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Dan Solin is the New York Times bestselling author of the Smartest series of books which include: The Smartest Investment Book You’ll Ever Read, The Smartest 401(k) Book You’ll Ever Read, The Smartest Retirement Book You’ll Ever Read, The Smartest Portfolio You’ll Ever Own, 7 Steps to Save Your Financial Life Now and The Smartest Money Book You’ll Ever Read. He is also the author of Does Your Broker Owe You Money? His latest book is: The Smartest Sales Book You’ll Ever Read.

I am not going to keep you waiting. Here is the question your broker hopes you’ll never ask:

What about Bill Miller?

You may remember Bill. In an article in Money Magazine in January 2004, he was described as the country’s greatest mutual fund manager . As the manager of the Legg Mason Value Trust (LMVTX ), Miller had just beat the S&P 500 for 13 years in a row. Money computed the odds of doing so at 149,012 to 1. It was rare to read an article about him where his name was not followed by either guru or investing genius.

Andy Sewer, Fortune’s managing editor, described Miller in a November 2006 article as the greatest money manager of our time .

Miller was the poster child for active management. Brokers used his track record to justify their selection of funds for which the fund manager sought to beat the markets. After all, wasn’t Miller proof that someone had this skill?

Miller went on to beat the S&P 500 for two more years. Clearly, he had the mojo. Investors thought so. At its peak, his fund had over $21 billion in assets.

Then the train went off the tracks.

Don’t Confuse Luck With Skill

The recent performance of his fund is so bad (including a decline of 55% in value in 2008), the fund is ranked by Morningstar close to the bottom of its rankings for the past three, five and 10 years. His three-year record is particularly dismal. His fund had an annualized loss of 20%, compared to a loss of only 9% for the S&P 500.

Investors fled in droves. Assets plunged to a little over $4 billion.

Now, Miller’s experiencing the ultimate fall from power: He’s being eased out of his fund. A new co-manager, Sam Peters, has been appointed .

Investors often confuse luck with skill. The financial media is quick to anoint someone on a lucky streak as the next financial wizard, but just because you flip a coin and get 10 or 15 heads in a row doesn’t mean you are a skillful coin flipper. Over an extended period of time — say, 20 years or more in investing — it all averages out.

So the next time your broker tells you about a great performing fund with a hot fund manager, or shows you five-year historical returns, ask him the question he dreads most.

Then run for the door. Call Vanguard, Fidelity, Charles Schwab or one of the other major fund families, and tell them you want a globally diversified portfolio of low-cost stock and bond index funds, in an asset allocation appropriate for you. I provide details in my book, The Smartest Investment Book You’ll Ever Read.