In order to solve this riddle, we only have to figure out what happens when you’ve been cloned twice and whether the answer to this should be 1⁄3 or 1⁄4. The first step is correct, the subjective probability of being the original should be 1⁄2 after you’ve pressed the cloning button once. However, after we’ve pressed the cloning button twice, in addition to the agent’s who existed after that first button press, we now have an agent that falsely remembers existing at that point in time.
Distributing the probability evenly between the agent’s who either had that experience or remember it: we get a 1⁄3 chance of being a false memory and a 2⁄3 chance of it being a real memory. If it is a real memory, then half of that—that is a 1⁄3 - is the probability of being the original and the other half—also 1⁄3 - is the chance of being the first clone.
So, the answer at the second step should be 1⁄3 instead of 1⁄4. Continued application will provide the answer for 100 copies.
I wrote a response to this post here: