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
Your die does not “remember” what you rolled last time. Every roll has a 1/20 chance to roll any given number.
If you roll the die X times, however long it takes until you roll a 1, and then roll once more, the chance of a 1 on the “once more” roll is still 1/20…just like it is for every single individual roll you make, ever.
The only reason the odds of rolling back-to-back 1s are lower is because that calculates the chances of **both** rolls being 1s – the first roll has a 1/20 chance for a 1, the second roll has a 1/20 chance for a 1, but the odds that they’ll **both** be 1s is very small. That doesn’t change the fact that each one is still a 1/20 chance **on its own**.
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