What are your chances of being struck by lightning today? Only one in 256 million.

That's close to zero, but not quite. Over the course of one year, your chances "improve" to one in 400,000. Over your lifetime, it's one in 5,000.

And given enough time, everyone is struck by lightning.

Even your portfolio
Unexpected -- even random -- events are a fact of life for every investor, whether you're invested in growth or value stocks, large-cap or small-cap stocks, blue chips or innovators.

Take securitizers Fannie Mae (NYSE:FNM) and Freddie Mac (NYSE:FRE), for instance. As quasi-governmental agencies, they attracted investors at home and abroad who believed that the securities were almost as safe as the government's -- and they paid better.

In the last year, however, both have lost 80% of their value, and with the companies' liquidity drying up (and with it, their ability to do business), shareholders are hoping that the Fed hasn't exhausted its largess with that $30 billion guarantee on potential losses from JPMorgan Chase's (NYSE:JPM) acquisition of Bear Stearns.

Natural disasters, corporate malfeasance, economic downturns, unexpected competition -- any of these can affect a company's future. If you invest in the market, you'll want to know how likely those unpredictable events are.

Maybe, maybe not
We know the mathematical odds of being struck by lightning, but the likelihood that another bank will go belly up as a result of the credit crisis is less determinable.

And Pentagon decision-theory analyst Daniel Ellsberg has demonstrated that the precision with which we can determine the chance of something happening matters -- at least when it comes to making decisions.

As psychologists Chip Heath and Amos Tversky explain, when events are reasonably likely, we would rather bet on known, precise odds. This phenomenon, which is known as ambiguity aversion, explains why investors shy away from companies whose futures seem uncertain -- even if that uncertainly also seems likely to end in a big win.

But that aversion does us a disservice -- because whether a scenario is likely to happen is only one piece of the puzzle. What matters most -- as anyone who's had a close brush with lightning will tell you -- is what happens if a scenario plays out.

Roll the dice
Let's take a look at Baidu.com (NASDAQ:BIDU). When we recommended the leading Chinese search engine in the November 2006 issue of Motley Fool Rule Breakers, the company was on a tear -- absolutely destroying foreign competitors while growing its own share of the Chinese search market to 62%. With more than 1 billion Chinese still waiting to get online, the opportunity for growth was tremendous.

Of course, there were risks associated with buying "the Google of China," most notably competition from Yahoo! (NASDAQ:YHOO) and the real Google (NASDAQ:GOOG). But Baidu had the home field advantage: It understood cultural differences better than foreign multinationals (it turns out Chinese don't mind advertisers paying for better search placement -- a deal Google was unwilling to entertain), has better connections (founder Robin Li is a national hero), and is a source of nationalist pride.

Additionally, there was -- and still is -- no guarantee that China wouldn't experience some hiccups along its path to development, that Baidu's technology wouldn't fall woefully behind its better-capitalized competitors, or that an irate Politburo wouldn't shut down Internet search altogether over a hypothetical blogger's faux pas mentioning a 1989 event in "T________ Square."

These were all very real risks, albeit of varying degrees of likelihood, and a lot of investors let these uncertainties prevent them from investing -- missing the fact that even a reasonable and conservative estimate of the odds would show that investing in Baidu would have made plenty of sense.

Play the odds
So let's consider an unconventional approach to valuing Baidu:


Government shuts down Internet search in name of "national security"

Utter technological obsolescence

Catastrophic Chinese economic meltdown

Loses some market share

Baidu grows to just one-quarter the size of Google







Effect on Return












Expected Value



*Value is the probability multiplied by the return.

Even taking into consideration some fairly extreme scenarios, a portfolio of similar bets could be expected to average a 174% return, almost a three-bagger.

In other words, it was a reasonable bet.

As it turned out, China experienced double-digit GDP growth in 2007 (again). Baidu has continued to increase its market share -- the Chinese Internet Network Information Center pegs its share of the Chinese search market at 75%. Worldwide, Baidu has the third-largest market share -- beating out Microsoft's (NASDAQ:MSFT) MSN search engine.

The company has grown LTM sales 231% (trailing 12 months) and LTM earnings 260% since September 2006. Investors who bought around the time of the recommendation are up 258% so far.

Profit from uncertainty
Of course, as an intelligent and Foolish investor, you would love to take advantage of the greatest stocks the Street misses. Evaluating potential investments through the lens of probability can help you do that.

In fact, a similar approach has led Fool co-founder David Gardner and his team at Rule Breakers to nine recommendations -- besides Baidu -- that have already more than doubled. You can get full access to all of our research and recommendations, including our top two picks for new money now, by accepting a free 30-day guest pass to Rule Breakers. All you have to do is click here. There's no obligation to subscribe.

Despite his mild fear of heights, Ilan Moscovitz is on the hunt for tomorrow's highfliers. He owns share of Google. Google and Baidu.com are Rule Breakers recommendations. Microsoft is an Inside Value selection. JPMorgan is an Income Investor pick. Is it a bird? Is it a plane? No, it's the Fool's disclosure policy.