@NealNealNeal,
You are actually making a couple of mistakes... we are going to start with the magic number fallacy. Then we have to talk about graphs (these are probably not what you are thinking... but we might get there).
You are asking the odds of flipping a coin 1000 times and having it come up heads every time. This is a magic number... because this particular sequence of coin flips is something that for you would have meaning.
However, statistically speaking... getting heads 1000 times in a row is
equally likely as any another sequence of coin flips. Do you understand this?
The powerball numbers yesterday were 08 12 26 39 42 11. This is no more or less likely than getting 01 02 03 04 05 06. Any combination is equally likely... you just ascribe meaning to one and not to the other. Someone might think that if the numbers came up 01 02 03 04 05 06 that would be proof of something. In reality it is not more proof of anything than 08 12 26 39 42 11. The numbers have to be something and one sequence is no less likely than another.
Are you with me so far?