The SEC requires that the words "Past Performance is No Guarantee of Future Performance" be included in every mutual fund prospectus. This notice should be posted in casinos, not in prospectuses.
Casinos and the law of of large numbers
The "law of large numbers," which is often called the "law of averages," is a corollary of the law of probability in statistics. Probability applies to events involving inanimate objects like numbered balls, dice, cards, etc. Probability gives the odds of any particular result from manipulating those objects.
These odds are based on probabilities, i.e., the past performance of the object(s) being used for prediction. However, the law of large numbers says: in the short run past performance in casino games is NOT a predictor of future results.
For example, the law of averages says that over the long run you will get 50 percent heads and 50 percent tails from flipping a coin. The larger the number of coin tosses, the closer you'll come to results that are exactly 50/50. But in the short run, either heads or tails can come up. No one can predict which.
It doesn't matter what the last result was or even what several recent results of the coin toss were. The same goes for recent recent rolls of a roulette ball or dice in craps. In the short run "luck" or "chance" rules over casino games. That's why the SEC's warning against using past performance ought to be prominently posted in casinos!
Pari-mutuel betting -- investing
The other kind of gambling, the kind that applies to investing, concerns use of human wisdom i.e., your "smarts," to predict the future result of an event involving living beings, such as a horse race or a baseball game. Odds for pari-mutuel betting aren't based on "luck." They're based on popularity.
For example, the horse with the most bets on it will have the highest odds, e.g., 2 to 1. The "long-shot" will have the lowest odds, e.g., 20 to 1. These odds determine how much the money the winners collect.
Because stock investing is a continuous activity, and not a time-delimited event like a horse race, there are no posted odds. Each individual investor wins only when they sell their stock and only if they get more than they paid for it. They "win," but the "race" keeps going.
Past performance can indicate future results
Just as gamblers at the track try to pick the best horse, investors choose a company or a group of companies (i.e., a mutual fund or an ETF) they think will out-compete similar companies. Investors believe their investment will "win" for them at some particular point in the future.
Not only will being an "educated" investor give a person a better chance of making good predictions about companies and funds; almost every investor alive, whether novice, sophisticated, or seasoned broker relies on knowledge of past results for a company or fund to judge its future prospects.
So why does the SEC warn investors against using past performance? Perhaps because novices look at last year's results for a mutual fund, and if it's high they buy. Performance is important, but novices should learn that price is even more important. The whole point of investing is to buy at a low price and sell at a higher price. That's how money is made.
For example, good performance by a fund or a company could mean the price is already too high. That investment may have been "overbought" by the crowd piling on to grab a piece of the latest "bubble." When this happens, past results do indeed indicate future performance -- they indicate future performance will decline.
This kind of thing is what novice investors need to learn. Investors need to be informed enough to assess what past performance means in any given case. That is why the SEC's warning against using past performance is advice investors should take with a grain of salt.