Does God ever really change his mind?

Numbers 23:19  God is not a man, that he should lie, nor a son of man, that he should change his mind. Does he speak and then not act? Does he promise and not fulfill?
And the reason is given here that God will not change his mind, because "God is not a man," it is because of his nature, so this cannot be read as "I will not change my mind in this instance."
For if God can really change his mind, then the answer is yes, he does speak, and then not act, he does actually promise, and not fulfill.
Isaiah 31:2 Yet he too is wise and can bring disaster; he does not take back his words.

If God says unconditionally, "I will do this," yet knowing that he might have to change his mind, then what he said previously was not true, this then would be a lie, God knew it might not be true, and said it was true. But God does not lie, and thus he does not really say "This will occur" or "I will do this," unconditionally, and then change his mind.
Revelation 21:8 But the cowardly, the unbelieving, the vile, the murderers, the sexually immoral, those who practice magic arts, the idolaters and all liars-- their place will be in the fiery lake of burning sulfur. This is the second death.
If God were to lie, he would come under this condemnation. Now God might be saying the best he knows in any given situation. But still, to say something you know might not be true, as if it were unconditionally true, is telling a lie.

1SA 15:35 "And the Lord regretted that He had made Saul king over Israel."
This may well mean "grieved" here, though, and a change of response: "I have rejected him as king" (1 Sam. 16:1), but this need not imply a change of overall plan. Now it seems there is no one word in English that expresses "change of action" without other overtones (repent, relent, regret all have other implications beyond just "change"). But God did not promise Saul permanent kingship, as he did to Jesus:
PS 110:4 The Lord has sworn and will not change his mind: "You are a priest forever, in the order of Melchizedek."
So when he says to Saul:
1SA 15:29 "He who is the Glory of Israel does not lie or change his mind; for he is not a man, that he should change his mind."
This is in accordance with what Daniel wrote:
DA 2:21 He changes times and seasons; he sets up kings and deposes them.
Thus God's actions with Saul were in accordance with this description, his plan was unchanged, though his response to Saul had changed. And as in Numbers 23:19, we see the reason given, that God will not change his mind, it is because of his nature ("He is not a man") and not because of the situation, God is not saying "I will not change my mind this time." Because the opposite, that is if God were to change his mind, would not be for him to simply take another valid option, it would be, God tells us here, to lie.

2 Kings 20:1 In those days Hezekiah was sick and near death. And Isaiah the prophet, the son of Amoz, went to him and said to him, "Thus says the Lord: 'Set your house in order, for you shall die, and not live.' "
I think we have "die" here in two senses, Hezekiah needed to get his heart in order or he would die physically. He died to self instead, and thus he died in another sense, in order to live:
Isaiah 38:13 ... day and night you made an end of me.
Romans 8:13 For if you live according to the sinful nature, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live...
Isaiah 38:15-16  But what can I say? He has spoken to me, and he himself has done this. I will walk humbly all my years because of this anguish of my soul. Lord, by such things men live; and my spirit finds life in them too.
Now this is certainly an unexpected interpretation, and a perhaps more acceptable one to most people would be to say this was conditional, which it well may have been. But I would still prefer this other option, as also in the case of Nineveh repenting, where Jonah's prophecy was indeed fulfilled, Nineveh was overthrown (as Augustine pointed out, and the same word "overthrow" is used in "whose hearts he turned" in Ps. 105:25), but they were overthrown by repentance, instead of by annihilation.
But again, this prophecy with Jonah could also be conditional...

