Romans 9:16 So then it is not of him who wills, nor of him who runs, but of God who shows mercy.
Romans 9 has a particular subject:
1 I am speaking the truth in Christ—I am not lying; my conscience bears me witness in the Holy Spirit— 2that I have great sorrow and unceasing anguish in my heart. 3For I could wish that I myself were accursed and cut off from Christ for the sake of my brothers, my kinsmen according to the flesh. 4They are Israelites, and to them belong the adoption, the glory, the covenants, the giving of the law, the worship, and the promises. 5To them belong the patriarchs, and from their race, according to the flesh, is the Christ who is God over all, blessed forever. Amen. 6But it is not as though the word of God has failed.
Paul addresses a subject of great pain to him - the rejection of Jesus by the Jews. Not as individuals, for Paul is a Jew and he believes, but as a nation...or more accurately, as a tribe, the children of Abraham and Isaac.
Just as God chose the children of Jacob to be his chosen people, rather than the children of Esau (although individual descendants of Esau could join them, as could Gentiles even), God is now choosing to give life to the Gentiles.
“1Brothers, my heart’s desire and prayer to God for them is that they may be saved. 2For I bear them witness that they have a zeal for God, but not according to knowledge. 3For, being ignorant of the righteousness of God, and seeking to establish their own, they did not submit to God’s righteousness. 4For Christ is the end of the law for righteousness to everyone who believes.”
But it will not last forever:
1I ask, then, has God rejected his people? By no means! For I myself am an Israelite, a descendant of Abraham, a member of the tribe of Benjamin. 2 God has not rejected his people whom he foreknew. (Chapter 11)
25 Lest you be wise in your own sight, I want you to understand this mystery, brothers: a partial hardening has come upon Israel, until the fullness of the Gentiles has come in. 26And in this way all Israel will be saved, as it is written,
“The Deliverer will come from Zion,
he will banish ungodliness from Jacob”;
27”and this will be my covenant with them
when I take away their sins.”
28As regards the gospel, they are enemies of God for your sake. But as regards election, they are beloved for the sake of their forefathers. 29For the gifts and the calling of God are irrevocable.
Again, this is speaking in generalities, for individual Jews will and are saved, and most Gentiles are still destined to hell.
But as individuals, Paul continues to affirm:
1For the Scripture says, “Everyone who believes in him will not be put to shame.” 12 For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him. 13For “everyone who calls on the name of the Lord will be saved.” (Chapter 10)