I understand what the GP was saying now (see my sibling comment). The gambler’s fallacy can apply the other way, e.g. “This die has rolled over 3 many times, s

I understand what the GP was saying now (see my sibling comment). The gambler’s fallacy can apply the other way, e.g. “This die has rolled over 3 many times, so it will probably roll 3 or lower next time.” So that's not really the issue. Your dice example is not illustrating the point the GP is trying to make. It’s just comparing the probabilities of two outcomes of the same distribution (the sum-of-two-dice distribution). This has nothing to do with the selection effect the GP is talking about. That would be recording the value of the die that rolled highest (i.e. taking the maximum over dice) and then focusing on the same die next time (i.e. not taking the maximum over dice). It’s comparing the probability distribution of max {X_1, X_2, X_3, ...} with the probability distribution of any individual X_i. If A is sampled from the former and B is sampled from the latter, P(B < A) > P(B > A).