2SA 24:16 When the angel stretched out his hand toward Jerusalem to destroy it, the Lord relented from the calamity, and said to the angel who destroyed the people, "It is enough! Now stay your hand!"
PS 106:45 for their sake he remembered his covenant and out of his great love he relented.
Not "he changed his mind," but "because of his covenant," he changed his response. If his covenant causes the relenting, then  the reason he relents is because he keeps his covenant, so this verse gives the reason for the change: it is because God doesn't change!
Thus when God relents, it is in accordance with his nature, because of his unchanging character:
JOEL 2:13 "Rend your heart and not your garments. Return to the Lord your God, for he is gracious and compassionate, slow to anger and abounding in love, and he relents from sending calamity."
Here is another verse to consider:
JER 15:6 "You who have forsaken Me," declares the Lord, "You keep going backward.  So I will stretch out My hand against you and destroy you;  I am tired of relenting!"
So here there is a delay of action while God is relenting, the relenting is continuous, a sustained attitude of withholding judgment, and the change that comes is to stop restraining this judgment, i.e. the change is to stop relenting! So to say that "relent" means a change of mind in reference to God seems not to be supported here.
Now certainly if peoples' actions change, then God's response may indeed change (Jer. 18:7-10), but God foresees the future, this means that God has not changed his plan, in other words, he is not reacting, but acting:
JER 18:6-8 "O house of Israel, can I not do with you as this potter does?" declares the Lord. "Like clay in the hand of the potter, so are you in my hand, O house of Israel. If at any time I announce that a nation or kingdom is to be uprooted, torn down and destroyed, and if that nation I warned repents of its evil, then I will relent."
He tells us his ways! And thus here, even according to the Open View, God's overall plan does not change, so God cannot be said to have taken an unforeseen course, and changed his mind.

And we may note that the Open View says "repent" in reference to God doesn't mean God repents from sinning. So no one is taking "repent" here in the usual sense, neither the open view nor the closed view people.

JNH 3:10 When God saw what they did and how they turned from their evil ways, he had compassion and did not bring upon them the destruction he had threatened.
Now this may have been conditional, without an explicitly stated condition, here is an example like this:
MT 8:31 The demons begged Jesus, "If you drive us out, send us into the herd of pigs."
MK 5:12 The demons begged Jesus, "Send us among the pigs; allow us to go into them."
In Matthew, a condition is stated "if you drive us out", in Mark, the condition is not stated, so this may have happened in Jonah's prophecy as well, with an unstated condition.
But if "overthrow" can mean either overthrow by destruction or by repentance, then the destruction was implied initially. There it there is a need to explain how "what he said" can mean "what he implied," for "God relented of the disaster that he had said he would do to them," we read in Jonah 3:10 (though the NIV has "threatened" here). The word "said" here is the Hebrew word "dabar", which has a wide range of meanings. In one place, the NAS translates "dabar" as "meant", in Ex. 16:23, so I think this word can mean "implied".
And here are two more verses about implied conditions:
DT 9:25 So I fell down before the Lord the forty days and nights, which I did because the Lord had said he would destroy you.
Here God said "he would destroy them", and no condition is stated, then Moses prays and destruction is averted. This is a very similar situation to Jonah and the Ninevites.
But there was a condition, it is implied in Dt. 9:25, however, in the account in Exodus, the condition is stated:
EX 32:10 Now leave me alone so that my anger may burn against them and that I may destroy them.
Here is the condition, "leave me alone," and Moses did not leave God alone, and thus fulfilled the condition to avert the destruction. But it may be also said, with Dt. 9:25 in view, that "God did not do what he said he would do" (the NIV again has "threatened"), this is also a parallel with Jonah:
Exodus 32:14 So the Lord changed His mind about the harm which He said He would do to His people.
So we may say here also that "God said he would destroy them," and we may also say that "God said he would destroy them if Moses did not pray." Both statements are true, and it is the version of the statement without the implied condition that is in view in Jonah 3:10.
Now another point arises, we may ask when we are told that God really changed his mind, and his overall plan: What does that imply that God thought would not happen? And also, there are other questions:
Why didn't God destroy the Ninevites right away, if that was his plan?
Why did God send Jonah, and spoil his plan?
How can we trust God, if he can take action, and spoil his own plan himself?
How can we say that God didn't lie to the Ninevites, if he threatened unconditional destruction, yet he knew it might not happen?
Why did Jonah seem to have a better grasp of the situation than God did? He thought the Ninevites would probably repent, and thus he ran.
Why did the Ninevites seem to know better than God did? They thought they could repent, and God, apparently, did not.
Why didn't God keep the Ninevites from repenting after Jonah preached to them, like he did with the sons of Eli (1 Sam. 2:25) and with Amaziah (2 Chr. 25:16)?
Now we have to question God's unconditional promises, for the situation may change, and God may have to change his plan.
Also, God may act in a way that spoils his plan, not only may the situation change, and cause a change of plan, but God may do something that wrecks his own plan.
And we also need not always follow God's counsel, for another choice may turn out better, even from his perspective. Only Scripture says differently:
2 Corinthians 2:9 For this is why I wrote, that I might test you and know whether you are obedient in everything.
Which must imply being obedient in all of God's directions to us, we must be obedient in everything, that is "the test" Paul mentions here, implying not to do this is to fail.
Acts 11:17  So if God gave them the same gift as he gave us, who believed in the Lord Jesus Christ, who was I to think that I could oppose God?
Which clearly implies we should not do this.

