The Christian position is a bit complicated.
Its not as simple as
"Good God only does good things. Allowing evil isnt a good thing. Therefore, good God doesnt exist.".
Lets look at some verses which provide the explanation.
- The Lord is good to all, and His tender mercies are over all His works. - Psalm 145:9
- No one is good but One, that is, God. - Mark 10:18
The second verse tells us that we are all evil. The first verse tells us that God is good to all, no exceptions. This means that God is good towards evil people.
When Bible talks about good, it does not talk about pleasure outweighting the pain.
It talks about life and the praise of God.
Therefore, good God is God who creates life, God who is praised. Good God is God who is good to all, therefore God who gives life to all. That is the Bible's definition for good God.
God good to all would be God who gives life to all, to both good and evil people.
So really, when we define good as "an increase of life, and an increase of praise of God", we see that the existence of evil does not negate God being good. Rather, God giving life to evil people would still be counted as good action.
Since we are all evil, and God gave eternal life to us, that means how God is good to us.
Therefore, evil is not the opposite of good, by Bible's standards. Rather...
In fact, the existence of evil is good since existence itself is good.
I guess if I had to put it in the forms of premises and conclusion, it would look like:
P1) Creating all life is a good action
P2) Creating all life caused evil to exist
C) The existence of evil is good, since it is the result/part of a good action
Therefore, its not that evil results in greater good. Its that a good action has evil as its part/result.
Existence of evil is good, if we assume that existence itself is good. Therefore God, being the creator of all existence, is good.
Okay, lets put it through definitions:
1. Good God being defined as God who is good to all
2. Good being defined as giving of life
3. God who is good to all is God who gives life to all
4. Giving life to all would mean giving life to evil people
5. Good God is God who gives life to evil people
Same logic can be applied to existence and explain the existence of evil.
Again, it really depends on how "good" is defined, and Bible defines good in a different way than most other books. Its not as simple as "pain vs. pleasure". When Bible talks about good, it has many meanings. I gave examples of some meanings that can be used, but I am pretty sure there is more to it as Bible is a 2000 page book.