At the end of Once Upon a Time in America, when Noodles visits Deborah and asks her about Senator Bailey (who later turns out to be Max), she first denies to know him but shortly after we learn that she is indeed affiliated to him and even has a son with him (who indeed looks like the young Max).
But while I could understand that Max maybe above all other reasons just wanted to "steal" Deborah from Noodles out of his anger over his betrayal, I wonder what drove Deborah to him, given that she never had a high opinion about Noodles' way of life and especially his friend Max. What was her motivation to start a relationship with him, especially one that lasted so long and spawned a son?
Or is there any chance that she did not know about Bailey's true identity? Yet I think she had already seen (and known) Max back in the 30s. But maybe she only realized it later when she was already in a relation with him (since she seems to know it when Noodles visits her in the 60s).