When dealt a pair of Aces against a strong dealer hand, players should prioritize strategy and risk assessment. They must evaluate the dealer's upcard and their own game position, deciding whether to split the Aces for greater potential returns or keep them as a strong hand. It's important to understand the dealer's chances of improving their hand and the associated payouts. Players should aim to balance the potential for wins against risks, while considering their strategy and the casino's rules. A thoughtful approach can enhance outcomes and effectively manage risks.