The King and His Kingdom
"What is a prophecy?"
A prophecy is the future told in advance by God through a prophet.
I foretold the former things long ago, my mouth announced them and I made them known; then suddenly I acted, and they came to pass. For I knew how stubborn you were; the sinews of your neck were iron, your forehead was bronze. Therefore I told you these things long ago; before they happened I announced them to you so that you could not say, `My idols did them; my wooden image and metal god ordained them.' Isaiah 48:2-5
"Isn't 'fulfilled prophecy' just a guess or luck or coincidence?"
And we have the word of the prophets made more certain, and you will do well to pay attention to it, as to a light shining in a dark place, until the day dawns and the morning star rises in your hearts. 2 Peter 1:19-21
Above all, you must understand that no prophecy of Scripture came about by the prophet's own interpretation. For prophecy never had its origin in the will of man, but men spoke from God as they were carried along by the Holy Spirit.
"Does the Old Testament contain any prophecies about the Messiah?"
Yes! The Old Testament contains about FOUR HUNDRED AND TWENTY-FIVE prophecies about the Messiah. Here is a small sample (in roughly chronological order):
The beginning of the gospel about Jesus Christ, the Son of God.
John 1:1-3, 14
In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the One and Only, who came from the Father, full of grace and truth.
--BORN OF A VIRGIN
Therefore the Lord himself will give you a sign: The virgin will be with child and will give birth to a son, and will call him Immanuel. 700 B.C.
But after he had considered this, an angel of the Lord appeared to him in a dream and said, "Joseph son of David, do not be afraid to take Mary home as your wife, because what is conceived in her is from the Holy Spirit. She will give birth to a son, and you are to give him the name Jesus, because he will save his people from their sins." All this took place to fulfill what the Lord had said through the prophet: "The virgin will be with child and will give birth to a son, and they will call him Immanuel" --which means, "God with us."
--FROM THE HOUSE OF JUDAH
Once more a remnant of the house of Judah will take root below and bear fruit above. 700 B.C.
Matthew 1:1-2, 16
A record of the genealogy of Jesus Christ the son [descendant] of David, the son of Abraham: Abraham was the father of Isaac, Isaac the father of Jacob, Jacob the father of Judah and his brothers, and [a later] Jacob the father of Joseph, the husband of Mary, of whom was born Jesus, who is called Christ.
--FROM THE ROOT AND STUMP OF JESSE
In that day the Root of Jesse will stand as a banner for the peoples; the nations will rally to him, and his place of rest will be glorious. 700 B.C.
A shoot will come up from the stump of Jesse; from his roots a Branch will bear fruit. The Spirit of the LORD will rest on him-- the Spirit of wisdom and of understanding, the Spirit of counsel and of power, the Spirit of knowledge and of the fear of the LORD-- and he will delight in the fear of the LORD. He will not judge by what he sees with his eyes, or decide by what he hears with his ears; but with righteousness he will judge the needy, with justice he will give decisions for the poor of the earth. He will strike the earth with the rod of his mouth; with the breath of his lips he will slay the wicked. Righteousness will be his belt and faithfulness the sash around his waist. 700 B.C.
And again, Isaiah says, "The Root of Jesse will spring up, one who will arise to rule over the nations; the Gentiles will hope in him."
Matthew 1:1-2a, 5-6, 16
A record of the genealogy of Jesus Christ the son of David, the son of Abraham: Abraham was the father of Isaac,... Obed the father of Jesse, and Jesse the father of King David. ...and Jacob the father of Joseph, the husband of Mary, of whom was born Jesus, who is called Christ.