[m3047]

Maybe the null hypothesis needs to be that older people have more experience of "random" and therefore expect or tolerate more variance before rejecting "chance".

But they say that the effect is relatively small, or that their age guessing is "not as good as we had expected".

I'd be prone to misinterpreting the question.

If somebody asked me if the sequence "HTHTHTHT" is more or less likely to occur than “HTHHTHTT” I'd be confused. Ok, are they rejecting that they're equally likely out of hand, and if so why? At least subconsciously. If forced to suggest one or the other I'd offer the latter even though I know it's not mathematically correct.

Additionally most of the problems I deal with have to do with probability within a continuous run and in a run of 1000 heads/tails and some quick and dirty Monte Carlo I get:

    m3047@sophia:~/temp> ./sequences.py | grep -E 'HTHTHTHT|HTHHTHTT'
     11 HTHTHTHT
      6 HTHHTHTT
    m3047@sophia:~/temp> ./sequences.py | grep -E 'HTHTHTHT|HTHHTHTT'
      8 HTHTHTHT
      3 HTHHTHTT
    m3047@sophia:~/temp> ./sequences.py | grep -E 'HTHTHTHT|HTHHTHTT'
      5 HTHTHTHT
      4 HTHHTHTT

So I'd be wrong in practice at least with whatever PRNG is being utilized or maybe I'm just lucky. Always good to test and ask questions.