how do you know you are actually one of the ones God has chosen to be cast in to the lake o fire?
Because I believe in the Lord Jesus Christ and his atoning sacrifice on my behalf. By this faith we are saved.
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life" (John 3:16)
If you believe in Christ you have eternal life, meaning you are elect.
"He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him." (John 3:36)
Those who do not believe, do not believe, because they are not Christ's sheep, meaning they are not of the elect.
"But ye believe not, because ye are not of my sheep, as I said unto you." (John 10:26)
Christ sheep are given to him by the father, and he contrasts his sheep from the world as a whole.
"I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine." (John 17:9)
We did not choose Christ, he chose us.
"Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you."
(John 15:16)
I could go on and on and on and on and on. Election is taught all throughout scripture.
so God would be unjust and unrighteous if He failed to provide the opportunity for all to be saved.
"14 What shall we say then? Is there unrighteousness with God? God forbid. 15 For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
16 So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.
17 For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth.
18 Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth.
19 Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?
20 Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
21 Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory," (Romans 9:14-23)
I know the doctrine of unconditional election can be offensive form a human point of view, but it is true, and it is taught clearly all throughout God's word. He even addresses your very objection in Romans 9. Either you believe God's word or you don't. I'm very sorry if the truth offends your human sensibilities.