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This study (based on the abstract) did not make much sense to me, except
for the last sentence. It seems
clear to me that it was the authors who "misunderstood" randomness, particularly
its implications to human evolution.

Nothing in this world — other than imaginations
of mathematicians — is random. No, not even the algorithm
that generated the "random" numbers in this study. Homo sapiens evolved
to think of the
world as causal, where sequencing of events matters vitally. We don’t just tally the outcome and await luck (or misfortune)
to strike again. Instead, we try to predict outcome from the past, and
come up with mechanistic explanations for events (and we call the good
ones science). There may be some philosophical reasons to argue that
causality is an illusion of human creation, but it works, millions of
years ago as well as today.

Going back to the study. The authors argue that the optimal strategy is
to track the marginal distribution of the outcome, and bet on the
maximum of this distribution. That’s plainly wrong. Not having read the fulltext, I am not sure how they instructed the
subject about the randomness of the task. But my guess is that they
lied — they told them that these were "real" random numbers. Given
enough domain knowledge, memory, and processing capacity, such as a moderate PC today, the best strategy is probably to uncover (by hacking?) the pseudo-random number generator algorithm and its seed, thus gaining 100% predictive power.

The behavioral differences among patients and with the secondary tasks
are interesting, but the best they show is that humans differ (inter-
and intra-individually) in the process by which they approach seemingly
random sequences.  While tracking only the marginal distribution would be an adequate strategy in the case of
"true" random sequences, it’s not clear that humans are good
"marginalizers" who can keep track of the outcome disregarding their
conditionals. Rather, it seems to be we are better — or at least
biased to be — "sequencers" or sequential pattern recognizers.

Both processes can happen at the same time. And in fact, we have to
marginalize the distribution of events because of our limited
memory/processing capacity. Thus, having patients of different kinds or
secondary tasks that tax different components of the resources is
likely to change the way in which subjects track events. No, I am not
suggesting that a particular hemisphere or part of the brain is
responsible for this versus that functions/resouces. I am fed up with
that in my own research domain.