Could someone explain why putting sequences of same choice is invalid?
Sure, a probability of having many tails continously is low but how is it not random?
Randomness is never about the output; it is a property of the source.
So what is not random, is that the frequency of people that output repeating sequences is higher than the quotient of that sequence among all possible sequences of the same size.
The issue of the initial paper is that it claims to conclude that people aged > 60 are less random, when they simply output a fully-repeating sequence with a slightly higher rate (which is not surprising taking into consideration that there are much, much fewer of them).
It's not that the single values sequences are invalid, it's that they're occurring with a greater frequency than by chance
The players are just trying to sound smart basically
P(all heads | bad faith) ≫ P(any given "random"-looking string | bad faith)
therefore
P(bad faith | all heads) ≫ P(bad faith | any given "random"-looking string)
So if you want to exclude bad faith responses, the best strategy (by Neyman–Pearson, if you want to think of it that way) is to remove "all heads" responses (and similarly for "all tails").
This explanation leads me to think that the decision of what is random in the study is based on human perceptions of randomness, not actual statistical randomness. Although any sequence is equally (un)likely to be rolled, 1111111111 would stand out from the other sequences much more than 3156263441.