From Enrico Fermi to Bill Bennett

Recent articles have reported that conservative commentator Bill Bennet lost up to $8 million over the last decade playing slot machines and video poker at casinos. These might cause us to wonder how much time he spent in casinos over this period.

If we assume the payout on the machines was 96 percent (over time, one loses 4 percent of what one bets), then the $8 million loss is 4 percent of the total amount bet over this time. The latter would thus be about $200 million, of which he'd get back $192 million, the total of much smaller amounts recycled through the machines and recounted many times.

So how long does it take to bet $200 million?

Let's assume that Bennett pulled the lever on the $500-a-pull machines he preferred a rabbit-fast five times per minute on average (factoring in breaks). That's $2,500 per minute and $150,000 per hour. If we divide $200 million by $150,000 per hour, we get more than 1,300 hours of pulling machine levers, which is almost eight months worth of full 40-hour weeks spent in casinos over the decade!

The calculation suggests that the $8 million estimate of his losses may be high or that the machines had lower payouts or that he was even more enamored of gambling than previously thought. Given the games he played and only his documented losses, however, Bennett's claim that he gambled occasionally and more or less broke even is laughably innumerate. His Book of Virtues should have contained a section on arithmetic rectitude.

In summary, doing a few back-of-the-envelope calculations can sometimes be quite revealing, not just in physics, but in journalism as well.

Answer: We need to find out how much land area there is on Earth and what the population is. The Earth is a sphere whose radius is about 4,000 miles. Since the formula for the surface area of a sphere is 4pi*r^2, we find that the earth has a surface area of about 200 million square miles. There are 5,280 feet per mile so there are 5280^2 square feet per square mile, which means that 200 million square miles contains about 5.6 x 10^15 square feet. Multiplying this by .3 (since only 30 percent of the Earth's surface is land) yields about 1.7 x 10^15 of land surface area. Dividing this by approximately 6 billion humans gives each of us about 280,000 square feet to call our own. Taking the square root of this figure reveals that we each would have a square a bit more than 500 feet on a side. Of course, most of these parcels would be inhospitable.