Is it accurate to say that if I was to trade something, my probability of success can't be worse than random?
It seems to be that your main point is this: No matter what, my chances cannot be worse than random and if my trading system has an edge that is greater than the percentage of the transaction that is transaction cost, then I am probabilistically likely to make a profit? In general, yes, that is true, but... Consider this very bad strategy: Buy one share of stock and sell it one minute later, and repeat this every minute of the day. Obviously you would bleed your account dry with fees. However, even this horrible strategy still meets your criteria because: if this bad strategy had an edge beyond the transaction fees you would likely still make a profit. In other words, your conclusion reduces to an uninteresting statement: If there were no transactions fees, then if your trading system has an edge then you will likely make a profit. Sorry to be the bearer of bad news, but IMHO, that statement, and others made in the question are just obvious things stated in convoluted ways. I don't want to discourage you from thinking about these things though. I personally really enjoy these type of thought experiments. I just feel you missed the mark on this one...