> 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.
> the kind of sequence you’d get if you really rolled a die
Well, there is no such sequence. The instruction is incoherent.
You could take it as meaning "Construct a sequence that you think will convince others that it came from a random source". That would be coherent. And then it would be legitimate to eliminate responses that were all-heads ("clearly didn't even try"). But then what are you measuring? The comparative understanding of older and youger people concerning random sources, or the Gambler's Paradox? Their comparative expertise in human psychology? Their comparative willingness to move the mouse-pointer over the screen?
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.
> the kind of sequence you’d get if you really rolled a die
Well, there is no such sequence. The instruction is incoherent.
You could take it as meaning "Construct a sequence that you think will convince others that it came from a random source". That would be coherent. And then it would be legitimate to eliminate responses that were all-heads ("clearly didn't even try"). But then what are you measuring? The comparative understanding of older and youger people concerning random sources, or the Gambler's Paradox? Their comparative expertise in human psychology? Their comparative willingness to move the mouse-pointer over the screen?