You are probably familiar with roulette. It's a favorite game among novice gamblers because it's so easy to play. What could be easier than picking red or black? A recent television program covered the significance of the tracking board that accompanies every roulette table. This is where the house conveniently displays what happened in the previous spins of the wheel.

Daunting probabilities
A roulette wheel has 38 numbered spaces on it:

  • 18 are red
  • 18 are black
  • Two are green (0 and 00)

During each spin of the wheel, you've got a 47.36% chance that the little ball will land on red (18/38). The same odds hold true for black. If you bet $10 and win, you pocket an additional $10. So, on average, if you plan to make 100 bets at $10 apiece, you'll be wagering a total of $1,000. After those 100 bets, you should have around $947.20 left. So, the casino would profit $52.80 (just more than 5%) of your hard-earned money.

Let's put 5% into context
Just in case losing 5% doesn't sound too bad, let's put that into context. Currently, you and I are earning about 1% per year on our cash holdings. Experts such as Warren Buffett have pegged expectations for stock market growth at 6% to 7% per year. In roulette, the odds are stacked against you to the tune of -5% every time you play. The longer you play, the more likely you are to lose even more.

Wait, it gets worse
But long ago, some very smart casino owner realized a way to increase his profits by 30% overnight! How? If you guessed that little tracking board, you're exactly correct. You see, those casinos really understand human behavior. When players noticed that red came up several times in a row, they started altering their betting patterns. So, instead of half the bets going toward red and half toward black, people began betting more heavily on whichever color had not come up last. For those who study behavioral finance, this has been termed the gamblers' fallacy. Now, remember each spin of the wheel is a completely independent trial. What happened in the previous spins of the wheel has absolutely no impact on what the future outcomes will be.

Understanding human behavior
Why are humans so easily swayed and influenced by a previous spin that has absolutely no impact on future outcomes? It turns out that we have a need to search out patterns and assign causality to random events. This is particularly true of a long series of events. Imagine you flipped a coin seven times and it came up heads each time. If you required each person who witnessed this series to wager $10 on the outcome of the next flip, most would bet on tails.

The field of behavioral finance is a new one. It's also incredibly important that investors understand and avoid the most common decision traps. So how does this influence investor behavior? I'll provide two examples.

Past performance is no guarantee of future success
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Unfortunately, mutual fund performance, in the long run, is determined mainly by low fees. Funds that have low turnover, low taxes, and low expense ratios tend to outperform the averages. That is the best predictor of future fund performance. Funds with high fees and turnover tend to perform worse than those with low fees. That's right, indexing works. There are also some actively managed funds with long track records of success. Our Champion Funds newsletter service seeks out those very funds each month.

Here's a very personal example. Back in early 2003, I found that a stock I owned was trading at $14 per share. This same company had $11 per share in cash on its balance sheet and no debt. I know what you're thinking: Boy, what a clunker.

Well, not exactly. It also was one of the top brands in the world. The company was Apple Computer (NASDAQ:AAPL), which also happened to be the first stock I ever bought, some 17 years earlier. Needless to say, I knew the company and followed it for a long time. We owned two iPods and two Apple computers. By the time I got done running through the numbers, I happily decided this was a slam dunk at $14. However, in the brief time I spent running the numbers, the stock had rocketed up to $17 per share. Being a bargain shopper and not wanting to pay top dollar, I decided to enter a limit order at $16 per share.

I never saw $16 again, and at time of this writing, the stock rests at more than $62 per share. By the way, I sold my shares on the way up at around $40, so don't take this as a recommendation to buy Apple at this price.

The point is that just because something has a run-up doesn't mean it's going to come back down again. I made this mistake even after reading about Warren Buffett making a similar mistake with Wal-Mart (NYSE:WMT) many years before. Experts in behavioral finance call this anchoring. It's simply when investors allow a previous stock price to influence their behavior. Although I thought the company was seriously discounted, I didn't buy it because I wanted to get in at the bottom. I knew the company. I knew about anchoring. And I still made the mistake.

Similarly, a stock that drops doesn't necessarily have to rebound. In chapter eight of The Intelligent Investor, the author points to Inktomi, which in March 2000 traded at more than $231 per share. In September 2002, the stock closed at 25 cents. Along the way, I'm sure many investors chose to hold because they were waiting for it to go back up again.

That's no surprise, given the fact that people tend to treat gains and losses much differently. Gains are pleasant, but don't have the same impact of the devastation a loss can have on an investor's psyche. That's why so many people hold on to stocks (even as they are collapsing), because they are just hoping to get back to even. For all you Google (NASDAQ:GOOG) shareowners, notice that Inktomi provided the best-of-breed search engine at the time. Google is certainly a much stronger and more mature company than Inktomi. However, I believe time will show that the current market valuation of $55 billion is way too high.

So as you invest, tune out the mainstream press, and don't bother following the herd. When everyone is bragging about making money, be very cautious. And finally, when opportunities present themselves, be mentally prepared to take action and resist those built-in human defenses.

Remember, one of the best years ever for investors was 1974. Nixon was getting impeached, inflation was at 12%, there were riots in most of the major cities. Only the prepared were brave enough to recognize just how cheap stocks were then. As Benjamin Graham said, "If you are shopping for common stocks, choose them the way you would buy groceries, not the way you would buy perfume."

Recognize gambling for what it is, a losing proposition. Don't fall prey to your own mental accounting tricks by categorizing your gambling losses differently than other losses or expenses. Never gamble more than you can comfortably afford to lose. Better yet, invest in yourself. Each month in Motley Fool Rule Your Retirement, thousands of members are learning how to avoid these decision traps and chart a course for their own financial independence. Why not take a free trial?

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Buck Hartzell spends his days managing Motley Fool Rule Your Retirement . At night he enjoys watching the World Poker Tour on TiVo. He does not own shares in any of the companies mentioned. The Motley Fool is investors writing for investors .