We've all been there before. You buy a stock, and it immediately proceeds to plummet.

Now you're faced with a decision: Do I sell and get rid of this loser? Do I sit tight? Or (gulp) do I back up the truck and buy more shares? Here's a framework for considering whether or not to double down on a stock when it's sinking.

Should you double down?
A casino has less than a 1% edge over blackjack players who play the game correctly. However, many players fail to do certain things, like double down when they have an 11 (and thus are in prime position to hit 21) and the dealer shows a five or a six (and is in prime position to go bust).

Players who fail to maximize their bets when the odds are heavily in their favor are in effect giving away free money to the casinos. Over the long term, not maximizing those opportunities will drastically reduce their probability of winning.

Application to investing
Just as in blackjack, investors are free to increase or decrease their investments at any given time. So when should investors, faced with heavy losses, double down on a stock?

Unfortunately, there are no hard and fast rules. Instead, it's all about the odds in each unique situation. When investors buy shares in a company, it's because they think the odds are stacked in their favor. Perhaps you thought that Washington Mutual's (NYSE: WM) retail branch network and strong deposit base justified a much higher stock price.

Unfortunately, WaMu suffered as the housing market tanked and additional credit problems surfaced. The key question here is, "Is the thesis still intact?" Do I still think Washington Mutual's value is much higher than its stock price in light of its deteriorating credit quality? Just my two cents, but at nearly 50% of book value, WaMu's shares look like a favorable risk/reward proposition -- but only for investors with at least a two-year outlook. And only for investors who are comfortable with the reported book values of banking stocks like WaMu, Merrill Lynch (NYSE: MER), and Morgan Stanley (NYSE: MS), which have all recently taken sizable writedowns.  

Always know the odds
In blackjack, updating the odds when cards are shown is easy. If I have an 11, and the dealer is showing a bust card, then it's an easy decision for me to double down, because the odds have heavily shifted in my favor. In investing, however, there are a lot more factors that affect the odds than in a simple blackjack game.

One great example of how to reinterpret a company's prospects based on additional information is fellow Fool Christopher Singley's analysis of Inside Value recommendation First Marblehead (Nasdaq: FMD), in which he reupdates his view of First Marblehead's value after highly significant information was released.

Bringing down the house
In a nutshell, investors faced with losses need to figure out how any additional news affects the probabilities. If you bet on a football game, and then find out the star quarterback is out with the flu, then the odds have shifted against you. If, however, you find out the third-string kicker is out with the flu, then the odds probably haven't changed at all. Once you reupdate the odds on a stock, check out the stock price. Has it over- or underreacted? Then act accordingly.

Related Foolishness:

First Marblehead is an Inside Value and Hidden Gems pick. Washington Mutual is an Income Investor recommendation. Try any one of our investing services free for 30 days.

Fool contributor Emil Lee is an analyst and a disciple of value investing. He doesn't own shares in any of the companies mentioned above. Emil appreciates your comments, concerns, and complaints. The Motley Fool has a disclosure policy.