I don't know enough about the RNG experiments to say whether this optimal stopping actually occured.
Another way figures could be inflated is if a subject is expected to do a set number of trials. If they start badly and get disheartened, they are much more likely to drop out compared to those who just so happen to start well. Since they don't complete their pre-set number of trials, their data maybe removed from the results, skewing the results in a positive direction.
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