I recently was asked to consult with an investor who had been lucky enough, or smart enough, to buy Facebook stock in September 2012, when the price had fallen to about $20 per share. At the time I spoke with him, the firm’s stock had reached $76, leaving this investor with the potential to earn a huge profit.

After pointing out that his original investment had grown to a fairly significant percentage of his overall portfolio, I suggested that he sell at least some of the company’s stock and diversify his holdings. His response was: “What could go wrong? I only paid $20 for it.”

This line of thinking is caused by a common mental accounting mistake, one I call the belief that you’re playing with what’s known as the “house’s money.” It is also one of the surest ways I know to turn a sizable fortune into a small one. To help the investor in question consider the issue in the proper context, I related the following tale…

By the third day of their honeymoon in Las Vegas, a pair of newlyweds had lost their $1,000 gambling allowance. That night in bed, the groom noticed a glowing object on the dresser. He realized it was the $5 chip he had saved as a souvenir. The number 17 was embossed on the chip’s face. Taking this as an omen, he donned his green bathrobe, rushed down to the roulette tables and placed the $5 chip on the square marked 17. Sure enough, the ball hit 17. The 35:1 bet paid $175. He let his winnings ride, and once again the little ball landed on 17, paying him $6,125.

And so it went, until the lucky groom was about to wager $7.5 million. The floor manager intervened, claiming that the casino didn’t have the money to pay should 17 hit again. Still clad in his bathrobe, the young man taxied to a better-financed casino. Once again, he bet it all on 17, only to lose everything when the ball fell on 18.

Broke and dejected, the groom walked back to his own hotel room. “Where were you?” asked his bride. “Playing roulette,” he responded. “How did you do?” she queried. His reply: “Not bad. I lost $5.”

The “Legend of the Man in the Green Bathrobe” illustrates the mistake of “mental accounting,” the tendency to value some dollars less than others, and thus to waste them. Dollars that are earned the hard way tend to be treated with greater reverence.

It’s likely that if our groom had earned the money the hard way, he never would have made such a bet. On the other hand, it’s easy come, easy go. Mental accounting, in this case, allowed the man in the green bathrobe to think of the $7.5 million he had just lost as the “house’s money.” Investors make this same mistake.

To further illustrate my point, I then related this next story. A friend had bought Cisco when it was trading at just $5. The stock represented a relatively small portion of his portfolio. When the stock reached $140, this was no longer the case.

When I asked my friend if he would buy more of the stock at its current price, he said, “No.” I explained that if he wouldn’t buy any, he must believe that it was either too highly valued or he was currently holding too much of the stock, and it was too risky to have that many of his eggs in one basket.

Despite the logic, my friend steadfastly refused to sell some of his shares for the following reason: His cost was only $5, and the stock would have to plummet about 95 percent before he would post a loss. I then asked him if he owned a green bathrobe.

A year later, Cisco was trading at about $16 and my friend was still holding it. Mental accounting had caused him to make the same mistake as our groom. He had considered his unrealized gain to be the “house’s money.”

Making the mental accounting mistake of believing that you are playing with the house’s money can be avoided by developing and maintaining the discipline to adhere to a written investment policy statement (IPS) and rebalancing table. This will force you to get up and walk away with the “house’s money” if a position in a single stock, or asset class, grows beyond the maximum tolerance range established by your plan.

And if you don’t have a plan that includes such tolerance ranges, you should take the time to develop one. Doing so, and then adhering to it, will prevent you from making many of the behavioral errors I discuss in my book, Investment Mistakes Even Smart Investors Make and How to Avoid Them.