Are you saying that it's unreasonable to suppose that some people can make money day trading in the long run? I was just illustrating a simple model you might use to test that theory.

I'm saying it's not reasonable to think that a private individual can make a long-term profit day-trading, skilled or not. It's quite reasonable to suppose lots of impossible things.

How does your model account for magnitude?

There are professional day traders who earn an income over the long run by day trading. This is a true fact. It seems like you are trying to contradict this fact… or do I misunderstand what you are saying?

The model I gave was the simplest model I could think of that would let you test the theory that skill is a factor in day trading. It was an illustration of how someone with mathematical training might think about statistics like "80% of day traders lose money" without jumping to the false conclusion that all traders eventually lose money.

> There are professional day traders who earn an income over the long run by day trading. This is a true fact.

Got anything to back up this "fact"?

> The model I gave was the simplest model I could think of that would let you test the theory that skill is a factor in day trading.

You can't assume the existence of skill proves the existence of long-term profits.

Nor can you even assume that a good up/down ratio proves skill without considering the magnitude of the ups and downs or the impact of compounding.