Choosing a number and betting that you will see it increases the probability that you will wrongly believe that you have seen that number in the future to a value that does not depend on how long that number is. P(hallucinate number N|placed a bet on N) >> P(hallucinate number N).
Yes, I completely agree. To show that I understand your point, I will suggest possible numbers for each of these variables. I would guess, with very low confidence, that on a daily basis, P(hallucinate a number) might be something like 10^-7, that P(hallucinate a 30-digit number N) might be something like 10^-37, and that P(hallucinate a 30-digit number N | placed a bet on N) might be something like 10^-9. Obviously, p(correctly guess a 30-digit number) is still 10^-30.
Even given all of these values, I still claim that we should be interested in P(hallucinate a 30-digit number N | placed a bet on N). This number is probably roughly constant across ostensibly sane people, and I claim that it marks a lower bound below which we should not care about the difference in probabilities for a non-replicable event.
I am not certain of these claims, and I would greatly appreciate your analysis of them.
Choosing a number and betting that you will see it increases the probability that you will wrongly believe that you have seen that number in the future to a value that does not depend on how long that number is. P(hallucinate number N|placed a bet on N) >> P(hallucinate number N).
Yes, I completely agree. To show that I understand your point, I will suggest possible numbers for each of these variables. I would guess, with very low confidence, that on a daily basis, P(hallucinate a number) might be something like 10^-7, that P(hallucinate a 30-digit number N) might be something like 10^-37, and that P(hallucinate a 30-digit number N | placed a bet on N) might be something like 10^-9. Obviously, p(correctly guess a 30-digit number) is still 10^-30.
Even given all of these values, I still claim that we should be interested in P(hallucinate a 30-digit number N | placed a bet on N). This number is probably roughly constant across ostensibly sane people, and I claim that it marks a lower bound below which we should not care about the difference in probabilities for a non-replicable event.
I am not certain of these claims, and I would greatly appreciate your analysis of them.