打牌与投资

爱德华·索普(Edward O.Thorp) 解释在股市赚钱和在赌场靠记牌(card counting)赚钱的相似和区别。

我就不全文翻译了。大意是，

相似点：股市长期向上，市场先生每天给你发牌，会给你有微小的优势，你本金100万，亏平均亏10000，赚平均赚10500。你要是天天来玩的话长期积累下来是赚钱的，每天平均赚500，一年赚12万。在赌场也是，懂得记牌的话会有微小的优势（比如51%），虽然每局都很可能输，但是长期积累下来你的净值是向上的。

不同点：股市里市场先生每天发一张牌，所以你的盈亏要很久才能因为大数定律稳定收敛到平均值上，甚至几年时间都还是运气不好。赌场里你可以一周打个4000局，相当于和股市的市场先生连续16年每天见面领牌，你的盈亏很快就会向长期均值收敛，运气因素很小，记牌的优势能充分反映出来。

怪不得都说索普是量化投资之父。量化投资的精髓就是找优势(have an edge)+多次下小注(bet often)，靠大概率来稳定收益。

Q: How are casinos similar to the stock market?

A: Imagine you are investing in an index fund. The casino is Mr. Market, who offers you a collection of bets. If you choose an index fund, say VTSAX [the Vanguard Total Stock Market Index fund], on a typical day it randomly fluctuates by 1%. But there is a long-term drift in your favor of about one twentieth of a [percentage point]. So if you had $1 million in your portfolio in such an index, Mr. Market will come to you each day and say, “Let’s flip a coin. If it’s 50/50, then you’ll win $10,000 or lose $10,000. But I’ll pay you $500 if you play that day.” If you play for one day, you’ll be at $9,500 or at $10,500. If you play for a year, the chances are moderately good that you’ll be ahead because those $500 payments add up and overcome the fluctuation. Maybe a third of the years, you’ll be down and unhappy. But if you play for 10 years or 20 years, then those $500 payments just keep adding up.

Warren Buffett has also devoted his life to compounding. So a similar process happens at blackjack tables. If you’re counting cards, you have a little drift in your favor. But in blackjack you play 100 hands an hour, and in a week you may play 4,000 hands. In a casino, you get to the long run fairly quickly.