, then proceeded to roll my “real” roll, would I have reduced the odds of rolling a 1 to (1/20 * 1/20), given that I’ve just rolled a 1 prior?

This is the logic I’m having trouble reasoning about and I’d appreciate it if anyone could clarify what is or is not accurate about the assumptions being made in this scenario.

In: Mathematics

Answer 1

Say you are going to roll the dice twice. Right now you have a 1/20 X 1/20 chance of rolling two 1’s. Now you roll one dice and it lands on a 1. You pick up the dice again ready to roll the 2nd time. You are no longer going to roll the dice twice so you dont have 1/20 X 1/20 chance of hitting two 1’s. You are only rolling the dice once so you have a1/20 chance of hitting a 1. What happens before you roll the dice doesn’t influence future rolls.