Coin Probability and the Bullion Craze

I inherited a small coin collection and I had recently been searching for silver Mercury dimes to fill in the holes.  I didn't realize how the recent bullion craze was destroying silver coins until I went into a former coin shop and told the man I had a collection of Mercury dimes. The man gruffly told me all he did was bullion now and these coins weren't for good collections. I said "Well how about coins for shitty collections?" He just grumbled and I pressed on and found a bucket full of Walking Liberty Half dollars that I guess he was going to destroy and pulled out a near uncirculated coin and bought it for cheap.  I felt like I was saving a dog from the pound.  This is a good segue to an interesting article on coin probability (exciting eh?).

The probability of finding certain vintages of coins in your pocket is not equal.  This is dependent of the size of its mintage, how long it has been in circulation, and collector pressure.  How long would it take to find specific coins?  Well now someone has done the maths so you don't have to.

Back in 1999, Shiyong Lu, now at Wayne State University, and Steven Skiena, at SUNY Stonybrook, set out to calculate this. They began by recognizing that the probabilities of finding different coins are not equal. The probability of finding a coin from a given year is dependent on its mintage—how many coins of that type were issued that year—how long the coin has been in circulation, and something called collector pressure. The higher the mintage, the higher the probability of finding a coin. However, the higher the age, the lower the chances, because coins get taken out of circulation due to getting lost, whether behind furniture or otherwise. Collector pressure, the final factor, refers to how much collectors try to find a given coin. The higher the collector pressure, the lower the chance of finding that coin, because other collectors are trying to also obtain it and are taking it out of circulation.

For pennies, if you look at coins only from 1959 or newer, the year when wheat pennies were replaced with pennies with the Lincoln Memorial that most of us are familiar with, we can eliminate the difficulty of dealing with collector pressure. So Lu and Skiena set out to calculate the number of pennies needed to collect before they received a complete set of pennies from 1959 to 1997. First, they examines some pennies and calibrated their model to understand how age affects the number of coins in circulation, given their data on mintage.

After crunching the numbers the researchers found that 684 pennies must be collected to get on from every year.  So give it a test and get your hands stinky with coins.
Source Social Dimension