Oh, right, I missed that your simulation has 1⁄3 Heads. Thank you for your patient cooperation in finding mistakes in your arguments, by the way. So, why is it ok for a simulation of an outcome with 1⁄2 probability to have 1⁄3 frequency? That sounds like more serious failure of statistical test.
Nothing out of the ordinary. The Beauty will generate the list with the same statistical properties. Two lists if the coin is Tails.
I imagined that the Beauty would sample just once. And then if we combine all samples into list, we will see that if the Beauty uses your model, then the list will fail the “have the correct number of days” test.
Which is “Beauty is awakened today which is Monday” or simply “Beauty is awakened on Monday” just as I was saying.
They are not the same thing? The first one is false on Tuesday.
(I’m also interested in your thoughts about copies in another thread).
So, why is it ok for a simulation of an outcome with 1⁄2 probability to have 1⁄3 frequency?
There are only two outcomes and both of them have 1⁄2 probability and 1⁄2 frequency. The code saves awakenings in the list, not outcomes
People mistakenly assume that three awakenings mean three elementary outcomes. But as the simulation shows, there is order between awakenings and so they can’t be treated as individual outcomes. Tails&Monday and Tails&Tuesday awakenings are parts of the same outcome.
If this still doesn’t feel obvious, consider this. You have a list of Heads and Tails. And you need to distinguish between two hypothesis. Either the coin is unfair and P(Tails)=2/3, or the coin is fair but whenever it came Tails, the outcome was written twice in the list, while for Heads—only once. You check whether outcomes are randomly spread or pairs of Tails follow together. In the second case, even though the frequency of Tails in the list is twice as high as Heads, P(Tails)=P(Heads)=1/2.
Oh, right, I missed that your simulation has 1⁄3 Heads. Thank you for your patient cooperation in finding mistakes in your arguments, by the way. So, why is it ok for a simulation of an outcome with 1⁄2 probability to have 1⁄3 frequency? That sounds like more serious failure of statistical test.
I imagined that the Beauty would sample just once. And then if we combine all samples into list, we will see that if the Beauty uses your model, then the list will fail the “have the correct number of days” test.
They are not the same thing? The first one is false on Tuesday.
(I’m also interested in your thoughts about copies in another thread).
There are only two outcomes and both of them have 1⁄2 probability and 1⁄2 frequency. The code saves awakenings in the list, not outcomes
People mistakenly assume that three awakenings mean three elementary outcomes. But as the simulation shows, there is order between awakenings and so they can’t be treated as individual outcomes. Tails&Monday and Tails&Tuesday awakenings are parts of the same outcome.
If this still doesn’t feel obvious, consider this. You have a list of Heads and Tails. And you need to distinguish between two hypothesis. Either the coin is unfair and P(Tails)=2/3, or the coin is fair but whenever it came Tails, the outcome was written twice in the list, while for Heads—only once. You check whether outcomes are randomly spread or pairs of Tails follow together. In the second case, even though the frequency of Tails in the list is twice as high as Heads, P(Tails)=P(Heads)=1/2.