I've always wondered about that. Why does God, after having Satan thrown into the bottomless pit at the beginning of the Millennium, set him free after the thousand years had passed?
I think it's to prove one final lesson.
Those Tribulation saints who survive, and go into the Millennium in their physical bodies will continue to have children. (So many so, that Satan will be able to raise a gigantic army from among them for one final battle against God).
Those children, and their children's children, etc., will be raised in a perfect environment, being ruled by Jesus with a rod of iron. They will superficially worship Jesus, but their hearts will be in rebellion to Him.
God lets Satan out to show, once and for all, that it's not a person's environment that makes them bad, it's what is inside of them. It's our nature. And no amount of paradise will change us if we are not regenerated through Christ.
It's kinda like many "stars" these days. They have the world at their feet - money, power, adulation - and they end up doing terrible things. They destroy themselves and others, despite "having it all".
Anyhoo, that's my two cents.
The battle of Armageddon is when the beast, and the world, go against Jerusalem, the Jews, Israel, and Jesus comes back with all the saints, and defeats the world, and saves Israel.
The kingdom is restored to the Jews, Israel, and Jesus and the saints rule over the people that God spared at the battle of Armageddon, which the Bible says one sixth of the people.
When Jesus defeats the world, the beast, humanity, the man of sin that Satan influenced to deceive the people, gets thrown in to the lake of fire, and Satan gets thrown in to the bottomless pit.
There is peace on earth for 1000 years for Satan is not influencing the people, and Satan is loosed from the bottomless pit, and deceives the people and they go against the saints, and God rains fire down on them, and devours them, and the millennial reign is over.
The people that God spared at the battle of Armageddon still have punishment coming, for they followed the beast, and took the mark of the beast, but God postponed it until the end of the millennial reign.
Also it appears as if the bottomless pit is a reference to Satan being on a leash, for right now Satan is considered in the bottomless pit, for when the beast kingdom comes about the beast ascends from the bottomless pit which means Satan is off his leash, and will deceive all people that do not love God to follow him, and the beast kingdom, which God can then end this sin business on earth.
Right not Satan is on a leash, and can only deceive so much, but in the future will be off his leash concerning the wicked, which the Bible says he is restrained right now, until the time of the end when he appears as the beast, then he is not restrained concerning the wicked, off his leash, ascends from the bottomless pit.
So Satan being in the bottomless pit in the millennial reign is a reference that he is on a leash, but this being on a leash causes him to be restrained where he cannot influence at all, which is referenced by the angel shackling Satan with a great chain.
Satan is in the bottomless pit right now for he is on a leash, and can only influence so much, but he is the prince of the power of the air, so he is not really in a bottomless pit, so it much be a reference that he is on a leash, for he ascends from the bottomless pit as the beast, but Michael and his angels defeated Satan and his angels, and threw them to earth, where the earth became the habitation of devils which is their holding cell, and they deceive all people that do not love God, and hold the testimony of Jesus.
So Satan is not really in a bottomless pit for he is the prince of the power of the air, and gets kicked out of the sky, and thrown to earth, and ascends from the bottomless pit to deceive the wicked, so it must be a reference that Satan is on a leash when he is in the bottomless pit, and not on a leash when he is not in the bottomless pit.
So it appears that the reason Satan is still allowed to be around, and not be punished during the millennial reign is so he can deceive the people that God spared at the battle of Armageddon at the end of the millennial reign, so they will go against the saints so God can defeat them, for they still have punishment coming, and since God allowed them to abide by the Old Testament feast of tabernacles, and go up year after year to worship the LORD it could be that it made them right with God according to the Old Testament physical covenant, so God allowed them to be deceived by Satan and break that covenant, so He can put them down, for there is no way they can have spiritual salvation for they took the mark of the beast in which there is no reversal, and no salvation.