I'm sorry, I didn't read the rest of your post after seeing the 0.5^99 estimate of the probability of being the original because the math looked very wrong to me, but I didn't know why.
While I agree there is nothing controversial about saying that after one step you have a 50% chance of being the original, I'm pretty sure it is not true that you only have a 25% chance after two steps.
Yes, if you are the original after step one, you have a 50% chance probability of still being the original after step two. So, I Oi is the probability of being the original after step i, then P(O2|O1) = 0.5,... (read more)
I'm sorry, I didn't read the rest of your post after seeing the 0.5^99 estimate of the probability of being the original because the math looked very wrong to me, but I didn't know why. While I agree there is nothing controversial about saying that after one step you have a 50% chance of being the original, I'm pretty sure it is not true that you only have a 25% chance after two steps. Yes, if you are the original after step one, you have a 50% chance probability of still being the original after step two. So, I Oi is the probability of being the original after step i, then P(O2|O1) = 0.5,... (read more)