Tuesday, March 20, 2012

Chances Are

Someone I know once referred to the lottery as a tax on bad math skills. And, indeed, one of the reasons I rarely play the lottery (I think at most twice in my life) is that I am aware of the astronomically low probability of winning. And if there is one thing I have learned over the years, it’s that I’ve never had any success with random chance (or blind luck). So I tend to avoid casinos and lotteries—and even horse-racing (ironically, given where I live). (And don’t even get me started on real estate, which is the biggest scam in the world.)
Economist Felix Salmon has a blog post up about a “get rich quick” video that CNN/Money had been running (it’s since been taken down) which purports to explain how you can “beat the odds” in the lottery.

Lustig’s advice is simply bizarre: he reckons that you should buy lottery numbers in sequence, and that you should never buy “quick-pick” (randomly-generated) tickets. In fact, if you’re going to play the lottery, the rational way to play the lottery is to do the exact opposite of Lustig’s advice.

I found this an interesting point. In terms of strict probability, it makes no difference if you pick the numbers yourself or have a computer pick random numbers, and it even makes no difference if you pick sequential numbers or not. After all, 20, 21, 22, 23, 24 is just as probable as 5, 18, 35, 44, 58. In fact, there is no reason to even avoid playing the numbers that won the previous drawing. Lotteries don’t have a memory. 
But, in the extremely unlikely event you win, your chances of not having to share the payout apparently improve if you use random numbers:

The reason is that when lotteries have big prizes, those prizes are parcelled out between everybody who had the winning numbers. For instance, in August 2010, Lustig had a winning ticket in a draw where the jackpot was $197,985.84. But so did someone else — so he ended up winning only half that amount. And if you want to minimize your chances of overlapping with someone else, you’re much better off accepting a set of random numbers than you are using some kind of human-generated method. Remember when 110 people all had the winning numbers 22, 28, 32, 33, and 39, just because those numbers were printed in fortune cookies?

Birthdays, for example, are common lotto fodder, and it is not especially improbable for many people to have the same birthday, even if you add the year. So if you use your birthday to generate your lotto picks, you’ll likely find many other people who share your birthdate—and your lottery winnings. 
And many people played Hurley’s lottery numbers from Lost—and had to share the payout when four of the numbers actually did win.
But there are benefits to lotteries—they help finance education, after all, which is not  bad thing.
Scratch-off games are a different kettle of fish, and at least one person figured out how to crack them. But even roulette wheels are not perfect, as engineer Joseph Jaggers—the famous “man who broke the bank at Monte Carlo”—can tell you.

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