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Here's a fun little mind-bender: You toss two coins. What are the chances you end up with one head?

Most people instinctively would say one in three - either no heads, one head or two heads. In fact, the answer is two in four - the possibilities are no heads, head-tail, tail-head and two heads.

It's a very easy example of probability given by physicist (and former Star Trek writer) Leonard Mlodinow in his new best-selling book, The Drunkard's Walk: How Randomness Rules Our Life.

Here's a harder, more provocative one that ultimately can teach us a lesson about investing: Understanding the career of Sherry Lansing, who ran Paramount's Motion Picture Group for 12 years. In her first few years after being named the first woman to lead a major studio in 1992, she was Hollywood's chosen one, with critically acclaimed blockbusters like Forrest Gump, Braveheart and Titanic. She could do no wrong.

After many strong years, though, there was a reversal of fortune. Suddenly, she could do nothing right. By the time Ms. Lansing left Paramount, her reputation had taken a serious blow. She had it once, but lost it.

Mr. Mlodinow is fascinated by Ms. Lansing's story and scoffs at that conventional wisdom. People, he told me in an interview, don't just lose it, unless there is some cataclysmic event in their lives. "It makes no sense, so you have to look at other theories to get at the truth."

What he did was look at market share figures: In the final six years of Ms. Lansing's reign at Paramount, market shares of the company were 11.4 per cent, 10.6, 11.3, 7.4, 7.1 and 6.7, respectively. That decline led to her firing, but Mr. Mlodinow says the story shouldn't end there: The year after Ms. Lansing left, Paramount's market share rebounded to 10 per cent - with hit movies she had green-lighted. If she had stayed on for one more year, he maintains, "she would have been right back on top again" and the media would have heralded her as the comeback kid.

So what can investors take from this? The most obvious answer is not to just accept conventional wisdom, but to question it. Ask yourself if it makes sense. Mr. Mlodinow would agree, but he would also want us to reach another conclusion on what really happened to Ms. Lansing. In his view, she simply had a long spate of good luck, followed by a shorter run of bad luck.

Mr. Mlodinow is a big believer in luck and randomness. His provocative point, which he backs by mathematical theory, is that it's luck, not expertise, behind streaks of success - from picking Hollywood hits to picking stocks. Ms. Lansing may be a skilled leader but she works in a business where randomness rules - tastes and trends can change dramatically from when you give the green light to a film to when it gets to the screen. Good movies fail all the time while bad movies succeed. You can't predict what will happen.

But if Hollywood is all about luck and randomness, consider the stock market, a much bigger and more complicated example. In Mr. Mlodinow's view, there are so many unpredictable factors in the stock market that it's impossible to have real expertise. "If you talk about people consistently timing the market, in my view that's completely impossible," he says.

So, if a mutual fund manager beats the market 10 years in a row, it doesn't mean he's smarter than the rest, he's just lucky. As an investor, you shouldn't buy a mutual fund based on that 10-year streak because that period of performance is no real indicator of future performance. To be statistically confident of a fund's performance, you need a sample of 100 years, so looking at five or 10 isn't enough.

As I'm listening to Mr. Mlodinow, he makes me want to just put all my money into an index exchange-traded fund. If you can't beat the index over the long term, then at least you match it. Interestingly, when I ask Mr. Mlodinow what an investor should do, that's his exact advice. He believes no investor should pay a premium for a fund based on the fact that it has had a successful record of a few years or a star portfolio manager.

It's hard to decide whether Mr. Mlodinow's views are disconcerting or liberating. It certainly would be a comfort to blame bad luck every time you misstep. And who can really dispute that there's a lot randomness in the market? Just think of the countless contradictory opinions from experts out there on any given subject: All of those experts are working from the same set of numbers but are reaching opposite conclusions.

But I can't help but to think that I do better the more I research, the more I know. Just to decide where to invest, even what ETFs to invest in, what the options are, takes a lot of hard work. And there is a real difference in risk factors. I may not be able to predict where the economy will be in five years or even where the price of oil will be in five weeks, but I do understand the difference in risk between a blue-chip stock and a penny stock.

So my plan is to continue to look for great stocks, and attribute any profits to good luck. But just to be sure, maybe I'll add some ETFs to my portfolio.

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