Random Coins, $20 a Pound?

Here’s a fun bar bet you can try yourself. You’ll need a relatively big pile of U.S. dimes, quarters, and half dollars — no pennies, nickels, or dollar coins, or this won’t work — and a regular kitchen scale. (I’m not sure if you’ll be able to find that in your local bar, so either come prepared or lend me some literary license.) Place a few handfuls of coins on the scale, adding or removing until the lot weighs as close as you can get to one pound as possible. Then make your bet:

Tell your friend (or whomever is on the other side of the bet) that you can predict the total value of those coins within, say, ten cents.

And then “predict” that their value is exactly twenty dollars. You should win virtually* every time — because a pound of any amount of those three coins should come out to that amount, regardless of the individual numbers of any one denomination coin. (But pay attention to that asterisk — we’ll get there, no worries!)

Why? It’s a mix of history and just plain dumb luck.

Nearly 250 years ago, the United States government set specifications for the three coins in question, via the Coinage Act of April 2, 1792. At the time, each of those three coins contained silver, helping the new country’s currency maintain intrinsic value. Likely to ensure that the coins’ melt value reflected their stated value, Congress mandated that those coins weights be proportional to their denominations.

Over time, the metallic mix used to create these coins changed — it was too expensive to make silver coins, and Congress needed to adjust. On July 23, 1965, President Lyndon B. Johnson signed the Coinage Act of 1965, which removed silver from the mix used for dimes and quarters. By 1971, the same was true for the half dollar. But the 1965 Act didn’t change the proportionality rule established in the nation’s infancy — by law, a dime weigts 20% of a half dollar coin, and a quarter similarly weighs 50% of a half dollar. And because — with the exception of that 1965-1970 period — the three coins are minted from the same ingredient mix, any weight of any combination of those coins will always be worth the same, regardless of the make up of the denominations. (That 1965-1970 period, and the silver coins from before that date, is what requires the asterisk above.)

But one pound of those coins amounting to $20 specifically, as opposed to a less-round number? That appears to be a coincidence. There’s nothing in the laws establishing those specifications that says Congress intentionally placed the value of one pound of those coins at $20, or at any other specific value for that matter. And there’s some solid evidence that it was wholly unintentional, because the $20 value isn’t precise. A pound of dimes/quarters/half dollars, if you take the decimal places out a bit, comes out to $20.0085 — so it’s actually closer to $20.01 than the nice even number articulated above. So leave in that ten-cent buffer when you make your bet!

Bonus fact: In 1851, the United States reduced first-class postage from five cents to three cents, which normally would have been a welcome change. But in an era where the post was a major form of communication and purchasing was done almost entirely using coins and small bills, people weren’t happy — it meant they had to carry around a lot of pennies all the time. In response, the government issued a three-cent piece. When the price of postage again fell — to two cents — in 1883, the three-cent coin became so unpopular, the government discontinued it.

From the Archives: Why (Some) Coins Have Ridges: Because they were made of silver, previously.