要懂得计算概率

投资智囊

编者前言：

股市不是赌场，但它与赌场有很多相似的地方。在赌场中，庄家最怕的是玩21点算牌的人，因为在所有赌博游戏中，只有包括21点（Blackjack）在内的两三种扑克牌游戏是赌客能够根据概率而胜过庄家的。然而，大多数赌客不懂得计算概率。同样，大多数股民也不懂得计算风险。不论你选择什么投资产品，在交易之前，你都要问自己：我有多大的把握一定会赢？凭什么我就知道某支股票一定会涨？我的信号系统是否经过历史的反复验证？如果有一天你能对自己说：这种情况/信号我已经遇到过无数次，每次交易都会赢，这一次也不会例外…… 那时你就距离成功不远了。

编者：三维预测网站 - 3DForecast.com


Lessons From the Poker Table

By Donald Luskin, SmartMoney.com, July 15, 2005


This week in Las Vegas, 5,619 contestants are vying for the 36th annual World Series of Poker's No-Limit Texas Hold-'Em Championship. The total prize pool is $52,818,610 — by far the richest purse in the history of sports.

Just think about what's at stake. $7.5 million goes to the first-place winner. Any player who finishes in ninth place or better gets at least a million. The smallest prize is $12,500 — and that goes to the player who finishes in 560th place.

Yet compared with the stock market, this is penny-ante stuff. That $52.8 million prize pool represents only five one-millionths of the $11.4 trillion market capitalization of the S& 500.

Or look at it this way. That $52.8 million is what the S& 500 pays, on average, in dividends every 137 minutes — 24 hours a day, seven days a week, 365 days a year.

So don't envy the swaggering high-rollers battling it out in Vegas. If you invest in stocks, you're already playing in the biggest game the world has ever known. And yes, investing in stocks is very much a game. In fact, even though it takes place on vastly larger scale, it is very much like poker.

We'll take a look at some of the similarities — but I want to start with a key difference. Poker is a zero-sum game — what the winners win, in the aggregate, has to be equal to what the losers lose. But stock investing is not a zero-sum game. If we posit that, over time, stocks tend to have positive returns, then investors overall will be winners.

Yes, certain investors who make enough bad decisions will lose money in stocks. And during bear markets just about everyone will lose, at least for a while. But the stock game offers something that poker just can't match: Over time, the game itself has a built-in positive expected return for all the players.

Of course the biggest similarity between poker and investing in stocks is that both involve an intriguing combination of luck and skill. Sometimes it seems that the luck element predominates. In poker, there are times when the hand that figures to be the worst will still win the pot, based on the random turn of a single card. And in investing, sometimes you'll double your money when some company whose stock you bought gets acquired, out of the blue, by another company. Or just as likely, you could lose a bundle when some company you've researched thoroughly suffers an unexpected setback.

But there's no doubt in my mind that, over time, skill will prevail in both games. The best poker players can beat poor players even with weak cards. And the best investors can make money even in weak markets. The best have to learn to take their lumps with dignity, because lumps there will surely be. But in the long run, the best poker players and the best investors will come out on top.

Another important similarity between poker and investing is that both games pit professionals against amateurs. In poker, this is how the professionals make the majority of their money — by playing opponents they know to be weaker. What's so remarkable about this fact is that weaker players continue to play the pros — and happily, too.

Several weeks ago I had the opportunity to meet one of the world's top-ranked professional poker players in his Las Vegas home. He told me that he was looking forward to the thrill of the World Series, but he said that kind of event is not how he earns his living nowadays. His bread and butter comes from private games in which he plays against wealthy businessmen and celebrities — all of whom fancy themselves to be poker experts, and who love to hang out with high-profile professionals even though they consistently lose money to them.

Now when you play poker, chances are you just go up against people like yourself around the kitchen table, or perhaps at online poker web sites. But when you make a trade in the stock market, you are most assuredly playing at the same table as the best in the business. Next time you trade a stock, ask yourself who might be on the other side of the transaction. Sure, it could be another individual investor just like you — or it could be Warren Buffett, George Soros, or any of thousands of other professionals who are even more skilled (but whose names you never see in the headlines).

I'm not trying to scare you. It's possible that you can beat the pros at investing. It's even possible to beat the pros at poker. In fact, 2003's World Series winner was an amateur. But don't have any illusions that it's easy. Poker and investing are tough games, and the professionals have all the advantages.

There's one thing in both games that amateurs and professionals have in common: Both are working from incomplete information. In poker, nobody knows what the next card to be dealt will be. And in the stock market, no one knows what company news or economic development will hit tomorrow's headlines.

So in the absence of complete information, one of the things that good players do to win is to play the probabilities. Here's an example from Texas Hold-'Em. Suppose you've been dealt the king of spades and the ace of spades face down. There are four common cards in the middle of the table — two spades and two hearts — so you've got four to a flush. One more card will be dealt in the middle of the table, so you've got one shot to fill your flush.

How do you quantify your chances? Well, you know there are 13 spades in the deck — and you've already seen four of them, so there are nine left. And you know that there are 52 cards in the deck, and you've already seen six of them, so there are 46 left. So there are nine cards that make you winner, and 37 that don't. That makes the odds against you 37 to 9, which is about the same thing as 4 to 1.

Your opponent bets $10. Should you call him? It depends how much is in the pot. If there's $100 in the pot, then putting in $10 gives you a 10 to 1 prospective payoff — way better than the 4 to 1 odds that you will make your flush. Based on the true odds, you should have to bet $25 — but your opponent has made a mistake, and has allowed you to see that last card for just $10.

So do it — in fact, you should raise. You may end up winning or losing, depending on what that last card turns out to be. But after hundreds of hands, if you keep getting 10 to 1 odds when your real chances are 4 to 1, you'll be a big winner in the long run.

In stocks we call this "value investing," and as I've been saying in this column for months, there's just this kind of bet available in stocks right now. Based on today's consensus forward earnings, and today's long-term interest rates, the S& 500 is about 45% undervalued relative to historic norms.

In poker terms, you have the opportunity to make a $10 bet in stocks that should really cost you $14.50. So do it — in fact, you should raise.