Funny you should mention the Miller/Urey experiment. The atmosphere that Miller used to simulate the "early earth" atmosphere was a hydrogen-rich mixture of methane, ammonia, and water vapour. Modern scientists now believe that the earth's atmosphere was actually made mostly of carbon dioxide, nitrogen and water vapour. Infact, it was in the 1970s that Belgian biochemist Marcel Florkin was already declaring that the Miller/Urey theory of the early atmosphere "has been abandoned". under those conditions you would get nothing similar to amino acids. Modern text books cover this up by saying "You still get organic molecules". However, these "organic molecules" are things like Cyanide and Formaldehyde. If you are unfamiliar with what Formaldehyde does, I think you should know that it is so toxic that it's fumes alone fry proteins and kill embryos. Doesn't sound like life-friendly stuff to me.
Even if amino acids are formed, you then have to get the exact number of the correct amino acids to link in the correct from to link up to form a protein molecule. After that, you'd need dozens of protein molecules (again, in the correct sequence) to form a living cell. This may sound rather simple but the odds against it are astronomical. Imagine putting a sterile, balanced salt solution in a test tube. Then put in a living cell and poke a hole in it so it's contents leak into the solution. You now have all the molecules you need to make life, right? You've already accomplished more than Miller did. Only, the thing is, you can't make a living cell. The cell is now dead and it's like trying to make a rock fall up all the way to the moon.
Furthermore, even if you are able to get life, never does any mutation of any kind ever provide a living organism with any more information. For example, imagine there is a type of beetle (with wings) living in a certain area. This area becomes uninhabitable so the beetle population moves, one half more inland, the other to a small island off the coast. Let's say that, after years of mutation, the island population of beetles no longer has their wings because whenever they tried to fly, they were blown out to sea by the strong winds. Due to this, only the beetles with missing or deformed wings survived to breed. On the other hand, the inland population retains their wings. So, the island beetle's adapted to their surroundings, but they gained no extra genetic information.