There are several synonyms for the phrase "dead certainty" that can be used to convey the same meaning. One such term is "surefire", which means guaranteed or certain. Another is "inevitable", which suggests that something is bound to happen no matter what. "Foregone conclusion" is another phrase that can be used to describe a situation that is already determined and unlikely to change. Alternatively, "absolute certainty" can be used to emphasize the unshakability of a particular outcome. Whatever phrase is chosen, the intention is to communicate a state of complete and unwavering certainty regarding a specific circumstance or event.