This code-based approach is a very concrete approach to the problem, by the way, so thank you.
if you want to use custom chance then you shouldn’t actually count not interrupted Monday if the Tuesday was interrupted.
Sure. So let’s go back to the first way you had of calculating this:
for n in range(100000):
day, coin = interruption()
if day is not None:
interrupted_coin_guess.append(coin == 'Heads')
else:
not_interrupted_coin_guess.append(coin == 'Heads')
print(interrupted_coin_guess.count(True)/len(interrupted_coin_guess))
# 0.3006993006993007
The probability this is calculating is a per-experiment probability that the experiment will be interrupted. But Beauty doesn’t ever get the information “this experiment will be interrupted”. Instead, she experiences, or doesn’t experience, the interruption. It’s possible for her to not experience an interruption, even though she will later be interrupted, the following day. So this doesn’t seem like a helpful calculation from Beauty’s perspective, when Prince Charming busts in through the window.
The beauty gets the information “This experiment is interrupted” when she observed the interruption on her awakening. She never gets the information “This experiment is not to be interrupted” because the interruption could happen on the other awakening.
This means that specifically in the awakening that the experiment is interrupted/some random low probable event happens, the Beauty can determine how the coin landed in this particular experiment better than chance, contrary to other awakenings.
This code-based approach is a very concrete approach to the problem, by the way, so thank you.
Sure. So let’s go back to the first way you had of calculating this:
The probability this is calculating is a per-experiment probability that the experiment will be interrupted. But Beauty doesn’t ever get the information “this experiment will be interrupted”. Instead, she experiences, or doesn’t experience, the interruption. It’s possible for her to not experience an interruption, even though she will later be interrupted, the following day. So this doesn’t seem like a helpful calculation from Beauty’s perspective, when Prince Charming busts in through the window.
The beauty gets the information “This experiment is interrupted” when she observed the interruption on her awakening. She never gets the information “This experiment is not to be interrupted” because the interruption could happen on the other awakening.
This means that specifically in the awakening that the experiment is interrupted/some random low probable event happens, the Beauty can determine how the coin landed in this particular experiment better than chance, contrary to other awakenings.