The Refiner's Fire Response:
Read in context, you would see that God gave Pharoah NINE CHANCES to comply with His wishes to "let His people (the Israelites) go". NINE plagues to give Pharaoh a chance to see exactly WHO was in charge! Let's take a look what these "chances" were:
First Plague: The Nile waters Turn to Blood
The Nile, the river of Egypt, was the Egyptians' idol. The Nile's waters nourished the land and determined the welfare of all the people. The Egyptians thirsted after blood when they slaughtered the Hebrews' children, and now God gave them blood to drink. Now the source that brought the Egyptians life brought death instead (Exod. 7:14-25).
Second Plague: The frogs
The frogs represented the Egyptian fertility goddess, Isis, that was supposed to help women in childbirth. Frogs were everywhere: in their houses, in their beds, and at their tables. They could not eat, drink, or sleep without their precious god. The frog that symbolized life was left to be raked in heaps of rotting piles of death (Exod. 8:1-15).
Third Plague: The Lice
The lice which came up to live out of the dust of the earth represented the Egyptians' god of the earth, Seth. Matthew Henry notes that lice were small despicable, inconsiderable animals, and yet, by their vast numbers, they rendered a sore plague to the Egyptians. God could have plagued them with lions, or bears, or wolves, or with vultures or other birds of prey; but He chose to do it by these contemptible instruments (Exod. 8:16-19).
Fourth Plague: The Flies
The stinging, disease-carrying flies ruined the land. Beelzebub, the prince of the power of the air, has been glorified as the god of flies, the god of Ekron. The fly was always present at idolatry sacrifices. It seems that the god partook of those in this manner. This fourth plague came upon the Egyptians only. It made Israel a separate and Holy People (Exod. 8:20-32).
Fifth Plague: The Disease of Livestock
A great number of cattle died by a sort of pestilence. The Egyptians made the Hebrews poor and so God caused great loss to the Egyptians. This disease afflicted only the Egyptian livestock. The Egyptians believed animals were possessed by the spirits of gods. The bull was sacred in Egypt, identified in it markings to their god Apis. This pestilence, God's Word tells us, did not affect the Hebrew livestock (Exod. 9:1-7).
Sixth Plague: The Boils
Again God demonstrated His ability to control nature. When the death of their cattle didn't convince the Egyptians, God sent a plague that seized their own bodies. And they took ashes of the furnace, and stood before Pharaoh; and Moses sprinkled it up toward heaven; and it became a boil breaking forth with blains upon man, and upon beast (Exod. 9:10). Sores in the body were looked upon as punishment for sin, a means by which to call one to repentance. None of the Hebrews had any boils. This plague was a direct attack on the shamanism of the medico-mystical processes in Egypt (Exod. 9:8-12).
Seventh Plague: The Hailstorm
Moses gave the people a one-day warning before this plague. The notice was given because the sorcerers of Egypt were also agricultural shamans who supposedly controlled the weather. Those who feared the Lord went into shelter (showing us that God had mercy on some of the Egyptians). Those who did not believe God and took no shelter died in the fields (Ex. 9:21). There was ice and fire mingled with the hail, very grievous, such as there was none like it in all of the land of Egypt. The hail killed both men and cattle, and battered down the herbs, vegetable gardens, fruit trees, and other plants. God, in His judgment, caused it to rain or hail on the Egyptians and not on the Hebrews (Exod. 9:13-35).
Eighth Plague: The locusts
By this time, Pharaoh's people, his magicians, and advisors, began to rebel. Pharaoh stood alone against God. Moses stretched forth his rod over the land of Egypt, and the LORD brought an east wind upon the land all that day, and all that night; and when it was morning, the east wind brought the locusts. And the locusts went up over all the land of Egypt, and rested in all the coasts of Egypt: very grievous were they; before them there were no such locusts as they, neither after them shall be such. The plague was then sent which devastated the land and hence the power of the gods and shamans of agriculture. Pharaoh sent for Moses and pretended to repent. He asked Moses to pray to God to take the locusts away. And the LORD turned a mighty strong west wind, which took away the locusts, and cast them into the Red Sea; there remained not one locust in all the coasts of Egypt (Exod. 10:13-14, 19).
