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Is it accurate to say that if I was to trade something, my probability of success can't be worse than random?
One key piece missing from your theory is the bid/ask spread. If you buy a stock for $10, you usually can't immediately turn around and sell it for $10. You can only sell it for whatever someone is willing to pay for it.  So virtually any random investment (stocks, bonds, forex, whatever) immediately loses a small amount of value, and over the long run you will almost certainly lose money if you buy/sell at random.