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Despite that the letter-writer is "completely convinced" that individuals can be "hard-wired" for alcoholism, this seems extremely unlikely to me, given what I know about genes and evolution.
To conclusively prove this one way or the other, the following study would need to be performed:
A large number of twins separated at birth -- both identical and fraternal -- would have to be located. (I believe this to be quite feasible.) Then the extent of their alcoholism at some adult age would need to be assessed with some uniform yardstick.
If the difference between the alcoholism of the pairs of fraternal twins were significantly more than that of the pairs of identical twins, this would be virtually conclusive proof that alcoholism is genetic. If, instead, the fraternal-twin differences and the identical-twin differences were essentially the same, this would tend to prove alcoholism is *not* genetic.
And, Yes! I think that the facts of this issue are crucial to answering the letter-writer's question. If there is no basis for concern about the children's "alcoholism genes", then there is no pressing reason to inform them of the father's past alcoholism.
What should be done is to educate them convincingly about the very real dangers of alcoholism.