The Odds of Everything Are 100%
Some of you have seen the news about unusual weather in New England. Tonight we have the heat back on in part of the house, and hot water for the first time since Sunday. David and I spent a couple of days racing up and down to the basement managing a variety of permanent and temporary sump pumps. We have had a small flood and a small fire and only a little damage and are really lucky compared to the guy in Massachusetts whose car fell into a sinkhole and the poor folks in Rhode Island whose houses and cars are underwater in conditions that are just unspeakable. It has been a hell of a March. I don't really mind eating cold food and taking cold showers... well, I do mind, I mind a lot, but if forced to choose, would choose the Internet. At least right now we we have that.
This storm, we are told, was either a one in 100 or a one in 500 year event. It follows two weeks on the heels of a storm that was also a one in 100 year event. It's been sixty or eighty years since we had weather like this in New England, depending on which storm you are talking about. What are the odds that we would have two of these one in 100 buggers within two weeks?
Actually, the odds of anything going wrong are 100% if you wait long enough. Try it for yourself. Think of a low probability event like a hurricane, or earthquake - one in a hundred odds - and mentally put millions of endlessly replenishable balls in a jar, 99% white balls and 1% of black balls. If you start drawing balls out one after another and continue long enough, the odds are 100% that sooner or later you will draw two black balls in a row.
Would Warren Buffett write flood insurance for two events like this in a single month? Yes, for a price that was at least double the estimated odds (and preferably triple or more). He would also limit how much capital he risked to an amount that wouldn't cripple Berkshire Hathaway.
This is how to think about risk -- don't bet the ranch if you can't afford to lose it.
You, of course, aren't going to pay Warren Buffett 3x the risk price for flood insurance. So what's your alternative? Either buy national flood insurance, or live on a hill. (Take it from a former insurance analyst.)



Excellent Way To Help People Think About Probability Analysis
Alice,
This is a great example of using a low-probability event that personally impacted you to help people understand probability analysis and insurance pricing. I am a total idiot in that area and still think it is impossible to know how to price certain insurance or reinsurance risks. For example, what factors go into Ajit Jain's pricing some of those famous one-off ("facultative"?) reinsurance or insurance risks, like how do you set the premium on a $10 billion face amount policy payable to the country of China in the event of a terrorist attack while the Olympic Games are underway in that country.
Then there's the lottery. Warren is famous for saying "I'd never buy a lottery ticket, but if you give me one I won't refuse it." You live in a state that offers Powerball lottery tickets for sale (not many states left that don't!). The odds of winning the grand prize are 1 in 195 million, or thereabouts. Does the white marble/black marble analogy hold there, or does the "reset" button get pushed after each week's draw? I have never played the lottery, but should I consider doing so if it got above some large number, say $300 million (= probably only $100 million when you take the cash instead and after all federal and state withholding taxes)? Is there any probability-based reason to consider buying a ticket when the pot gets extremely large? What if it's a warm spring day and instead of taking a taxi uptown for 10 bucks, Warren walks it. While we know there is not a chance he would do that, do you think he might justify in his own mind buying ten lottery tickets with the ten dollars he didn't spend by walking instead of riding? Think he's ever put on an Axl Rose wig and sneaked into the convenience store somewhere if the pot got that large and bought himself a lottery ticket?
Just wondering....
great questions and a lot of them!
Hi there,
so warren thinks about lotteries, he understands their economics thoroughly (they're a tax). he thinks lotteries are socially evil. there is no reason to buy a ticket on a larger pot, but people do it because they would win such a large amount even at such low odds. lotteries are a paticularly vicious form of tax because they're extremely regressive and tend to discourage initiative, self-reliance and realism in favor of fantasizing and delay.
Warren would take a lottery ticket because it's a free option. In fact he is alert to opportunities that resemble free lottery tickets - you can occasionally find them in business. No matter how low the odds, there is a remote chance of paying off - why turn down a free option?
He would never pay for a lottery ticket. One of the striking things about him, he never lets circumstances (e.g., the taxi savings) distract him from the fundamental underlying principal. The taxi savings are a separate event from the lottery. They have an opportunity cost and a better use for the savings would be to invest it.
The black/white marble analogy does hold for lottery tickets. The reset button gets pushed every week, but the number of marbles is infinite so the odds don't change day to day. And if you played the lottery long enough (millions of times, or billions) the odds are 100% that eventually you would win. But, and here is the critical but, the expected cost of your tickets far outweighs the expected payoff. You would be better off investing that money. This is why lotteries are profitable for states -- their payouts are way less than the proceeds received.
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