Friday, February 10, 2012

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.


18 dollars worth, for Comments/Questions click here.:

Dr. Math said...

I have been wanting to do an experiment like this except with nickels. Speaking of nickels I have a 1977 Canadian nickel with a reverse in UNC. and an obverse with some scratches therefore in F-VF. Can you tell me what it's worth?

Man said...

I have been wanting to do an experiment like this except with nickels.
--Still early in the year you can probably start a running count of nickels you find, no need to keep them. Excel or Google Spreadsheet is the easiest way.

Speaking of nickels I have a 1977 Canadian nickel with a reverse in UNC. and an obverse with some scratches therefore in F-VF.
--About $0.10 but that is mostly metal value, even in UNC it would be $0.20.

Anonymous said...

now how long would it take to get an S (proof) penny form every year?

Man said...

now how long would it take to get an S (proof) penny form every year?

I have never found any proof coin in my change. So probably 1,000 years.

That said some roll hunters I know have found dozens of proofs, so judging from a 5 year roll searcher they found 50 unique proofs (all coins) then at a rate of 1 million coins per year.
They can get every proof cent made from 1959-1997 in 15 years.

matt44o said...

I have this big 1878 one dollar coin and i was wondering how much it is. I also have 2 1968 half dollar coins and two more 1964 half dollar coins that i was also wondering how much they are worth

Man said...

1878 one dollar coin about $30.00
1968 half dollar coins about $5.00 each
1964 half dollar coin about $12.25 each

Anonymous said...

Being Russian, I'm of course doing this for Russian coins, specifically ten-copecks (them being the only coin type still reasonably circulating for which it is possible to get a full 1997-2011 set without either involving coins with five-digit mintages [and thus about as obtainable from circulation as 1943-S cents would be, or maybe a little less so] or having just four coins in the entire set including mintmarks).
Result: it takes about a dozen to even have anything of the older (pre-2006) type; it takes around three or four hundred (equivalent to about 30 pre-2006 coins) to collect all the pre-2006 dates (1997 and 1999 are the hardest to find); now figure in the fact that I'm in Moscow and it's incredibly hard to get a SPB coin (fortunately that gets easier the older the coin is, so for 1999 the SPB coin is only about twice as uncommon as the Moscow coin; unfortunately that also means that to get a 2010 or 2009 SPB I need quite some luck (2011 SPBs are weirdly not known to exist)), and the answer is that it takes about a thousand coins, or a little more, to get a full date-and-mintmark set. Fortunately they're literally a nickel a dozen (or even a little cheaper), and even a thousand costs a total of $3-4 :-)
Note, by the way, that unlike the cent version, this doesn't look like a proper Coupon Collector's: if someone's missing only a few coins from the full set, I can pretty confidently say that they are some of 1997, 1999, and/or the varieties of 2006 - anything else would mean the guy got really (un)lucky.

...So what, how? :-)
January First-of-May

Man said...

Being Russian, I'm of course doing this for Russian coins...

I hope most people at least try to collect like this. Like you pointed out 1997 is not that old but they can quickly become an enjoyable quest to find.

matt44o said...

how much is one full book of us state coins worth?

Man said...

how much is one full book of us state coins worth?

If you have both P and D just $25.00.

State quarters just have face value.

matt44o said...

how much is an 1865 penny

Man said...

1865 penny about $10.00 in good

Anonymous said...

Series 2009, 1 dollar bill
H 26369989A
the first "2" in the left side serial number is lower down than the others. Any extra value?

Man said...

2009, 1 dollar bill
H 26369989A
the first "2" in the left side serial number is lower down than the others.


Turned digit error about $10.00 in extra-fine.

matt44o said...

how much is a 1917 Great Britain penny?

Man said...

1917 Great Britain penny about $0.75

matt44o said...

do you have any expertise or know any website or websites that can estimate the value or stamps?

Man said...

do you have any expertise or know any website or websites that can estimate the value or stamps?

Sorry, no.

You try and start here...
http://www.psestamp.com/links.chtml