> so that if another person is shown your sequence of digits from 1 to 6, he/she should not be able to tell whether these numbers were produced by a real die or just “made up” by somebody. That instruction is a flaw in the experiment. It's always impossible to tell, for any given sequence, whether it was produced by a fair die. There's nothing an experimental subject can do to make the impossible more impossible. > t…
>It's always impossible to tell, for any given sequence, whether it was produced by a fair die. If the sequence is long enough you can model how likely it is to have been produced by a fair die. Are all numbers equally distributed? Are some numbers more likely to follow or not follow other numbers? Are some patterns repeating? Of course any sequence can be produced by a fair die, but you can still create some objecti…
Anecdote time:
A few years ago with my friends we were discussing how easy is to roll 5 dices simultaneously and get the same result in all of them. This is a possible way to win a popular game here https://en.wikipedia.org/wiki/Generala We estimated how often you can roll the dices and the probability, and we estimated that you must try during 2 or 3 hours to get that result.
We were young, had a lot of free time, so one of my friend started rolling 5 dices while he was talking with us and eating. After about 2 hour he got the 5 equal dices in a roll. (IIRC he tried again, with a similar result.)
(Note that 2 or 3 hours is consistent with how this outcome is used in the game to win automatically. It's possible to get this in a normal game, but it's not super common.)
Also, each time you add a dice, the time increase exponentially. With 6 dice it's 14-21 hours, like a day. With 7 dice it's like a week. With 9 dice is like a month. With 10 dice is half a year. 1000 dice will take longer (and x6 if you want to get only 6s instead of any repeated number).
(Note that parallelizing this to all humans only adds 14 dices. If everyone on Earth start rolling 24 dices, it will take like half a year until one of us get 24 equal dices.)