Ninth Plague: The Darkness
The Egyptians rebelled against the light of God's Word and they were justly punished with darkness. This thick darkness was over Egypt three days, but the people of Israel had light where they dwelt. What a picture of dark and light, of being lost and saved. The children of God walked in the light while Pharaoh and his people wandered in the darkness.
This plague was an attack on the power of the supreme deity of Egypt, the sun god Re or Amun-Re. The Egyptians could do nothing but stay in their homes and consider what they had experienced up to now, regarding the power of the God of the Israelites. Even then, Pharaoh refused to yield (Exod. 10:21-29).
Tenth Plague: The Death of the Firstborn
God said in Exodus 13:2, Sanctify unto me all the firstborn, whatsoever openeth the womb among the children of Israel, both of man and of beast: it is mine.
Nelson's Illustrated Bible Dictionary explains the importance of the firstborn: God placed a special claim on the firstborn of man and beast (Ex. 13:11-13). This meant that the nation of Israel attached unusual value to the eldest son and assigned special privileges and responsibilities to him. Because of God's claim on the first offspring, the firstborn sons of the Hebrews were presented to the Lord when they were a month old. Since the firstborn was regarded as God's property, it was necessary for the father to redeem, or buy back, the child from the priest. Early Hebrew laws also provided that the firstlings of beasts belonged to the Lord and were turned over to the sanctuary (Ex. 13:2; 34:19; Lev. 27:26). The firstborn's birthright was a double portion of the estate and leadership of the family. As head of the home after his father's death, the eldest son customarily cared for his mother until her death, and provided for his unmarried sisters until their marriages. He was the family's spiritual head and served as its priest. In figurative language, the term firstborn stands for that which is most excellent.
The significance of the death of every firstborn in Egypt, from the house of Pharaoh to the slaves and the livestock, was great. But Israel would be spared so that there would be an obvious distinction between those who belong to the YAWH and those who do not (Exod. 11:1-10).
How many chances SHOULD God haven given the Egyptians? If they couldn't understand that YHWH was in charge say, by the second or third plague, then that indicates that they probably wouldn't have listened to God after the thousandth plague!
Now, let's discuss "hardening of the heart". The following is an indepth explanation borrowed, in part, from The Christian Think Tank:
The bottom line is that God KNEW that Pharoah's heart was hardened, and so He allowed a struggle to happen: During the first 5 plagues, Pharaoh hardened his own heart without any help from God (Exodus 7:13,14,22; 8:15,19,32; 9:7). Then God does it (9:12); then Pharaoh and his officials do it together (9:34-35), then God does the rest.
The point of the hardening is given the following passages to show that God CAN perform these miracles/judgments:
Exodus 10: 1 Then the LORD said to Moses, "Go to Pharaoh, for I have hardened his heart and the hearts of his officials so that I may perform these miraculous signs of mine among them.
Exodus 11: 10 Moses and Aaron performed all these wonders before Pharaoh, but the LORD hardened Pharaoh's heart, and he would not let the Israelites go out of his country.
Exodus 14: 17 But take this staff in your hand so you can perform miraculous signs with it."
The miracles/signs/judgments themselves had an end-goal: so that the Egyptians would know that YHWH was God (and therefore come into a positive relationship with him - Exodus 14:4, 17); and so that the Israelites would know that YHWH had delivered them from their oppression with power, and was therefore a God they could depend on for their needs (Exodus 10.1), and so that the whole world would hear about God - 9:16. In other words, the end goal seems to be to wake everybody up concerning the true and living God.
From Lamentations 3 we know that God "sends hardness of heart" as a punishment: 59 You have seen, O LORD, the wrong done to me. Uphold my cause! 60 You have seen the depth of their vengeance, all their plots against me. 61 O LORD, you have heard their insults, all their plots against me- 62 what my enemies whisper and mutter against me all day long. 63 Look at them! Sitting or standing, they mock me in their songs. 64 Pay them back what they deserve, O LORD, for what their hands have done. 65 Put a veil over their hearts, and may your curse be on them! 66 Pursue them in anger and destroy them from under the heavens of the LORD.
What this means is that the judgments of God were not because of the later hardenings, but that the later hardenings were judgments themselves. (This motif also shows up in Joshua, where the kings who were being evicted from the land for atrocious crimes were "hardened" so they would fight Israel. (Jos 11:19.)