Open theism suffers from a major dilemma. On the one hand, in fielding the problem of evil, open theists appeal to divine ignorance as a mitigating or exculpatory factor. For instance:
According to open theism, God has sovereignly decided to create a world with libertarianly free creatures and, since there are no true (would-) counterfactuals of creaturely freedom for God to know and since, according to open theists, libertarian freedom is incompatible with meticulous foreknowledge, God could not know for sure ahead of time what kinds of choices his free creatures will make. God would seem to be less blameworthy for not preventing evils that he didn’t know in advance would happen.
On the other hand, open theists contend that God can anticipate the future with a high degree of probability. For instance:
…we would affirm God's comprehensive and exact knowledge of the possibilities of the future–and, as has already been said, of the gradually changed likelihood of each of those possibilities' being realized. And as the probably of a choice's being made in a certain way gradually increases toward certainty, God knows that also, often, no doubt, before the finite agent herself is aware of it. W. Hasker, God, Time, and Knowledge (Cornell, 1998), 189.Many prophecies, in fact, have a conditional character, such as “If a nation does not do such and such, then it will be destroyed” (see Jeremiah 18:7–10, for example). Second, many prophetic predictions are based upon existing trends and tendencies, which provide God with enough evidence to foresee the future (Hasker 1989, 195). (Hasker places Jesus' prediction about Peter in this category, by the way.) Finally, some prophecies simply reveal what God has already decided to bring about in the future (Hasker 1989, 195). Since God's own actions in the future are up to God, it is possible for God to know about them even though they are contingent, so it is possible for prophecies to reveal them.
Indeed, it's an essential component of religious devotion to say that God can be trusted to keep his promises.
To the extent that proponents accentuate divine ignorance as a distinctive element and advantage of an open theist theodicy, they undercut the claim that God can accurately anticipate the future and thereby be trusted to keep his promises.
Conversely, to the extent that proponents accentuate God's high probabilistic knowledge of the future, they undercut the appeal to divine ignorance to exonerate God in relation to evil.