One of the attributes good gamblers must develop is a poker-face, the ability to not to give away what cards they have in their hand. Likewise, good gamblers must learn how to look for "tells;" the slight rise of a eyebrow, a nervous twitch, drumming fingers, or other subtle hint into what their opponents hold. Gamblers' ability to pull off a bluff is directly related to their ability to put on a poker-face.
Theologies that believe that God never changes His mind must believe that God has a great poker-face because time and again God warns that something is going to happen but it never occurs. If God knows from the start that He going to carry out His threat, then the warning must be a bluff on God's part.
Throughout scripture there are many examples of God initially saying one thing, then doing something else in the end, but none more famous that God's threat to destroy Ninevah. God calls Jonah to go the the great city and tell its citizens that in 40 days Ninevah would be overthrown. However, the people repent and cry out to God for mercy and God grants it. Assuming that God never changes His mind and that God knew all along that He wasn't going to destroy the city then this was one of the greatest bluffs in human history. God couldn't let Jonah in on the con job however, because if Jonah knew that in the end God had no intention of destroying the city, Jonah might have developed some "tell" that could give the bluff away. So God kept Jonah in the dark and reinforced His false seriousness by having Jonah spend three days in the belly of a giant fish.
There must be some other explanation to what happened in Ninevah than the one just described for God is never deceitful. What God says He intends to do, He fully expects to follow through on. Anything else means God is making idle threats and being dishonest. So then, why wasn't Ninevah destroyed? Because God can and does change His mind based on the actions of humans.
Indeed, Jonah knew this and that's why he ran away, "for I knew that you are a gracious God and merciful, slow to anger, and abounding in steadfast love, and ready to relent from punishing" (Jonah 4:2, emphasis added). To relent of something means to "give in, as to influence or pressure." God relented from punishing the Ninevites because they influenced God by their acts of repentance and prayers. The Ninevites had hope that they could influence God, "Who knows? God may relent and change his mind; he may turn from his fierce anger, so that we do not perish" (Jonah 3:9).
That their acts of repentance did indeed influence God is revealed in the next verse, "When God saw what they did, how they turned from their evil ways, God changed his mind about the calamity that he had said he would bring upon them; and he did not do it" (Jonah 3:10 emphasis added). This shows that God doesn't need to have a poker-face, that He wasn't bluffing when He sent Jonah to warn the city of their coming destruction. God fully intended to destroy Ninevah at the time Jonah proclaimed God's message. God was not at all being deceitfulness, but God did change His mind.
This is such wonderful news for us. It means that our prayers and our actions make a difference. Just as the Ninevites influenced God and persuaded Him to change His mind, so God is influenced by and responds to us.