For example, you might happen to learn that a particular brand of tennis shoes has suddenly become very popular among college students. You could invest in the stock of the company that makes the shoes in order to profit from this information. In reality, though, there are thousands of other like-minded people who are trying to guess the latest trends and make a killing in the stock market. Thus, it is likely that prices in the stock market for the shoe company already reflect the information you are trying to profit from. As a result, you will have difficulty making an abnormal profit by investing in the company.
Many studies suggest that it is difficult to beat the market.
For example, if you buy a lottery ticket it only pays off in one state of the world. You could estimate the expected payoff by multiplying the payoff in the lucky state by the probability of that state occurring.