I have a normal, fair six sided die. I roll the die, but if I roll a 6 I keep rerolling the die until I get a result that is not a 6.
What are my chances of getting an even final result? Is it 2/5th? Or does it approach 2/5th?
I'm fairly certain that (ignoring the time it takes to roll the die) this scenario is the same as if I had a fair five sided die, but I don't know how to prove it.