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

I will say, as a former casino manager, that the thought that the odds will change from roll to roll, hand to hand, spin to spin is how casinos make most of their money.