Hebrews 6:17-18  Because God wanted to make the unchanging nature of his purpose very clear to the heirs of what was promised, he confirmed it with an oath. God did this so that, by two unchangeable things in which it is impossible for God to lie...
Therefore God did not and will not change his purpose here, but can God ever change his purpose?
PS 33:10-11 The Lord foils the plans of the nations; he thwarts the purposes of the peoples. But the plans of the Lord stand firm forever, the purposes of his heart through all generations.
Romans 11:29 ... for the gifts and the calling of God are irrevocable.
"'Ametamelatos,' in biblical Greek occurring only here and in 2 Cor 7:10, means initially 'not to be regretted' (as 2 Cor 7:10; LSJ), and so 'irrevocable,' as of something one does not take back (BGD ... 'force of a legal axiom')" (Word Biblical Commentary)

JER 4:28 "Therefore the earth will mourn and the heavens above grow dark, because I have spoken and will not relent, I have decided and will not turn back."
Here is a parallel: "I have decided and will not turn back", "turn back" is parallel to "relent", for God to relent is to choose a different course, to change his action, but this does not necessarily imply a change of plan. Where God has said what he will do in the form of a promise, he will not change his actions in that area.

Here is another verse to consider in regard to the question as to whether God can change his mind:
GE 6:6 And the Lord was sorry that He had made man on the earth, and He was grieved in His heart. (NASB)
GE 6:6 The Lord was grieved that he had made man on the earth, and his heart was filled with pain. (NIV)
Here we may take the NIV translation, and say God was grieved, and his heart was pained, but he was not regretful.
And also we cannot say that God had a standby plan he knew would succeed in case man went completely astray, for there was the possibility that it might go all wrong, that he might fail completely, and that he would not be the invincible chess master. What if Noah had joined the Nephilim?
And we must also conclude that God did not think this would happen, but how could miss this possibility? For it certainly seems that according to the Open View, Noah could have refused...

Now here is a perfect example of translating "nacham," and of the way we can select here, and in these other verses:
Numbers 23:19 God is not a man, that he should lie, nor a son of man, that he should "nacham." Does he speak and then not act? Does he promise and not fulfill?
Now then, we have our choices before us for translating this word "nacham": "repent of sin," "relent from judgment," "be grieved," "be comforted," "change his mind."
Now of all these, only the last one fits, though the Open Theists will most likely say this means "change his mind in this instance."
Yet how, according to the Open View, would it have been a lie for God to curse Israel? According to Jer. 18, they had already forfeited God's blessing due to their rebellion, and twice God had said "Let me alone so I can destroy them, and I will make a greater nation out of you, Moses." And now Moses had also displeased God, and was not going to the promised land, so...
How would it have been a lie, for God to curse Israel?
Jeremiah 18:10 But if that nation does what displeases me and does not obey me, then I will forgo ("nacham"!) the good I promised to do to it.
So then from the Open View perspective, there would be no lie if God were to change his mind here, and thus this cannot mean "just this time because of the situation" in Num. 23:19, the situation actually pointed in the opposite direction, and so this is a general statement, saying that God will not change his mind.
Another reason is given, "He is not a man," it is also because of his nature, and again, not due to the situation.
Numbers 23:19  Does he speak and then not act? Does he promise and not fulfill?
But the Open View would say here, yes, he does speak and then not act, he does promise, and not fulfill, sometimes...