I happen to beling to mainstream Christianity and I'll explain it how we believe it. It seems to make much more sense this way.
First off, Jesus is God (Lets not debate trintiy -- just makes a difference in this explination)
We are all sinners. We are imperfect and sin many times. As sinners we can not ever deserve eternal life.
God is love, but God is also just and therefore must punish sin.
There seems to be a problem and this problem is solved through Jesus Christ. Jesus Christ died on the cross to pay the penalty for our sins. (Like if your child committed a horrible crime and you could take the punishment of death so that he/she could live -- you would be demonstrating an intense amount of love for that child).
The only way that Christ died for Adam's sin is that the sin we all have is due to Adam. So, Christ died for Adam's sin which we all have.....
I'm sorry but this is so far fetched. Why would god need to die for us - he's almighty, right? Also, he really didn't die, right? Unless he is gone from the universe completely, never to be present again. In your terms, it would work like this: Kidnappers take my son and demand $100,000 for his release. I give them the $100,000, get my son back, and then print $100,000 on my money machine at home. So basically I did not lose anything.
Did you know that up until a couple of hundred years ago the official church teaching was that god tricked satan. Originally satan was supposed to get jesus' soul as payment. Satan agreed to the terms put god pulled a fast one and resurrected his son leaving Satan to hold an empty bag. Funny how christanity has changed their doctrine since.