Achilles' War Prize Girl

Achilles asks that question very powerfully in the ninth book. Most of the other Greek kings had competed with each other to marry Helen and they all swore that they would protect whoever she picks for her husband, which ends up being Menelaus. Achilles wasn't part of that competition so he's not under any such obligation. So when Agamemnon has to give up his musical chair, he takes Achilles' war prize girl. But doesn't he also have a sense that he will die in the war? There is that tremendous self-consciousness that Achilles uniquely has because it has been prophesied that if he stays there in Troy fighting, he will die. If he goes home