Gotta Catch 'Em All

Recently read this article, The Probabilities of Pennies, that reviewed a published paper by professors who try to get at least one cent from each year 1959-1997. They used a formula known as the Coupon Collector’s Problem which is used a lot in computer science. As an engineer who had to study computer engineering I will let you know all these computer formulas are at best estimates and therefore lacking.

Back to the study they estimated it would take searching 684 random cents to get the 39 unique years and fill out an album (not full P, D, S album). There real life test had it completed in 630 cents.

The Cent Project is another survey that tried to estimate how many small and large type 1960 cents are circulating. Here you get 5,000 cents and separate them by year and type. This one did account for all the 1982, 1970, and 1960 varieties. Of course this is not counting wheaties, foreign cents, errors, or doubled dies.

I did the Cent Project using 1959-2008 cents and got these results.

Those dips you see correlate with the 1982, 1970, and 1960 varieties so they can be ignored for the Penny Probability crossover.

Results:

• With 5,000 cents I could have completed a 1959-2008 basic album 14 times.
• With 5,000 cents I could have completed a 1959-2008 full P,D,S album 5 times.
• With 5,000 cents I could NOT complete a 1959-2008 full P,D,S and variety album.

The normal design variety that were not found were:

• 1970-S Small Date (High 7)
• 1960 Small Date

Other notes:

• 1982 was the most common followed by 1994.
• 1965 was the least common followed by 1959.
• 4,456 = P, 446 = D, and 8 = S.
• 2,000 were Copper, 3,000 were Copper-Plated Zinc

Conclusion:
Same as the Coupon Collector's Problem indicates. It is simple to start the collection and make it big but the last few coins will take a long time to find. Everyone can collect coins and you will be surprised at the speed that it happens. Add nickels, dimes, and quarters to make the collection huge.