How can Wall Street take money from amateur day traders? This question was not taken well where I originally asked, despite my best intentions. This is a game theory question about short term day trading. A little backround on day trading verse investing  


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*Long term investment in stocks is not zero sum because the market grows

*A common quote is "90% of day traders lose money." For instance
It is often advised that although stock investing is good, day trading is bad and even negative sum as brokers and the government begins taking bigger cuts. However there is a small minority of compulsive day traders on Wall Street who are lucratively and reliably profitable (200000% gains). Some results are too eerie for me to believe it's luck. 
If it doesn't cause a fundamental change in assessment, I'll suppose day trading is zero sum. Here is the question

Suppose amateur day traders bet randomly. Then when they bet there's a 50% chance of the stock going up and them making money, or a 50% chance of the stock going down and them losing money.  How could an elite Wall Street trader take money from these random betters? 

 A: There are various models in economics that can give you some answers.
As mentioned before, there would have to be some asymmetry of information for professionals to be able to exploit "amateurs", who have inferior information.
However, if these amateurs were rational, they should realize they have inferior information, and not trade, since they would lose money in expectation. This intuition is formalized by the "no trade theorem". It would seem, then, that these amateurs are not rational, for if they were rational, systematic losses would not be an equilibrium outcome (not trading is a profitable deviation).
There is a second class of models, "noisy rational expectations models", where rational traders with information exploit what is called "noise traders" (which might be a version of the amateurs you describe). The seminal paper in this literature is this one. In these models, the professional traders acquire information at a cost and use it to exploit the noise traders, making systematic profits while noise traders lose money. Grossman, one of the authors, started a hedge fund after his academic career and was quite successful, and his trading is rumored to be influenced by his model. Hence, it does seem to capture the essentials of what you are trying to understand.
