## Big Numbers

If you buy one Mega Millions ticket, your probability of hitting the jackpot is one in 175,000,000. For all practical purposes it is zero. When I give my talk on lotteries, there is always someone in the audience who would argue that “but someone is winning and so can I.” The fact that someone is winning depends on the number of people buying tickets. It is difficult to visualize the large number of people buying tickets and the miniscule odds of winning. For example, the probability of you dying from an impact with a meteorite is larger than the odds of winning the jackpot.

I receive a lot of emails from strangers asking me to advertise their websites on my blog. I always check out their websites and I often find them either unrelated to math or boring. That is why I was pleasantly surprised when I was asked to write about a useful website: Understanding Big Numbers. In each post Liam Gray takes a big number and puts it into some perspective. For example, he estimates Mark Zuckerberg’s Hourly Wage by dividing Mark’s estimated wealth in 2011 by the number of hours Mark might have worked on Facebook. Facebook has existed for 7 years and, assuming 10 hours of work a day every day, we get 25,000 work hours. That is more than half a million dollars an hour.

Imagine someone calls Mark Zuckerberg and asks to talk to him for a minute. Mark wouldn’t be out of line to request nine thousand dollars for that. Lucky am I, that I do not need to talk to Mark Zuckerberg.

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It must be pointed out that this example is exaggerated. One, just
because it has only existed for 7 years doesn’t mean he wasn’t working
on it before it “existed” in any observable sense. Two, startup
founders are known to work 14- or 16-hour days, not just 10. So
that’s a factor of two. But far more importantly, those 10- or 14- or
16-hour days were spent working for a probability distribution of
possible payouts, the very high end of which you are actually seeing.
that people have worked on very hard for months or years, before and
after the actual Facebook, in addition to the ones you will never even
know about because they were abandoned long before they were recorded
anywhere where you have access to, you will find that his expected
wage at the time he worked was much more normal. Exercise for the
reader: how much effort must have been poured into variations on
Facebook that went nowhere to bring Mr. Zuckerberg’s expected wage
down to something sane, like \$500 per hour? How likely was that to
have actually happened? How much of Mr. Zuckerberg’s wealth remains,
therefore, to be explained by other factors, like collecting the
surplus of his employees’ productivity, (pre!)market overvaluation of