You asked people to try resolving the problem on their own. So here is my answer before I read further. I was motivated to find a reason for the doomsday math to be incorrect by your prompt.
I felt the mistake was the hidden ambiguity of this statement:
Assuming that you are a random person among all the people destined to be born.
How do we randomly sample the person? Imagine you had to code this as a simulation in Python. Which of the following algorithms does your program follow?
Pick uniformly randomly between Short and Long. If Short, then pick a number between 1 and 100 billion. If Long, then pick a number between 1 and 100 trillion.
Create a list [“Short-1”, “Short-2“, …, “Short-100-billion”, “Long-1”, “Long-2”, …, “Long-100-trillion”]. Pick a uniform random sample from this list.
The math you present matches the first algorithm. The math is different with the second algorithm. With the second algorithm we have:
P(sample beginning with Short) = 1/1001
P(sample beginning with Long) = 1000/1001
P(sample ending with 6 | sample beginning with Short) = 1⁄10
P(sample ending with 6 | sample beginning with Long) = 1/10000
P(sample ending with 6) = P(sample ending with 6 | sample beginning with Short) * P(sample beginning with Short) + P(sample ending with 6 | sample beginning with Long) * P(sample beginning with Long) ≈ 0.0002
P(sample beginning with Short | sample ending with 6) = P(sample ending with 6 | sample beginning with Short) * P(sample beginning with Short) / P(sample ending with 6) = 0.5
This matches the following experiment:
Run the program to pick a random sample.
If your sample does not end with 6, then restart.
You have a sample ending with 6. Check whether it begins with Short or Long.
You observe Short and Long with equal probability of 0.5 .
You said that you believe that the AI bubble is going to burst in the next few months. Could you phrase that as a testable prediction? For example, you’re 80% sure that in 6 months, the stock market price of Nvidia will be 80% of what it is today. This would help me understand your prediction better. Different people have different views on what “pretty certain” and “burst” means. I just want a clarification. I don’t want to argue about the prediction.