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Las Vegas is profitable because most gamblers know little or nothing about the games they’re playing and the odds against winning. Basically, players go to be entertained by the unexamined possibility of winning.

Millions of people do much the same in the casino of investing. We do it with our 401(k) plan choices. We do it with our “play money” choices. We even do it when we hire a financial adviser to make our choices for us.

The only difference between the two casinos is that in Las Vegas you lose your money and in the investing casino you get a lower return.

You can understand this by examining the odds and expenses we face when selecting a mutual fund. According to the Morningstar fund database, there were 684 managed large-blend funds at the end of 2012 with track records of at least 10 years. (Large-blend funds are the funds that invest in the largest domestic companies by market value.) As a group, these funds had an average annualized return over the last 10 years of 6.63 percent and an average net annual expense ratio of 1.28 percent.

Picking a winner in this group would have provided a big payoff — funds in the top 10 percent returned at least 8.31 percent, a big premium over the average.

Index funds that were built to duplicate the performance of the S&P 500 index, however, beat 66 percent to 69 percent of all the managed funds. The Vanguard 500 Index fund Admiral Shares, for instance, returned 7.09 percent while the Investor Shares, which require a smaller minimum investment, returned 6.99 percent. Other well-known funds that track the same index were inside that return range, including the Schwab S&P 500 Index Fund, the Fidelity Spartan 500 Index Fund and the SPDR S&P 500 exchange-traded fund.

What explains the small differences in returns for funds that track that same index? Differences in expenses and “tracking errors” — duplicating an index isn’t easy.

The most important fact, however, is that any of these basic index funds beat the average managed fund, as noted above. If you had simply invested in the oldest of these funds, the Vanguard 500 Index Investor Shares, your 6.99 percent return would have beaten the average managed fund by an annualized 0.36 percent.

Paying to play

But suppose we play to win. What are the odds? What would you have gained if you had selected one of the managed funds that did better? Those funds provided an average return of 8.04 percent. So if you had picked a winner, you would have gained an average of 1.05 percent a year.

The unexamined promise and prospect of picking a “winning” fund and gaining that 1.05 percent a year is what fills pockets of the mutual fund casino owners — and their croupiers.

Now look a little closer. To bet on a managed fund, we have to pay more. These funds have an average expense ratio of 1.28 percent a year. That’s 1.11 percent higher than the 0.17 percent expense of the Vanguard 500 Index Fund. So get this: To take a chance on improving your return by an average of 1.05 percent a year, you had to pay an extra 1.11 percent a year.

Would you buy a managed fund if the odds were presented in this way? Probably not. And that’s not all.

When you make a bet that you can select a winning managed fund, you don’t just bet on the pool of winners. Instead, you must select from the entire pool of funds. In this case, you only have a 34 percent chance of picking a winner. So you’re really paying $1.11 to win a prize of 36 cents.

When you figure the odds, picking winners is a losing proposition.

A safer bet

What I’ve just told you isn’t a special case. The same exercise can be done with any and all asset classes with similar, but not identical, results. This example actually understates the odds because the Morningstar database is limited to funds that survived the measuring period. Many did not.

The same math and odds apply, with added costs, if you pay a fund adviser to select winning funds for you. And that’s why you read about index fund investing in this column. It’s how you win the mutual fund game.

Scott Burns is a syndicated columnist and a principal of the Plano-based investment firm AssetBuilder Inc. Email questions to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .